Distribution of centrality measures on undirected random networks via the cavity method.

ABSTRACT: The Katz centrality of a node in a complex network is a measure of the node's importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its "global" character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability [Formula: see text] that a random node in the ensemble of undirected random graphs has centrality [Formula: see text] satisfies a set o

SUBMITTER: Bartolucci S 

PROVIDER: S-EPMC11459148 | biostudies-literature | 2024 Oct

REPOSITORIES: biostudies-literature