# Analyzing Egocentric Data: The `ego_netwrite` Function

The goal of the `ideanet` R package is to lower the barrier of entry to network analysis for students, entry-level scholars, and non-expert practitioners interested in relational measurement. Some researchers may have data and questions that are suitable to network analysis. And yet, getting comfortable with the tools available in R can prove to be an arduous and time consuming task. Moreover, network analysis in R can be far from straightforward: available tools in R are shared between several packages, each with their own strengths and weaknesses. This breadth of options can make it difficult to produce reliable results by making the correct function for a given measurement difficult to identify and, at worst, packages conflicting with each other and relying on different assumptions about the data. For many researchers, this can prove to be an effective deterrent when engaging in relational analysis. `ideanet` is a set of functions which leverages existing network analysis packages in R (`igraph`, `network`, `sna`) to provide high quality measurements seamlessly from the starting data.

This package, as part of the broader IDEANet project, is supported by the National Science Foundation as part of the Human Networks and Data Science - Infrastructure program (BCS-2024271 and BCS-2140024).

## Egocentric Data Processing and Analysis

Local, or egocentric, networks describe the relationships that exist between a focal actor (called “ego”) and their contacts (referred to as “alters”). Depending on how these networks are collected, they may also describe relationships that exist between each of the focal ego’s alters. The figures below illustrate how ego networks appear when 1. only ties between an ego and its alters are recorded, and 2. when ties between alters are available:

Most egocentric data also contain information describing characteristics of ego and their alters at the individual level. Researchers often collect egocentric data when efforts to capture sociocentric networks are impossible or highly impractical, such as in studies of hard-to-reach populations.

While sociocentric datasets typically store a single, large network, egocentric data usually contain several smaller networks (hereafter ego networks) that may or may not exist in isolation of one another. Users applying `ideanet` to egocentric data can use the `ego_netwrite` function to generate an extensive set of measures and summaries for each ego network in their data. Although egocentric data can be stored in a variety of ways, `ego_netwrite` requires a specific format that we believe makes the representation of egos, alters, and the ties between them more intuitive. This format divides egocentric data into three items:

1. An ego list containing information about various qualities and attributes of focal egos for each ego network. Each row in the ego list corresponds to a specific ego, which is given a unique ID number.
2. An alter list in which each row corresponds to a specific alter in an ego network. The first column in the alter list indicates the ego for which a given alter is associated, values for which should match the unique ID numbers contained in the ego list. The second column indicates the given alter; within each ego network, alters are also given a unique ID number. Subsequent columns contain qualities and attributes of alters and/or attributes of the ego’s relationship to alter.
3. (If available) An alter-alter edgelist in which each row represents an edge connecting one alter, i, to another alter j. If multiple types of relationships exist between i and j, each i-j-type combination is given its own row. The first column in this edgelist represents the ego whose network a tie appears in and values for which should match the unique ID numbers contained in the ego list. The next two columns represent the alters connected by a given tie and values for which should be unique ID numbers contained in the alter list. Any other columns contain attributes of the relationship between the two alters.

In some cases, users may have all the information contained in the above three items stored in a single, wide dataset. When this is the case, users may be able to use `ideanet`’s, `ego_reshape` function to split their data into these items. We recommend that users with such a dataset consult this function’s documentation:

    ?ego_reshape

### Current Support and Limitations

As of initial release, `ego_netwrite` supports the processing of ego networks with directed ties (in which each tie has a distinct sender and receiver) and undirected ties (in which ties merely represent a connection between actors). The function also supports multirelational networks in which edges may represent one of several different types of relationships between actors.

However, `ego_netwrite` does not currently support the processing of edge/tie weights, which signify the strength of connections between actors. The function assumes that all ties in a dataset are of equal strength when calculating measures. At present, we recommend that users employ other tools for calculating measures based on weighted edges.

Additionally, some egocentric datasets contain networks in which nodes in one ego network may also appear in another. In these cases, it is possible to aggregate individual ego networks with shared nodes into broader, more sociocentric structures. Theoretically, one could use the alter list and alter-alter edgelist created by `ego_netwrite` to construct a larger network. However, `ego_netwrite` itself assumes that each ego network in a dataset exists independent of all others. We advise users interested in constructing larger structures from individual ego networks to use other tools (or write their own code) in order to do so.

### Using `ego_netwrite`

To familiarize ourselves with `ego_netwrite` and other functions for ego networks, we’ll work with an example ego list, alter list, and alter-alter edgelist native to the `ideanet` package. These data are a simplified subset of ego networks collected in an online study using the “Important Matters” name generator question (NGQ). This question is frequently used to capture people’s close personal ties:

    library(ideanet)

    # Ego list
    ngq_egos <- ngq_egos
    # Alter list
    ngq_alters <- ngq_alters
    # Alter-alter edgelist
    ngq_aa <- ngq_aa

Let’s look over each of these data frames:

    dplyr::glimpse(ngq_egos)
    #> Rows: 20
    #> Columns: 9
    #> $ ego_id     <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, …
    #> $ age        <dbl> 41, 14, 35, 17, 43, 24, 12, 24, 44, 24, 12, 52, 26, 11, 18,…
    #> $ sex        <dbl> 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2
    #> $ race       <chr> "White", "Other", "White", "White", "White", "Other", "Whit…
    #> $ black      <lgl> FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FAL…
    #> $ white      <lgl> TRUE, FALSE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE, TRUE, TR…
    #> $ other_race <lgl> FALSE, TRUE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE,…
    #> $ edu        <dbl> 5, 7, 7, 6, 7, 6, 7, 6, 6, 5, 4, 5, 4, 4, 5, 5, 5, 6, 5, 5
    #> $ pol        <dbl> 3, 2, 3, 3, 2, 3, 3, 3, 6, 3, 1, 7, 4, 3, 4, 1, 4, 5, 2, 1

Our ego list contains information for the 20 egos in our dataset. The ego list also has information regarding the age, sex, race/ethnicity, educational attainment, and political leanings of each ego.

    dplyr::glimpse(ngq_alters)
    #> Rows: 67
    #> Columns: 14
    #> $ ego_id     <int> 1, 1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5,…
    #> $ alter_id   <int> 1, 2, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2…
    #> $ sex        <dbl> 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1,…
    #> $ race       <chr> "White", "White", "White", "Black", "White", "White", "Whit…
    #> $ white      <lgl> TRUE, TRUE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE…
    #> $ black      <lgl> FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALS…
    #> $ other_race <lgl> FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FAL…
    #> $ pol        <dbl> 5, 7, 2, 1, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 3, 2,…
    #> $ family     <lgl> TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALS…
    #> $ friend     <lgl> FALSE, TRUE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FA…
    #> $ other_rel  <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALS…
    #> $ face       <dbl> 5, 2, 4, 3, 1, 1, 3, 4, 5, 5, 3, 4, 4, 3, 3, 2, 2, 2, 5, 2,…
    #> $ phone      <dbl> 5, 2, 4, 1, 1, 1, 2, 2, 4, 3, 3, 1, 3, 1, 1, 1, 1, 1, 4, 2,…
    #> $ text       <dbl> 5, 4, 4, 1, 5, 5, 2, 4, 5, 4, 4, 3, 4, 4, 2, 3, 3, 4, 4, 2,…

