Cliques have interesting properties that make them an ideal subject for social network analysis. Their members are close-knit and share common interests, which makes cliques a potent force spreading influence. Since networks often contain multiple cliques, it is important to understand how they can influence one another. In this study, we propose model describes the opinion dynamics of intercon...

The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of lower bounds for the congested clique; indeed, it is now known that proving explicit congested clique lower bounds is as difficult as proving circuit lower bou...

The clique-transversal number τc(G) of a graph G is the minimum size of a set of vertices meeting all the cliques. The clique-independence number αc(G) of G is the maximum size of a collection of vertex-disjoint cliques. A graph is clique-perfect if these two numbers are equal for every induced subgraph of G. Unlike perfect graphs, the class of clique-perfect graphs is not closed under graph co...

Graphs of clique–width at most k were introduced by Courcelle, Engelfriet and Rozenberg (1993) as graphs which can be defined by k-expressions based on graph operations which use k vertex labels. In this paper we study the clique–width of perfect graph classes. On one hand, we show that every distance–hereditary graph, has clique– width at most 3, and a 3–expression defining it can be obtained ...

Let B and R be two simple graphs with vertex set V , and let G(B,R) be the simple graph with vertex set V , in which two vertices are adjacent if they are adjacent in at least one of B and R. For X ⊆ V , we denote by B|X the subgraph of B induced by X; let R|X and G(B,R)|X be defined similarly. A clique in a graph is a set of pairwise adjacent vertices. A subset U ⊆ V is obedient if U is the un...

The high-level contributions of this paper are as follows: We modify an existing branch-andbound based exact algorithm (for maximum clique size of an entire graph) to determine the maximal clique size that the individual vertices in the graph are part of. We then run this algorithm on six real-world network graphs (ranging from random networks to scale-free networks) and analyze the distributio...

1.1 Maximum Clique Problem Assume that the finite undirected simple graph is given, where V is the set of nodes, E is the set of edges. The arbitrary full graph is called a clique. The clique, which does not contain other cliques, is called a maximal Clique. The largest maximal clique is called a maximum clique. To extract all maximal cliques from the graph G. Many algorithms have...