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

TL;DR

This paper introduces the D-spectrum, a new framework based on nested subgraph chains, to analyze network structure and dynamics, demonstrating its effectiveness in identifying influential nodes in SIR spreading processes.

Contribution

The paper presents the D-spectrum as a novel structural analysis tool, connecting it to graph dynamical systems and applying it to real-world networks for epidemic modeling.

Findings

D-spectrum generalizes graph-cores and node degrees

D-spectrum correlates with spreading influence in SIR models

Nodes with similar D-spectra exhibit comparable spreading power

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.