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)
We give explicit formulae for obtaining the binary sequences which produce Stein-haus triangles and generalized Pascal triangles with rotational and dihedral symmetries .
Let C(n, p) be the set of p-compositions of an integer n, i.e., the set of p-tuples α = (α 1 ,. .. , α p) of nonnegative integers such that α 1 + · · ·+ α p = n, and x = (x 1 ,. .. , x p) a vector of indeterminates. For α and β two p-compositions of n, define (x + α) β = (x 1 + α 1) β1 · · · (x p + α p) βp. In this paper we prove an explicit formula for the… (More)
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results generalize previous determinant evaluations due to the first and third author [SIAM J. Matrix Anal. Appl. 23 (2001),… (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)
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)