English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a Gaussian matrix function of the adjacency matrix of artificial andreal-world networks. In particular, we study the Gaussian Estrada index---anindex characterizing the importance of eigenvalues close to zero. This indexaccounts for the information contained in the eigenvalues close to zero in thespectra of networks. Here we obtain bounds for this index in simple graphs,proving that it reaches its maximum for star graphs followed by completebipartite graphs. We also obtain formulas for the Estrada Gaussian index ofErd\H{o}s-R\'enyi random graphs as well as for the Barab\'asi-Albert graphs. Wealso show that in real-world networks this index is related to the existence ofimportant structural patterns, such as complete bipartite subgraphs(bicliques). Such bicliques appear naturally in many real-world networks as aconsequence of the evolutionary processes giving rise to them. In general, theGaussian matrix function of the adjacency matrix of networks characterizesimportant structural information not described in previously used matrixfunctions of graphs.

Exploring the "Middle Earth" of Network Spectra via a Gaussian Matrix Function