Just as described, the first column in the alter list is the ID number of the ego corresponding to each alter; the second column is the unique ID number for each alter within each ego network. In addition to information regarding the sex and race/ethnicity of each alter, this alter list contains dyadic data about the relationship between ego and alter. `family`, `friend`, and `other_rel` indicate whether an ego identified an alter as a family member, a friend, or another kind of relationship respectively. Further, the `face`, `phone`, and `text` columns indicate how frequently an ego reported communicating with an alter face-to-face, via telephone, or via text.

    dplyr::glimpse(ngq_aa)
    #> Rows: 123
    #> Columns: 5
    #> $ ego_id   <int> 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4…
    #> $ alter1   <dbl> 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3…
    #> $ alter2   <dbl> 2, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 8, 9, 10,…
    #> $ type     <chr> "friends", "friends", "friends", "friends", "friends", "frien…
    #> $ freqtalk <dbl> 1, 3, 4, 5, 3, 3, 3, 4, 3, 4, 3, 4, 4, 3, 4, 3, 3, 1, 1, 1, 5…

The first column in the alter-alter edgelist is the ID number of the corresponding ego, with the following two columns indicating the two alters connected by an edge within the ego’s network. The edgelist also contains a `type` variable indicating the type of relationship that exists between each pair of alters (`"friends"`, `"related"`, `"other_rel"`), and an additional variable indicating how frequently alters talk to one another.

It is worth remembering, as stated earlier, that alter-alter edgelists should be formatted to have unique rows for each unique edge-type combination. Let’s take a look at how this appears in one of our ego networks:

    ngq_aa %>%
      dplyr::filter(ego_id == 4)

ego_id | alter1 | alter2 | type | freqtalk
--- | --- | --- | --- | ---
4 | 1 | 2 | friends | 5
4 | 1 | 3 | friends | 3
4 | 1 | 4 | friends | 3
4 | 1 | 5 | friends | 3
4 | 1 | 6 | friends | 4
4 | 1 | 7 | friends | 3

Here we see that ego indicated the first six pairs of nodes in this edgelist as being connected by friendships. This edgelist also includes pairs of nodes that are connected as relatives, though we don’t display them above. Within the edgelist, each dyad is given its own row, and the type of relationship for each dyad is clearly identified in the `type` column.

Using the `ego_netwrite` function, we will generate an extensive set of measures and summaries for each of the 20 networks in this dataset. `ego_netwrite` asks users to specify several arguments pertaining to our ego list, alter list, and alter-alter edgelist. In order to familiarize ourselves with this function, we list these arguments below, organized by category.

Ego List Arguments

- `egos`: A data frame containing the ego list.
- `ego_id`: A vector of unique identifiers corresponding to each ego, or a single character value indicating the name of the column in egos containing ego identifiers.

Alter List Arguments

- `alters`: A data frame containing the alter list.
- `alter_id`: A vector of identifiers indicating which alter is associated with a given row in `alters`, or a single character value indicating the name of the column in `alters` containing alter identifiers.
- `alter_ego`: A vector of identifiers indicating which ego is associated with a given alter, or a single character value indicating the name of the column in `alters` containing ego identifiers.
- `alter_types`: A character vector indicating the columns in `alters` that indicate whether a given alter has certain types of relations with ego. These columns should all contain binary measures indicating whether alter has a particular type of relation with ego.
- `max_alters`: A numeric value indicating the maximum number of alters an ego in the dataset could have nominated.

Alter-Alter Edgelist Arguments

- `alter_alter`: A data frame containing the alter-alter edgelist, if available. If not provided, `ego_netwrite` will not provide certain measures.
- `aa_ego`: A vector of identifiers indicating which ego is associated with a given tie between alters, or a single character indicating the name of the column in `alter_alter` containing ego identifiers.
- `i_elements`: A vector of identifiers indicating which alter is on one end of an alter-alter tie, or a single character indicating the name of the column in `alter_alter` containing these identifiers.
- `j_elements`: A vector of identifiers indicating which alter is on the other end of an alter-alter tie, or a single character indicating the name of the column in `alter_alter` containing these identifiers.
- `aa_type`: A numeric or character vector indicating the types of relationships represented in the alter edgelist, or a single character value indicating the name of the column in `alter_alter` containing relationship type. If `alter_type` is specified, `ego_netwrite` will treat the data as a set of multi-relational networks and produce additional outputs reflecting the different types of ties occurring in each ego network.
- `directed`: A logical value indicating whether network ties are directed or undirected.

Additional Arguments

- `missing_code`: A numeric value indicating “missing” values in the alter-alter edgelist.
- `na.rm`: A logical value indicating whether `NA` values should be excluded when calculating continuous measures.
- `egor`: A logical value indicating whether output should include an `egor` object, which is often useful for visualizaton and for simulation larger networks from egocentric data.
- `egor_design`: If creating an `egor` object, a list of arguments to `srvyr::as_survey_design` specifying the sampling design for egos. This argument corresponds to ego_design in `egor::egor`.

Now let’s use `ego_netwrite` to process these ego networks:

    ngq_nw <- ego_netwrite(egos = ngq_egos,
                           ego_id = ngq_egos$ego_id,

                           alters = ngq_alters,
                           alter_id = ngq_alters$alter_id,
                           alter_ego = ngq_alters$ego_id,

                           max_alters = 10,
                           alter_alter = ngq_aa,
                           aa_ego = ngq_aa$ego_id,
                           i_elements = ngq_aa$alter1,
                           j_elements = ngq_aa$alter2,
                           directed = FALSE)

Upon completion, `ego_netwrite` stores its outputs in a single list object. In the following section, we’ll examine each of the outputs within this list and what they contain.

## Interpreting `ego_netwrite` Output

### Ego List

Alongside other outputs, `ego_netwrite` produces cleaned and reformatted versions of each of the three data frames it takes as inputs. Our ego list, stored in the `egos` object, is more or less the same. However, `ego_netwrite` may rename our original column for unique ego IDs as `original_ego_id` and create a new `ego_id` column to ensure consistent processing. We see this is the case here in how the function has handled our NGQ data:

    head(ngq_nw$egos)

ego_id | original_ego_id | age | sex | race | black | white | other_race | edu | pol
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 1 | 41 | 2 | White | FALSE | TRUE | FALSE | 5 | 3
2 | 2 | 14 | 1 | Other | FALSE | FALSE | TRUE | 7 | 2
3 | 3 | 35 | 2 | White | FALSE | TRUE | FALSE | 7 | 3
4 | 4 | 17 | 2 | White | FALSE | TRUE | FALSE | 6 | 3
5 | 5 | 43 | 1 | White | FALSE | TRUE | FALSE | 7 | 2
6 | 6 | 24 | 1 | Other | FALSE | FALSE | TRUE | 6 | 3

### Alter List

In contrast, `ego_netwrite`’s updated alter list is noticeably different from the alter list we started with. `ego_netwrite` calculates a set of frequently used node-level measures for each individual alter based on their position within their respective ego network. This set includes measure of node centrality and membership in isolated components, where applicable, and follows the original variables appearing in our alter list. Additionally, the first two columns of this data frame contain new unique ID numbers for alters and their corresponding egos to ensure the the alter list accurately links to our ego list and alter-alter edgelist. Note that alter IDs here are zero-indexed– this is done to maximize compatibility with the `igraph` package, which has been known to rely on zero-indexing.

    head(ngq_nw$alters)

ego_id | id | alter_id | original_ego_id | original_alter_id | sex | race | white | black | other_race | pol | family | friend | other_rel | face | phone | text | total_degree | closeness | betweenness_scores | bonpow | bonpow_negative | burt_constraint | burt_hierarchy | effective_size | reachability | eigen_centrality
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 0 | 1 | 1 | 1 | 1 | White | TRUE | FALSE | FALSE | 5 | TRUE | FALSE | FALSE | 5 | 5 | 5 | 0 | NaN | 0.00 | NA | NA | 1.0 | NA | 0 | 0.00 | NA
1 | 1 | 2 | 1 | 2 | 1 | White | TRUE | FALSE | FALSE | 7 | FALSE | TRUE | FALSE | 2 | 2 | 4 | 0 | NaN | 0.00 | NA | NA | 1.0 | NA | 0 | 0.00 | NA
2 | 0 | 1 | 2 | 1 | 1 | White | TRUE | FALSE | FALSE | 2 | FALSE | FALSE | TRUE | 4 | 4 | 4 | 0 | NaN | NaN | NA | NA | 1.0 | NA | 0 | NaN | NA
3 | 0 | 1 | 3 | 1 | 1 | Black | FALSE | TRUE | FALSE | 1 | FALSE | TRUE | FALSE | 3 | 1 | 1 | 2 | 0.75 | 0.05 | 1.2158433 | 1.3351669 | 0.5 | 0 | 2 | 0.75 | 1.000000
3 | 1 | 2 | 3 | 2 | 1 | White | TRUE | FALSE | FALSE | 3 | FALSE | TRUE | FALSE | 1 | 1 | 5 | 2 | 0.75 | 0.05 | 1.2158433 | 1.3351669 | 0.5 | 0 | 2 | 0.75 | 1.000000
3 | 2 | 3 | 3 | 3 | 1 | White | TRUE | FALSE | FALSE | 2 | FALSE | TRUE | FALSE | 1 | 1 | 5 | 1 | 0.50 | 0.00 | 0.7223054 | 0.4661861 | 1.0 | 1 | 1 | 0.75 | 0.618034

### Alter-Alter Edgelist

The alter-alter edgelist has been updated to to contain unique dyad-level ids, ego IDs, simplified ego and alter IDs (`i_id` and `j_id`, respectively), and the original id variables as they initially appeared in our input. As with alter ids in `alters`, `i_id` and `j_id` here are zero-indexed to maximize compatibility with the `igraph`.

    head(ngq_nw$alter_edgelist)

Obs_ID | ego_id | i_elements | i_id | j_elements | j_id | alter1 | alter2 | type | freqtalk
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 3 | 1 | 0 | 2 | 1 | 1 | 2 | friends | 1
2 | 3 | 1 | 0 | 4 | 3 | 1 | 4 | friends | 3
3 | 3 | 2 | 1 | 3 | 2 | 2 | 3 | friends | 4
4 | 4 | 1 | 0 | 2 | 1 | 1 | 2 | friends | 5
5 | 4 | 1 | 0 | 3 | 2 | 1 | 3 | friends | 3
6 | 4 | 1 | 0 | 4 | 3 | 1 | 4 | friends | 3

### Network-Level Measures

Beyond our modified inputs, `ego_netwrite`’s output contains a dataset providing `summaries` of each ego network. These summaries include measures of network size, number of isolates, fragmentation, centralization, and the prevalence of certain kinds of dyads and triads in the network.

    head(ngq_nw$summaries)

ego_id | network_size | mean_degree | density | num_isolates | prop_isolates | num_weakcomponent | size_largest_weakcomponent | prop_largest_weakcomponent | num_strongcomponent | size_largest_strongcomponent | prop_largest_strongcomponent | component_ratio | pairwise_strong_un | pairwise_weak_un | fragmentation_index | effective_size | efficiency | constraint | betweenness | norm_betweenness | dyad_mut | dyad_null | triad_003 | triad_102 | triad_201 | triad_300
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 2 | 0.0 | 0.0000000 | 2 | 1.0 | 2 | 1 | 0.5 | 2 | 1 | 0.5 | 1.00 | 0.0 | 0.0 | 1.0 | 2.0 | 1.0000000 | 0.5000000 | 1.00 | 1.0000000 | 0 | 1 | 0 | 0 | 0 | 0
2 | 1 | 0.0 | NaN | 1 | 1.0 | 1 | 1 | 1.0 | 1 | 1 | 1.0 | NaN | NaN | NaN | NaN | 1.0 | 1.0000000 | 1.0000000 | 0.00 | NaN | 0 | 0 | 0 | 0 | 0 | 0
3 | 5 | 1.2 | 0.3000000 | 1 | 0.2 | 2 | 4 | 0.8 | 2 | 4 | 0.8 | 0.25 | 0.6 | 0.6 | 0.4 | 3.8 | 0.7600000 | 0.4511111 | 6.00 | 0.6000000 | 3 | 7 | 3 | 5 | 2 | 0
4 | 10 | 8.6 | 0.9555556 | 0 | 0.0 | 1 | 10 | 1.0 | 1 | 10 | 1.0 | 0.00 | 1.0 | 1.0 | 0.0 | 1.4 | 0.1400000 | 0.3599197 | 0.25 | 0.0055556 | 43 | 2 | 0 | 1 | 14 | 105
5 | 3 | 2.0 | 1.0000000 | 0 | 0.0 | 1 | 3 | 1.0 | 1 | 3 | 1.0 | 0.00 | 1.0 | 1.0 | 0.0 | 1.0 | 0.3333333 | 0.9259259 | 0.00 | 0.0000000 | 3 | 0 | 0 | 0 | 0 | 1
6 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA

Users may find it convenient to combine `summaries` and `egos` into a single dataframe, as elements stored in each object may be used simultaneously in later statistical modeling. Combining the two objects is as simple as merging along the `ego_id` column:

    egos2 <- ngq_nw$egos %>%
      dplyr::left_join(ngq_nw$summaries, by = "ego_id")

    head(egos2)

ego_id | original_ego_id | age | sex | race | black | white | other_race | edu | pol | network_size | mean_degree | density | num_isolates | prop_isolates | num_weakcomponent | size_largest_weakcomponent | prop_largest_weakcomponent | num_strongcomponent | size_largest_strongcomponent | prop_largest_strongcomponent | component_ratio | pairwise_strong_un | pairwise_weak_un | fragmentation_index | effective_size | efficiency | constraint | betweenness | norm_betweenness | dyad_mut | dyad_null | triad_003 | triad_102 | triad_201 | triad_300
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 1 | 41 | 2 | White | FALSE | TRUE | FALSE | 5 | 3 | 2 | 0.0 | 0.0000000 | 2 | 1.0 | 2 | 1 | 0.5 | 2 | 1 | 0.5 | 1.00 | 0.0 | 0.0 | 1.0 | 2.0 | 1.0000000 | 0.5000000 | 1.00 | 1.0000000 | 0 | 1 | 0 | 0 | 0 | 0
2 | 2 | 14 | 1 | Other | FALSE | FALSE | TRUE | 7 | 2 | 1 | 0.0 | NaN | 1 | 1.0 | 1 | 1 | 1.0 | 1 | 1 | 1.0 | NaN | NaN | NaN | NaN | 1.0 | 1.0000000 | 1.0000000 | 0.00 | NaN | 0 | 0 | 0 | 0 | 0 | 0
3 | 3 | 35 | 2 | White | FALSE | TRUE | FALSE | 7 | 3 | 5 | 1.2 | 0.3000000 | 1 | 0.2 | 2 | 4 | 0.8 | 2 | 4 | 0.8 | 0.25 | 0.6 | 0.6 | 0.4 | 3.8 | 0.7600000 | 0.4511111 | 6.00 | 0.6000000 | 3 | 7 | 3 | 5 | 2 | 0
4 | 4 | 17 | 2 | White | FALSE | TRUE | FALSE | 6 | 3 | 10 | 8.6 | 0.9555556 | 0 | 0.0 | 1 | 10 | 1.0 | 1 | 10 | 1.0 | 0.00 | 1.0 | 1.0 | 0.0 | 1.4 | 0.1400000 | 0.3599197 | 0.25 | 0.0055556 | 43 | 2 | 0 | 1 | 14 | 105
5 | 5 | 43 | 1 | White | FALSE | TRUE | FALSE | 7 | 2 | 3 | 2.0 | 1.0000000 | 0 | 0.0 | 1 | 3 | 1.0 | 1 | 3 | 1.0 | 0.00 | 1.0 | 1.0 | 0.0 | 1.0 | 0.3333333 | 0.9259259 | 0.00 | 0.0000000 | 3 | 0 | 0 | 0 | 0 | 1
6 | 6 | 24 | 1 | Other | FALSE | FALSE | TRUE | 6 | 3 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA

