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Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its importance in many fields such as biology, social networks or network traffic analysis. The metrics proposed to shape communities are too lax and do not consider the internal layout of the edges in the community, which lead to undesirable results.… (More)

Let Φ(<i>x,y</i>)∈ ℂ[<i>x,y</i>] be a symmetric polynomial of partial degree <i>d</i>. The graph <i>G</i>(Φ) is defined by taking ℂ as set of vertices and the points of 𝕍 (Φ(<i>x,y</i>)) as edges. We study the following problem: given a finite, connected, <i>d</i>-regular graph <i>H</i>, find the polynomials… (More)

The complete generalized cycle G(d, n) is the digraph which has Z n × Z d as the vertex set and every vertex (i, x) is adjacent to the d vertices (i + 1, y) with y ∈ Z d. As a main result, we give a necessary and sufficient condition for the iterated line digraph G(d, n, k) = L k−1 G(d, n), with d a prime number, to be a Cayley digraph in terms of the… (More)

Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its applications in many fields such as biology, social networks, or network traffic analysis. Although the existing metrics used to quantify the quality of a community work well in general, under some circumstances, they fail at correctly capturing… (More)

Given a finite set V and a set S of permutations of V , the group action graph GAG(V, S) is the digraph with vertex set V and arcs (v, v σ) for all v ∈ V and σ ∈ S. Let S be the group generated by S. The Cayley digraph Cay(S, S) is called a Cayley cover of GAG(V, S). We define the Kautz digraphs as group action graphs and give an explicit construction of… (More)