Percolation on correlated random networks

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.

11 pages, 9 figure; to appear in Phys. Rev. E

References in corpus (7)

• Structure and tie strengths in mobile communication networks
• The entropy of network ensembles
• Percolation in living neural networks
• Disassortative mixing in online social networks
• A Hebbian approach to complex network generation
• Equilibrium statistical mechanics on correlated random graphs
• Microscopic energy flows in disordered Ising spin systems

Cited by in corpus (10)

• Percolation on complex networks: Theory and application
• Cavity-based robustness analysis of interdependent networks: Influences of intranetwork and internetwork degree-degree correlations
• Parallel processing in immune networks
• Organization and evolution of synthetic idiotypic networks
• Topological properties of hierarchical networks
• Alternative criterion for two-dimensional wrapping percolation
• Analogue neural networks on correlated random graphs
• Percolation transitions with nonlocal constraint
• Emergence of strongly connected giant components in continuum disk-spin percolation
• Insights in Economical Complexity in Spain: the hidden boost of migrants in international tradings