### Summary of Overall Dataset

Additionally, `ego_netwrite` provides an `overall_summary` that allows users to get a sense of the properties of a typical ego network in their dataset. Because certain measures are impossible to calculate for ego networks consisting of 0-1 alters, certain measures in `overall_summary` are only calculated for networks containing 2+ alters. Measures calculated in this way are specified as such in the `measure_descriptions` column.

    ngq_nw$overall_summary

measure_labels | measure_descriptions | measures
--- | --- | ---
Number of egos/ego networks | Total number of egos providing ego networks in dataset | 20
Number of alters | Total number of alters nominated by egos across entire dataset | 67
Number of isolates | Number of egos who did not report any alters in their personal network | 2
Number of one-node networks | Number of egos who reported only one alter in their personal network | 3
Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
Largest network size | Largest number of alters provided by a single ego | 10
Average network size | Average number of alters provided by a single ego | 3.35
Average network density | The average density of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.786296296296296
Average fragmentation | The mean fragmentation index score of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.215555555555556

### `igraph` Objects

Finally, `ego_netwrite` constructs `igraph` objects for each individual ego network and stores them in the `igraph_objects` list. Each element in this list is a sub-list corresponding to an individual ego. Let’s take a look at the elements of each sub-list:

    names(ngq_nw$igraph_objects[[1]])
    #> [1] "ego"        "ego_info"   "igraph"     "igraph_ego"

The `ego` item is simply the unique ID number for the ego corresponding to a given sub-list, and is mainly included to allow users to search for a specific ego within `igraph_objects`. Here we confirm that the sixth element in `igraph_objects` contains items corresponding to ego 4 in `summaries`:

    which(lapply(ngq_nw$igraph_objects, function(x){x$ego} == 4) == TRUE)
    #> [1] 4

`ego_info` contains additional information about the specific ego, stored as a single-row data frame. The information contained in `ego_info` is identical to that provided for the specific node in the ego list used as an input for `ego_netwrite`:

    ngq_nw$igraph_objects[[4]]$ego_info

| ego_id | original_ego_id | age | sex | race | black | white | other_race | edu | pol
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
4 | 4 | 4 | 17 | 2 | White | FALSE | TRUE | FALSE | 6 | 3

By default, `ego_netwrite` produces two `igraph` objects for each ego, which may be used for visualizations or for additional analyses. Depending on their needs, users may require a representation of an ego network in which the ego itself is either included or excluded from the network. The object entitled `igraph` contains the entire network with ego excluded, while the one entitled `igraph_ego` contains the network with ego included. Let’s take a look at the `igraph` object for ego 4:

    ngq_nw$igraph_objects[[4]]$igraph
    #> IGRAPH c8f3380 UN-- 10 43 --
    #> + attr: name (v/c), alter_id (v/n), ego_id (v/n), original_ego_id
    #> | (v/n), original_alter_id (v/n), sex (v/n), race (v/c), white (v/l),
    #> | black (v/l), other_race (v/l), pol (v/n), family (v/l), friend (v/l),
    #> | other_rel (v/l), face (v/n), phone (v/n), text (v/n), i_elements
    #> | (e/n), j_elements (e/n), ego_id (e/n), alter1 (e/n), alter2 (e/n),
    #> | type (e/c), freqtalk (e/n)
    #> + edges from c8f3380 (vertex names):
    #>  [1] 0--1 0--2 0--3 0--4 0--5 0--6 0--7 0--8 0--9 1--2 1--3 1--4 1--5 1--6 1--7
    #> [16] 1--8 1--9 2--3 2--4 2--5 2--6 2--7 2--8 2--9 3--4 3--5 3--6 3--7 4--5 4--6
    #> [31] 4--7 4--8 4--9 5--6 5--7 5--8 5--9 6--7 6--8 6--9 7--8 7--9 8--9

We see here that this network contains 10 nodes and 43 edges. These values reflect the 10 alters nominated by ego and the 43 edges ego reported existing between them. Also note that the alter- and edge-level attributes found in our original alter list and alter-alter edgelist are already embedded in this igraph object. The inclusion of these attributes may help users customize visualizations more easily. To show this in practice, let’s visualize ego 4’s `igraph` ego object which each alter’s respective node colored by their sex:

    ego4 <- ngq_nw$igraph_objects[[4]]$igraph_ego

    plot(ego4,
         vertex.color = igraph::V(ego4)$sex,
         layout = igraph::layout.fruchterman.reingold(ego4))
    #> Warning: `layout.fruchterman.reingold()` was deprecated in igraph 2.1.0.
    #> ℹ Please use `layout_with_fr()` instead.
    #> This warning is displayed once every 8 hours.
    #> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
    #> generated.

By default, nodes in the plotted `igraph` object will be displayed with their zero-indexed unique ID numbers as labels, while the node representing ego will be labeled “ego.”

## Processing Multiple Relationship Types

It is common for egocentric datasets to record several different types of relationships between individuals in the same ego network. Researchers may capture different types of relationships by using unique name generator questions for each relationship type, or by asking participants to describe the nature a relationship once it has been recorded. The NGQ dataset used here is an example of egocentric data with multiple relationship types: ties between ego and alter, as well as ties between alters, are specified as some combination of friendship, familial, and/or miscellaneous relations. Users may want to measure various aspects of ego networks with only a specific type of relationship in mind. Fortunately, `ego_netwrite` supports the processing of ego networks with different relationship types with minimal changes to how the function is used. However, `ego_netwrite`’s output changes somewhat when relationship types are taken into account. What follows is an overview of these changes.

