Large Communities in a scale-free network
Caio Alves, Rodrigo Ribeiro, Remy Sanchis

TL;DR
This paper proves that in a preferential attachment model with an edge-step, the resulting large-scale network contains a very large complete subgraph, demonstrating the emergence of significant community structures.
Contribution
It establishes the existence of large complete subgraphs in the GLP preferential attachment model with an edge-step, quantifying their size as a power of the network.
Findings
Existence of a complete subgraph of size t^α w.h.p.
Size of the subgraph scales as a power of the network size.
Results hold for a range of parameters p and ε.
Abstract
We prove the existence of a large complete subgraph w.h.p. in a preferential attachment random graph process with an edge-step. That is, we prove that the random graph produced by the so-called GLP model at time contains a complete subgraph of order , where , is any number such that , and is a parameter of the model.
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