Degree correlations in graphs with clique clustering
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Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.
Mann , P S , Smith , V A , Mitchell , J B O & Dobson , S A 2022 , ' Degree correlations in graphs with clique clustering ' , Physical Review. E, Statistical, nonlinear, and soft matter physics , vol. 105 , no. 4 , 044314 . https://doi.org/10.1103/PhysRevE.105.044314
Physical Review. E, Statistical, nonlinear, and soft matter physics
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DescriptionFunding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).
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