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arXiv · 1810.07004

D-chain tomography of networks: a new structure spectrum and an application to the SIR process

Ricky X. F. Chen·Christian M. Reidys·Andrei C. Bura
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Abstract

The analysis of the dynamics on complex networks is closely connected to structural features of the networks. Features like, for instance, graph-cores and node degrees have been studied ubiquitously. Here we introduce the D-spectrum of a network, a novel new framework that is based on a collection of nested chains of subgraphs within the network. Graph-cores and node degrees are merely from two particular such chains of the D-spectrum. Each chain gives rise to a ranking of nodes and, for a fixed node, the collection of these ranks provides us with the D-spectrum of the node. Besides a node deletion algorithm, we discover a connection between the D-spectrum of a network and some fixed points of certain graph dynamical systems (MC systems) on the network. Using the D-spectrum we identify nodes of similar spreading power in the susceptible-infectious-recovered (SIR) model on a collection of real world networks as a quick application. We then discuss our results and conclude that D-spectra represent a meaningful augmentation of graph-cores and node degrees.

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BibTeXRIS

Ricky X. F. Chen, Christian M. Reidys, Andrei C. Bura. 2018-10-12. D-chain tomography of networks: a new structure spectrum and an application to the SIR process. https://doi.org/10.1137/19m1243890

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