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• W1927871229 abstract "As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$ cliques means that they share at least $l<k$ vertices. In this paper we develop a theoretical approach to study clique percolation in Erdifmmode mbox{H{o}}else H{o}fi{}s-R'enyi graphs, which gives not only the exact solutions of the critical point, but also the corresponding order parameter. Based on this, we prove theoretically that the fraction $ensuremath{psi}$ of cliques in the giant clique cluster always makes a continuous phase transition as the classical percolation. However, the fraction $ensuremath{phi}$ of vertices in the giant clique cluster for $l>1$ makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for $l=1$. More interesting, our analysis shows that at the critical point, the order parameter ${ensuremath{phi}}_{c}$ for $l>1$ is neither 0 nor 1, but a constant depending on $k$ and $l$. All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation." @default.
• W1927871229 created "2016-06-24" @default.
• W1927871229 creator A5047149764 @default.
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• W1927871229 date "2015-10-07" @default.
• W1927871229 modified "2023-10-14" @default.
• W1927871229 title "Clique percolation in random graphs" @default.
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• W1927871229 doi "https://doi.org/10.1103/physreve.92.042116" @default.
• W1927871229 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/26565177" @default.
• W1927871229 hasPublicationYear "2015" @default.
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