### Different Types of Ego-Alter Relationships

When working with different types of relationships between egos and alters, relationship types should be stored as a series of logical or dummy variables in the dummy list. This is already the case in `ngq_alters`: we see that relationship types are coded in the columns `family`, `friend`, and `other_rel`:

To handle these codings in `ego_netwrite`, we need only add the `alter_types` argument. As described earlier in this vignette, `alter_types` takes a character vector containing the names of columns in the alter list storing type codings, which `ego_netwrite` uses to identify these columns when processing.

    alter_types_nw <- ego_netwrite(egos = ngq_egos,
                           ego_id = ngq_egos$ego_id,

                           alters = ngq_alters,
                           alter_id = ngq_alters$alter_id,
                           alter_ego = ngq_alters$ego_id,
                           # Note the inclusion of `alter_types` here
                           alter_types = c("family", "friend", "other_rel"),

                           max_alters = 10,
                           alter_alter = ngq_aa,
                           aa_ego = ngq_aa$ego_id,
                           i_elements = ngq_aa$alter1,
                           j_elements = ngq_aa$alter2,
                           directed = FALSE)

When ego-alter relationship types are accounted for, the ego-level `summaries` dataframe contains additional columns indicating the extent to which different types of ego-alter relationships are correlated with one another. The number of columns added reflects the number of unique pairs of relationship types for which correlations are calculated. Values within these columns are coded `NA` if all ego-alter relationships in a given network are of a single type; otherwise values should be interpreted as one normally would with correlations. We see here that egos 2-6 only reported having one type of relationship across all their nominated alters. By contrast, ego 1 included both friends and family members in their network, but these categories were mutually exclusive.

ego_id | alter_cor_family_friend | alter_cor_family_other_rel | alter_cor_friend_other_rel
--- | --- | --- | ---
1 | -1 | NA | NA
2 | NA | NA | NA
3 | NA | NA | NA
4 | NA | NA | NA
5 | NA | NA | NA
6 | NA | NA | NA

With multiple relationship types in hand, the `overall_summary` data frame is now considerably longer. Dataset-wide summaries are now given for specific types of relationships in isolation, as well as for all relationship types combined. Parenthetical phrases in the `measure_labels` column beginning with “Ego-Alter” indicate the specific relationship type described for a given measure:

measure_labels | measure_descriptions | measures
--- | --- | ---
Number of egos/ego networks | Total number of egos providing ego networks in dataset | 20
Number of alters | Total number of alters nominated by egos across entire dataset | 67
Number of isolates | Number of egos who did not report any alters in their personal network | 2
Number of one-node networks | Number of egos who reported only one alter in their personal network | 3
Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
Largest network size | Largest number of alters provided by a single ego | 10
Average network size | Average number of alters provided by a single ego | 3.35
Average network density | The average density of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.786296296296296
Average fragmentation | The mean fragmentation index score of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.215555555555556
(Ego-Alter family) Number of alters | Total number of alters nominated by egos across entire dataset | 25
(Ego-Alter family) Number of isolates | Number of egos who did not report any alters in their personal network | 10
(Ego-Alter family) Number of one-node networks | Number of egos who reported only one alter in their personal network | 5
(Ego-Alter family) Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
(Ego-Alter family) Largest network size | Largest number of alters provided by a single ego | 9
(Ego-Alter family) Average network size | Average number of alters provided by a single ego | 2.5
(Ego-Alter friend) Number of alters | Total number of alters nominated by egos across entire dataset | 32
(Ego-Alter friend) Number of isolates | Number of egos who did not report any alters in their personal network | 7
(Ego-Alter friend) Number of one-node networks | Number of egos who reported only one alter in their personal network | 4
(Ego-Alter friend) Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
(Ego-Alter friend) Largest network size | Largest number of alters provided by a single ego | 5
(Ego-Alter friend) Average network size | Average number of alters provided by a single ego | 2.46153846153846
(Ego-Alter other_rel) Number of alters | Total number of alters nominated by egos across entire dataset | 9
(Ego-Alter other_rel) Number of isolates | Number of egos who did not report any alters in their personal network | 15
(Ego-Alter other_rel) Number of one-node networks | Number of egos who reported only one alter in their personal network | 4
(Ego-Alter other_rel) Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
(Ego-Alter other_rel) Largest network size | Largest number of alters provided by a single ego | 5
(Ego-Alter other_rel) Average network size | Average number of alters provided by a single ego | 1.8

### Different Types of Alter-Alter Relationships

Overall, incorporating different relationship types between egos and their alters produces minimal changes to `ego_netwrite`’s outputs. The incorporation of different relationship types between alters, however, results in more extensive changes. To familiarize ourselves with these changes, we will ignore different types of ego-alter ties in our next example.

While relationship types between ego and alters are coded as a series of logical or dummy variables in the alter list, types of relationships between alters are stored as a single character column in the alter-alter edgelist. Each row in the alter-alter edgelist represents a unique dyad-type combination, which we illustrated earlier:

ego_id | alter1 | alter2 | type | freqtalk
--- | --- | --- | --- | ---
4 | 1 | 2 | friends | 5
4 | 1 | 3 | friends | 3
4 | 1 | 4 | friends | 3
4 | 1 | 5 | friends | 3
4 | 1 | 6 | friends | 4
4 | 1 | 7 | friends | 3

The `type` column in our alter-alter edgelist (`ngq_aa`) specifies whether a given alter-alter dyad entails a friendship, familial relationship, or miscellaneous relationship. To have `ego_netwrite` process these data according to relationship type, we pass this column as a vector into the function’s `aa_type` argument:

    aa_types_nw <- ego_netwrite(egos = ngq_egos,
                                ego_id = ngq_egos$ego_id,

                                alters = ngq_alters,
                                alter_id = ngq_alters$alter_id,
                                alter_ego = ngq_alters$ego_id,

                                max_alters = 10,
                                alter_alter = ngq_aa,
                                aa_ego = ngq_aa$ego_id,
                                i_elements = ngq_aa$alter1,
                                j_elements = ngq_aa$alter2,
                                # Note the inclusion of `aa_type` here
                                aa_type = ngq_aa$type,
                                directed = FALSE)

Incorporating alter-alter relationship types creates several new columns in our `alters` dataframe. In addition to the set of node-level measures `ego_netwrite` always generates, the function produces the same set of measures for each unique relationship type. This allows us to see each node’s centrality, for example, in its respective network of friendship and familial, and miscellaneous ties. These measures are given the same names as their counterparts for the overall ego network but have the name of their corresponding type appended to the end (e.g. `total_degree_friends`).

