Spreading on a complex network avoiding certain motifs

TL;DR

This paper investigates how excluding certain motifs from a network affects spreading processes, providing analytical insights into percolation behavior for exponential and scale-free networks.

Contribution

It introduces a novel analysis of motif exclusion effects on network percolation, with analytical solutions for specific degree distributions.

Findings

Excluding motifs subtly alters percolation thresholds.

Different degree distributions exhibit distinct percolation behaviors.

Analytical solutions are derived for exponential and scale-free networks.

Abstract

Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not reaching certain sub-classes of the network. We show that excluding nodes and edges from the network has a subtle effect on the percolation. We study two specific examples of degree distributions (exponential and scale free) for which analytical solutions can be obtained. The two cases exhibit qualitatively different behavior.