Generalized Recursive Circulant Graphs

Tang, Shyue-Ming; Wang, Yue-Li; Li, Chien-Yi

doi:10.1109/tpds.2011.109

Cited by 12 publications

(2 citation statements)

References 22 publications

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“…2 in [15]. Note that in [20], the authors propose a generalization of a class of recursive circulant graphs. However, it is worth pointing out that these generalized recursive circulant graphs belong to the set of circulant graphs, and hence are all vertex-symmetric.…”

Section: Introductionmentioning

confidence: 99%

Tuning the clustering coefficient of generalized circulant networks

Kooij

Horsevad

Bouffanais

2021

Physica A: Statistical Mechanics and its Applications

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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 C N,k . We show that the expression for the clustering coefficient of C N,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 C N,k , or by connecting, in two different ways, an additional node to some nodes of C N,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.

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Section: Introductionmentioning

confidence: 99%

Tuning the clustering coefficient of generalized circulant networks

Kooij

Horsevad

Bouffanais

2021

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Although the class of RCGs can provide a good flexibility on designing network systems, due to the restriction of 0 < c < d we can find that C(12; 1, 4) is an RCG (i.e., it is isomorphic with R(3 • 4 1 , 4)), while C(12; 1, 3) is not. To remove this restriction, Tang et al [25] proposed a more generalized definition of RCGs, called generalized recursive circulant graphs (defined later in Sect. 2), which can also be constructed recursively.…”

Section: Introductionmentioning

confidence: 99%