Tuning the clustering coefficient of generalized circulant networks

Robert E. Kooij, Nikolaj Horsevad Sørensen and Roland Bouffanais

Physica A: Statistical Mechanics and its Applications, 2021, vol. 578, issue C

Abstract: Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient on dynamical processes taking place on networks, some authors have focused on the construction of graphs with tunable clustering coefficients. These constructions are usually realized through a stochastic process, either by growing a network through the preferential attachment procedure, or by applying a random rewiring process. In contrast, we consider here several families of static graphs whose clustering coefficients can be determined explicitly. The basis for these families is formed by the k-regular graphs on N nodes, that belong to the family of so-called circulant graphs denoted by CN,k. We show that the expression for the clustering coefficient of CN,k reported in literature, only holds for sufficiently large N. Next, we consider three generalizations of the circulant graphs, either by adding some pendant links to CN,k, or by connecting, in two different ways, an additional node to some nodes of CN,k. For all three generalizations, we derive explicit expressions for the clustering coefficient. Finally, we construct a family of pairs of generalized circulant graphs, with the same number of nodes and links, but with different clustering coefficients.

Keywords: Circulant graphs; Clustered networks; Consensus dynamics; Complex networks (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:578:y:2021:i:c:s0378437121003617

DOI: 10.1016/j.physa.2021.126088

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