TL;DR
This paper studies a generalized percolation model on directed graphs, analyzing the probability of infinite clusters, their expected number, and the decay properties of cluster size and radius.
Contribution
It introduces a generalized percolation framework for directed graphs and derives relations for cluster probabilities and decay properties.
Findings
Relation between chosen site probability and cluster size
Expected number of infinite clusters calculated
Exponential tail decay of cluster radius and size established
Abstract
Suppose each site independently and randomly chooses some sites around it, and it is weakly (strongly) connected with them (if there choose each other). What is the probability that the weak (strong) connected cluster is infinite? We investigate a percolation model for this problem, which is a generalization of site percolation. We give a relation between the probability of the number of chosen sites around a site and the size of clusters. We also see the expected number of infinite clusters, and the exponential tail decay of the radius and the size of a cluster.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Complex Network Analysis Techniques · Theoretical and Computational Physics