ego_id | id | alter_id | original_ego_id | original_alter_id | sex | race | white | black | other_race | pol | family | friend | other_rel | face | phone | text | total_degree | closeness | betweenness_scores | bonpow | bonpow_negative | burt_constraint | burt_hierarchy | effective_size | reachability | eigen_centrality | total_degree_friends | total_degree_related | total_degree_other_rel | closeness_friends | closeness_related | closeness_other_rel | betweenness_scores_friends | betweenness_scores_related | betweenness_scores_other_rel | bonpow_friends | bonpow_related | bonpow_other_rel | bonpow_negative_friends | bonpow_negative_related | bonpow_negative_other_rel | burt_constraint_friends | burt_constraint_related | burt_constraint_other_rel | burt_hierarchy_friends | burt_hierarchy_related | burt_hierarchy_other_rel | effective_size_friends | effective_size_related | effective_size_other_rel | reachability_friends | reachability_related | reachability_other_rel
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 0 | 1 | 1 | 1 | 1 | White | TRUE | FALSE | FALSE | 5 | TRUE | FALSE | FALSE | 5 | 5 | 5 | 0 | NaN | 0.00 | NA | NA | 1.0 | NA | 0 | 0.00 | NA | 0 | 0 | 0 | NaN | NaN | NaN | 0.00 | 0 | 0 | NA | NA | NA | NA | NA | NA | 1.0 | 1 | 1 | NA | NA | NA | 0 | 0 | 0 | 0.00 | 0 | 0
1 | 1 | 2 | 1 | 2 | 1 | White | TRUE | FALSE | FALSE | 7 | FALSE | TRUE | FALSE | 2 | 2 | 4 | 0 | NaN | 0.00 | NA | NA | 1.0 | NA | 0 | 0.00 | NA | 0 | 0 | 0 | NaN | NaN | NaN | 0.00 | 0 | 0 | NA | NA | NA | NA | NA | NA | 1.0 | 1 | 1 | NA | NA | NA | 0 | 0 | 0 | 0.00 | 0 | 0
2 | 0 | 1 | 2 | 1 | 1 | White | TRUE | FALSE | FALSE | 2 | FALSE | FALSE | TRUE | 4 | 4 | 4 | 0 | NaN | NaN | NA | NA | 1.0 | NA | 0 | NaN | NA | 0 | 0 | 0 | NaN | NaN | NaN | NaN | NaN | NaN | NA | NA | NA | NA | NA | NA | 1.0 | 1 | 1 | NA | NA | NA | 0 | 0 | 0 | NaN | NaN | NaN
3 | 0 | 1 | 3 | 1 | 1 | Black | FALSE | TRUE | FALSE | 1 | FALSE | TRUE | FALSE | 3 | 1 | 1 | 2 | 0.75 | 0.05 | 1.2158433 | 1.3351669 | 0.5 | 0 | 2 | 0.75 | 1.000000 | 2 | 0 | 0 | 0.75 | NaN | NaN | 0.05 | 0 | 0 | 1.2158433 | NA | NA | 1.3351669 | NA | NA | 0.5 | 1 | 1 | 0 | NA | NA | 2 | 0 | 0 | 0.75 | 0 | 0
3 | 1 | 2 | 3 | 2 | 1 | White | TRUE | FALSE | FALSE | 3 | FALSE | TRUE | FALSE | 1 | 1 | 5 | 2 | 0.75 | 0.05 | 1.2158433 | 1.3351669 | 0.5 | 0 | 2 | 0.75 | 1.000000 | 2 | 0 | 0 | 0.75 | NaN | NaN | 0.05 | 0 | 0 | 1.2158433 | NA | NA | 1.3351669 | NA | NA | 0.5 | 1 | 1 | 0 | NA | NA | 2 | 0 | 0 | 0.75 | 0 | 0
3 | 2 | 3 | 3 | 3 | 1 | White | TRUE | FALSE | FALSE | 2 | FALSE | TRUE | FALSE | 1 | 1 | 5 | 1 | 0.50 | 0.00 | 0.7223054 | 0.4661861 | 1.0 | 1 | 1 | 0.75 | 0.618034 | 1 | 0 | 0 | 0.50 | NaN | NaN | 0.00 | 0 | 0 | 0.7223054 | NA | NA | 0.4661861 | NA | NA | 1.0 | 1 | 1 | 1 | NA | NA | 1 | 0 | 0 | 0.75 | 0 | 0

Similarly, the ego-level `summaries` dataframe contains new measures of network size, isolate counts, fragmentation, centralization, and dyad/triad prevalence for each unique relationship type. It also calculates correlations for each pair of relationship types between alters in a fashion similar to what we saw for ego-alter ties before.

ego_id | network_size | mean_degree | density | num_isolates | prop_isolates | num_weakcomponent | size_largest_weakcomponent | prop_largest_weakcomponent | num_strongcomponent | size_largest_strongcomponent | prop_largest_strongcomponent | component_ratio | pairwise_strong_un | pairwise_weak_un | fragmentation_index | effective_size | efficiency | constraint | betweenness | norm_betweenness | dyad_mut | dyad_null | triad_003 | triad_102 | triad_201 | triad_300 | network_size_friends | network_size_related | network_size_other_rel | mean_degree_friends | mean_degree_related | mean_degree_other_rel | density_friends | density_related | density_other_rel | num_isolates_friends | num_isolates_related | num_isolates_other_rel | prop_isolates_friends | prop_isolates_related | prop_isolates_other_rel | num_weakcomponent_friends | num_weakcomponent_related | num_weakcomponent_other_rel | size_largest_weakcomponent_friends | size_largest_weakcomponent_related | size_largest_weakcomponent_other_rel | prop_largest_weakcomponent_friends | prop_largest_weakcomponent_related | prop_largest_weakcomponent_other_rel | num_strongcomponent_friends | num_strongcomponent_related | num_strongcomponent_other_rel | size_largest_strongcomponent_friends | size_largest_strongcomponent_related | size_largest_strongcomponent_other_rel | prop_largest_strongcomponent_friends | prop_largest_strongcomponent_related | prop_largest_strongcomponent_other_rel | component_ratio_friends | component_ratio_related | component_ratio_other_rel | pairwise_strong_un_friends | pairwise_strong_un_related | pairwise_strong_un_other_rel | pairwise_weak_un_friends | pairwise_weak_un_related | pairwise_weak_un_other_rel | fragmentation_index_friends | fragmentation_index_related | fragmentation_index_other_rel | effective_size_friends | effective_size_related | effective_size_other_rel | efficiency_friends | efficiency_related | efficiency_other_rel | constraint_friends | constraint_related | constraint_other_rel | betweenness_friends | betweenness_related | betweenness_other_rel | norm_betweenness_friends | norm_betweenness_related | norm_betweenness_other_rel | dyad_mut_friends | dyad_mut_related | dyad_mut_other_rel | dyad_null_friends | dyad_null_related | dyad_null_other_rel | triad_003_friends | triad_003_related | triad_003_other_rel | triad_102_friends | triad_102_related | triad_102_other_rel | triad_201_friends | triad_201_related | triad_201_other_rel | triad_300_friends | triad_300_related | triad_300_other_rel | aa_cor_friends_other_rel | aa_cor_friends_related | aa_cor_other_rel_related
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 2 | 0.0 | 0.0000000 | 2 | 1.0 | 2 | 1 | 0.5 | 2 | 1 | 0.5 | 1.00 | 0.0 | 0.0 | 1.0 | 2.0 | 1.0000000 | 0.5000000 | 1.00 | 1.0000000 | 0 | 1 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 0.0 | 0.0 | 0 | 0.0000000 | 0.0000000 | 0 | 2 | 2 | 2 | 1.0 | 1.0 | 1 | 2 | 2 | 2 | 1 | 1 | 1 | 0.5000000 | 0.5 | 0.5000000 | 2 | 2 | 2 | 1 | 1 | 1 | 0.5000000 | 0.5 | 0.5000000 | 1.00 | 1.0000000 | 1 | 0.0 | 0.0000000 | 0 | 0.0 | 0.0000000 | 0 | 1.0 | 1.0000000 | 1 | 2.0 | 2.0 | 2 | 1.00 | 1.0000000 | 1 | 0.5000000 | 0.5000000 | 0.5000000 | 1.000000 | 1.00000 | 1 | 1.0000000 | 1.0000000 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | NA | NA | NA
2 | 1 | 0.0 | NaN | 1 | 1.0 | 1 | 1 | 1.0 | 1 | 1 | 1.0 | NaN | NaN | NaN | NaN | 1.0 | 1.0000000 | 1.0000000 | 0.00 | NaN | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0.0 | 0.0 | 0 | NaN | NaN | NaN | 1 | 1 | 1 | 1.0 | 1.0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.0000000 | 1.0 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1.0000000 | 1.0 | 1.0000000 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | 1.0 | 1.0 | 1 | 1.00 | 1.0000000 | 1 | 1.0000000 | 1.0000000 | 1.0000000 | 0.000000 | 0.00000 | 0 | NaN | NaN | NaN | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | NA | NA | NA
3 | 5 | 1.2 | 0.3000000 | 1 | 0.2 | 2 | 4 | 0.8 | 2 | 4 | 0.8 | 0.25 | 0.6 | 0.6 | 0.4 | 3.8 | 0.7600000 | 0.4511111 | 6.00 | 0.6000000 | 3 | 7 | 3 | 5 | 2 | 0 | 5 | 5 | 5 | 1.2 | 0.0 | 0 | 0.3000000 | 0.0000000 | 0 | 1 | 5 | 5 | 0.2 | 1.0 | 1 | 2 | 5 | 5 | 4 | 1 | 1 | 0.8000000 | 0.2 | 0.2000000 | 2 | 5 | 5 | 4 | 1 | 1 | 0.8000000 | 0.2 | 0.2000000 | 0.25 | 1.0000000 | 1 | 0.6 | 0.0000000 | 0 | 0.6 | 0.0000000 | 0 | 0.4 | 1.0000000 | 1 | 3.8 | 5.0 | 5 | 0.76 | 1.0000000 | 1 | 0.4511111 | 0.2000000 | 0.2000000 | 6.000000 | 10.00000 | 10 | 0.6000000 | 1.0000000 | 1 | 3 | 0 | 0 | 7 | 10 | 10 | 3 | 10 | 10 | 5 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | NA | NA | NA
4 | 10 | 8.6 | 0.9555556 | 0 | 0.0 | 1 | 10 | 1.0 | 1 | 10 | 1.0 | 0.00 | 1.0 | 1.0 | 0.0 | 1.4 | 0.1400000 | 0.3599197 | 0.25 | 0.0055556 | 43 | 2 | 0 | 1 | 14 | 105 | 10 | 10 | 10 | 5.8 | 2.8 | 0 | 0.6444444 | 0.3111111 | 0 | 0 | 1 | 10 | 0.0 | 0.1 | 1 | 1 | 3 | 10 | 10 | 5 | 1 | 1.0000000 | 0.5 | 0.1000000 | 1 | 3 | 10 | 10 | 5 | 1 | 1.0000000 | 0.5 | 0.1000000 | 0.00 | 0.2222222 | 1 | 1.0 | 0.3555556 | 0 | 1.0 | 0.3555556 | 0 | 0.0 | 0.6444444 | 1 | 4.2 | 7.2 | 10 | 0.42 | 0.7200000 | 1 | 0.3438003 | 0.2892389 | 0.1000000 | 2.619048 | 29.66667 | 45 | 0.0582011 | 0.6592593 | 1 | 29 | 14 | 0 | 16 | 31 | 45 | 10 | 30 | 120 | 8 | 77 | 0 | 82 | 4 | 0 | 20 | 9 | 0 | NA | -1 | NA
5 | 3 | 2.0 | 1.0000000 | 0 | 0.0 | 1 | 3 | 1.0 | 1 | 3 | 1.0 | 0.00 | 1.0 | 1.0 | 0.0 | 1.0 | 0.3333333 | 0.9259259 | 0.00 | 0.0000000 | 3 | 0 | 0 | 0 | 0 | 1 | 3 | 3 | 3 | 0.0 | 2.0 | 0 | 0.0000000 | 1.0000000 | 0 | 3 | 0 | 3 | 1.0 | 0.0 | 1 | 3 | 1 | 3 | 1 | 3 | 1 | 0.3333333 | 1.0 | 0.3333333 | 3 | 1 | 3 | 1 | 3 | 1 | 0.3333333 | 1.0 | 0.3333333 | 1.00 | 0.0000000 | 1 | 0.0 | 1.0000000 | 0 | 0.0 | 1.0000000 | 0 | 1.0 | 0.0000000 | 1 | 3.0 | 1.0 | 3 | 1.00 | 0.3333333 | 1 | 0.3333333 | 0.9259259 | 0.3333333 | 3.000000 | 0.00000 | 3 | 1.0000000 | 0.0000000 | 1 | 0 | 3 | 0 | 3 | 0 | 3 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | NA | NA | NA
6 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | 0 | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA

