% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/network-summary.R
\name{estrada_index}
\alias{estrada_index}
\title{Estrada Index}
\usage{
estrada_index(x)
}
\arguments{
\item{x}{Network input (matrix, igraph, network, cograph_network, tna object).}
}
\value{
A single numeric value — the Estrada index of the graph.
}
\description{
A graph-level spectral invariant derived from subgraph centrality:
\deqn{EE(G) = \sum_{i=1}^{n} e^{\lambda_i}}
where \eqn{\lambda_i} are the eigenvalues of the adjacency matrix. The
Estrada index equals the total number of closed walks in the graph,
weighted by walk length: \eqn{EE(G) = \sum_k M_k / k!} where \eqn{M_k} is
the number of closed walks of length \eqn{k}. It is the sum of subgraph
centralities across all nodes.
}
\details{
Matches \code{networkx.estrada_index} at machine epsilon (max relative
difference ~5e-15 across random test graphs).
}
\examples{
# Karate club
g <- igraph::make_graph("Zachary")
estrada_index(g)
}
\references{
Estrada, E. (2000). Characterization of 3D molecular structure.
\emph{Chemical Physics Letters}, 319(5-6), 713-718.
}
\seealso{
\code{\link{centrality_subgraph}} for the per-node equivalent
(sum of \code{subgraph_centrality(x)} equals \code{estrada_index(x)}).
}
