1. The Clustering Coefficient for Graph Products.
- Author
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Aguilar-Alarcón, Jhon J., Hernández-Gómez, Juan C., and Romero-Valencia, Jesús
- Subjects
TRIANGLES - Abstract
The clustering coefficient of a vertex v, of degree at least 2, in a graph Γ is obtained using the formula C (v) = 2 t (v) deg (v) (deg (v) − 1) , where t (v) denotes the number of triangles of the graph containing v as a vertex, and the clustering coefficient of Γ is defined as the average of the clustering coefficient of all vertices of Γ , that is, C (Γ) = 1 | V | ∑ v ∈ V C (v) , where V is the vertex set of the graph. In this paper, we give explicit expressions for the clustering coefficient of corona and lexicographic products, as well as for the Cartesian sum; such expressions are given in terms of the order and size of factors, and the degree and number of triangles of vertices in each factor. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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