Our `overall_summary` has also been expanded to show dataset-level summaries of each alter-alter relationship type. Parenthetical phrases in the `measure_labels` column beginning with “Alter-Alter” indicate the specific relationship type described for a given measure. Note here that measures relating to network size, number of isolates, and one-node networks remain the same across relation types, as ego-alter relationship types are not taken into account when calculating these measures. By contrast, measures of network density and fragmentation vary given the presence or absence of alter-alter ties.

measure_labels | measure_descriptions | measures
--- | --- | ---
Number of egos/ego networks | Total number of egos providing ego networks in dataset | 20
Number of alters | Total number of alters nominated by egos across entire dataset | 67
Number of isolates | Number of egos who did not report any alters in their personal network | 2
Number of one-node networks | Number of egos who reported only one alter in their personal network | 3
Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
Largest network size | Largest number of alters provided by a single ego | 10
Average network size | Average number of alters provided by a single ego | 3.35
Average network density | The average density of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.786296296296296
Average fragmentation | The mean fragmentation index score of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.215555555555556
(Alter-Alter friends) Number of alters | Total number of alters nominated by egos across entire dataset | 67
(Alter-Alter friends) Number of isolates | Number of egos who did not report any alters in their personal network | 2
(Alter-Alter friends) Number of one-node networks | Number of egos who reported only one alter in their personal network | 3
(Alter-Alter friends) Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
(Alter-Alter friends) Largest network size | Largest number of alters provided by a single ego | 10
(Alter-Alter friends) Average network size | Average number of alters provided by a single ego | 3.35
(Alter-Alter friends) Average network density | The average density of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.534444444444444
(Alter-Alter friends) Average fragmentation | The mean fragmentation index score of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.315555555555556
(Alter-Alter related) Number of alters | Total number of alters nominated by egos across entire dataset | 67
(Alter-Alter related) Number of isolates | Number of egos who did not report any alters in their personal network | 2
(Alter-Alter related) Number of one-node networks | Number of egos who reported only one alter in their personal network | 3
(Alter-Alter related) Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
(Alter-Alter related) Largest network size | Largest number of alters provided by a single ego | 10
(Alter-Alter related) Average network size | Average number of alters provided by a single ego | 3.35
(Alter-Alter related) Average network density | The average density of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.185185185185185
(Alter-Alter related) Average fragmentation | The mean fragmentation index score of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.811851851851852
(Alter-Alter other_rel) Number of alters | Total number of alters nominated by egos across entire dataset | 67
(Alter-Alter other_rel) Number of isolates | Number of egos who did not report any alters in their personal network | 2
(Alter-Alter other_rel) Number of one-node networks | Number of egos who reported only one alter in their personal network | 3
(Alter-Alter other_rel) Smallest non-isolate network size | Smallest number of alters provided by a single ego | 1
(Alter-Alter other_rel) Largest network size | Largest number of alters provided by a single ego | 10
(Alter-Alter other_rel) Average network size | Average number of alters provided by a single ego | 3.35
(Alter-Alter other_rel) Average network density | The average density of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.0666666666666667
(Alter-Alter other_rel) Average fragmentation | The mean fragmentation index score of personal networks provided by egos (networks with 0-1 alters excluded from calculation) | 0.933333333333333

Finally, each element in the `igraph_objects` list now contains an “`igraph`” and “`igraph_ego`” object for each alter-alter type, allowing users to look at specific kinds of relationships without having to subset the network themselves.

