Percolation on correlated random networks

TL;DR

This paper investigates how percolation processes affect the topology and resilience of correlated weighted networks, revealing the importance of weak ties in maintaining connectivity and the gradual nature of network disintegration.

Contribution

It introduces a model for correlated weighted networks and analyzes their percolation behavior under different link removal strategies, highlighting the role of weak ties in network resilience.

Findings

Weak ties are crucial for network connectivity.

Gradual shrinking of the giant component under failure.

Different percolation strategies affect network evolution.

Abstract

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks.