Computes the Estrada index, a graph-level spectral invariant $$EE(G) = \sum_{i=1}^{n} e^{\lambda_i}$$ where \(\lambda_i\) are the eigenvalues of the binary adjacency matrix. Edge weights are ignored. For an undirected network the index equals \(\sum_k M_k / k!\), where \(M_k\) is the number of closed walks of length \(k\), and it is the sum of the subgraph centralities of all nodes. For a directed network the eigenvalues may be complex. They come in conjugate pairs, so the sum of their exponentials is real and again equals the trace of \(e^A\), the weighted count of closed walks.
References
Estrada, E. (2000). Characterization of 3D molecular structure. Chemical Physics Letters, 319(5-6), 713-718.
See also
centrality_subgraph for the per-node measure. On an
undirected network its values sum to estrada_index(x).