    names(aa_types_nw$igraph_objects[[1]])
    #>  [1] "ego"                  "ego_info"             "igraph"
    #>  [4] "igraph_ego"           "igraph_friends"       "igraph_ego_friends"
    #>  [7] "igraph_related"       "igraph_ego_related"   "igraph_other_rel"
    #> [10] "igraph_ego_other_rel"

The availability of these new objects may be convenient for users who wish to visualize differences in the prevalence of certain types of alter-alter ties in a single ego network, as shown in the example below:

    ego7 <- aa_types_nw$igraph_objects[[7]]$igraph_ego
    ego7_friends <- aa_types_nw$igraph_objects[[7]]$igraph_ego_friends
    ego7_family <- aa_types_nw$igraph_objects[[7]]$igraph_ego_related
    ego7_other <- aa_types_nw$igraph_objects[[7]]$igraph_ego_other_rel

    ego7_layout <- igraph::layout.fruchterman.reingold(ego7)

    plot(ego7,
         vertex.color = igraph::V(ego7)$sex,
         layout = ego7_layout,
         main = "Overall Network")

    plot(ego7_friends,
         vertex.color = igraph::V(ego7_friends)$sex,
         layout = ego7_layout,
         main = "Friends")

    plot(ego7_family,
         vertex.color = igraph::V(ego7_family)$sex,
         layout = ego7_layout,
         main = "Family")

    plot(ego7_other,
         vertex.color = igraph::V(ego7_other)$sex,
         layout = ego7_layout,
         main = "Other Relationships")

You might notice that the number of columns and other elements of output grows substantially when `ego_netwrite` takes alter-alter relationship types into account, particularly if the number of unique types is quite large. Moreover, the `summaries` and `overall_summary` objects may grow even larger when `ego_netwrite` is asked to process both ego-alter and alter-alter types. While `ego_netwrite` provides all of this output in the interest of being exhaustive, some users may find its volume somewhat unwieldy. If this is the case, users may want to condense relationship types into a simpler set of categories to reduce the number of additional measures generated.

## Measuring Homophily, Heterophily, and Diversity

Network scholars are often interested in questions pertaining to homophily (in which nodes with similar properties form ties with one another), heterophily (in which nodes with different properties form ties), and diversity. While generating measures of these phenomena are not fundamentally difficult, they often entail implicit decisions made by users that automated workflows like `ego_netwrite` cannot easily anticipate. Consequently, `ideanet` offers a set of functions for popular measures of homophily, heterophily, and diversity in ego networks that users can apply at their own discretion once they have finished running `ego_netwrite`.

To see how we use these functions we’ll start with measures of diversity for categorical variables. Users should note that each of these functions takes columns from the `alters` dataframe as its inputs. Although we will not go into specific detail about each measure generated here, we encourage readers to consult `ideanet`’s documentation for a bit of added context.

    alters <- aa_types_nw$alters

    # H-Index
    race_h_index <- h_index(ego_id = alters$ego_id,
                            measure = alters$race,
                            prefix = "race")
    # Index of Qualitative Variation (Normalized H-Index)
    race_iqv <- iqv(ego_id = alters$ego_id,
                    measure = alters$race,
                    prefix = "race")

While the above measures of attribute diversity apply to networks belonging to egos, you might notice that they do not take ego’s own attribute values into account. Measures of homophily, by contrast, compare alter attributes to ego’s in order to gauge how likely ego is to form ties with similar others. Accordingly, measures of homophily in ego networks require additional arguments whose values can be extracted from the `egos` dataframe:

    egos <- aa_types_nw$egos

    # Ego Homophily (Count)
    race_homophily_c <- ego_homophily(ego_id = egos$ego_id,
                                      ego_measure = egos$race,
                                      alter_ego = alters$ego_id,
                                      alter_measure = alters$race,
                                      prefix = "race",
                                      prop = FALSE)
    # Ego Homophily (Proportion)
    race_homophily_p <- ego_homophily(ego_id = egos$ego_id,
                                      ego_measure = egos$race,
                                      alter_ego = alters$ego_id,
                                      alter_measure = alters$race,
                                      prefix = "race",
                                      prop = TRUE)
    # E-I Index
    race_ei <- ei_index(ego_id = egos$ego_id,
                           ego_measure = egos$race,
                           alter_ego = alters$ego_id,
                           alter_measure = alters$race,
                           prefix = "race")
    # Pearson's Phi
    race_pphi <- pearson_phi(ego_id = egos$ego_id,
                                ego_measure = egos$race,
                                alter_ego = alters$ego_id,
                                alter_measure = alters$race,
                                prefix = "race")

For measures of homophily on continuous measures, we offer a function for calculating Euclidean distance:

    # Euclidean Distance
    pol_euc <- euclidean_distance(ego_id = egos$ego_id,
                                  ego_measure = egos$pol,
                                  alter_ego = alters$ego_id,
                                  alter_measure = alters$pol,
                                  prefix = "pol")

Each of these functions produces a dataframe with two columns: an `ego_id` column for compatibility with other outputs and a second column containing the measure produced by the function for each ego network. These dataframes can be quickly merged into `egos` or `summaries` in order to extend analysis at the level of individual egos and/or their networks.

    egos <- egos %>%
      dplyr::left_join(race_h_index, by = "ego_id") %>%
      dplyr::left_join(race_homophily_p, by = "ego_id") %>%
      dplyr::left_join(pol_euc, by = "ego_id")

ego_id | original_ego_id | age | sex | race | black | white | other_race | edu | pol | race_h_index | race_prop_same | pol_euclidean_distance
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
1 | 1 | 41 | 2 | White | FALSE | TRUE | FALSE | 5 | 3 | 0.00 | 1.0 | 2.2360680
2 | 2 | 14 | 1 | Other | FALSE | FALSE | TRUE | 7 | 2 | 0.00 | 0.0 | 0.0000000
3 | 3 | 35 | 2 | White | FALSE | TRUE | FALSE | 7 | 3 | 0.32 | 0.8 | 0.5291503
4 | 4 | 17 | 2 | White | FALSE | TRUE | FALSE | 6 | 3 | 0.00 | 1.0 | 0.5477226
5 | 5 | 43 | 1 | White | FALSE | TRUE | FALSE | 7 | 2 | 0.00 | 1.0 | 1.0540926
6 | 6 | 24 | 1 | Other | FALSE | FALSE | TRUE | 6 | 3 | NA | NA | NA

## Exporting to `egor`

Some users may want convert their egocentric data into an `egor` object. `egor` objects are especially convenient for fitting exponential random graph models (ERGMs) using egocentric data, which allow researchers to simulate and estimate global network structures for settings where sociocentric data capture is not possible. `ego_netwrite` supports the option to create `egor` objects alongside other function outputs. However, because it is not a core dependency of `ideanet`, users must ensure that they have already installed the `egor` package before using this feature:

    install.packages("egor")

Once installed, users can specify `egor = TRUE` in `ego_netwrite` to create an `egor` object based on the ego list, alter list and alter-alter edgelist fed into the function. This object is given the simple name `egor`:

    egor

## Network Canvas Compatibility (`nc_read`)

`ideanet` includes a function specifically designed to read and process data generated by Network Canvas, an increasingly popular tool for egocentric data capture. This function, named `nc_read`, reads in a directory of CSV files exported from Network Canvas and returns a list of dataframes optimized for use with `ego_netwrite`.

Although `ideanet` does not contain examples of data generated by Network Canvas, we provide a detailed overview of how to work with `nc_read` in the Reading Network Canvas Data vignette, which you can access by running the following line of code:

    vignette("nc_read", package = "ideanet")