2014/10/20 by Francesca Arrigo, Michele Benzi, Arrigo, Francesca +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Interconnection Networks and Systems #Numerical Analysis (math.NA) #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.1410.5303
openalex publication_date 2014/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The total communicability of a network (or graph) is defined as the sum of\nthe entries in the exponential of the adjacency matrix of the network, possibly\nnormalized by the number of nodes. This quantity offers a good measure of how\neasily information spreads across the network, and can be useful in the design\nof networks having certain desirable properties. The total communicability can\nbe computed quickly even for large networks using techniques based on the\nLanczos algorithm.\n In this work we introduce some heuristics that can be used to add, delete, or\nrewire a limited number of edges in a given sparse network so that the modified\nnetwork has a large total communicability. To this end, we introduce new edge\ncentrality measures which can be used to guide in the selection of edges to be\nadded or removed.\n Moreover, we show experimentally that the total communicability provides an\neffective and easily computable measure of how "well-connected" a sparse\nnetwork is.\n