We do computational studies concerning the enumeration of maximal isolated cliques in graphs. Isolation, as recently introduced, measures the degree of connectedness of the cliques to the rest of the graph. Isolation helps both in getting faster algorithms than for the enumeration of maximal general cliques and in filtering out cliques with special semantics. We perform experiments with synthet...

Color the edges of the n-vertex complete graph in red and blue, and suppose that red k-cliques are fewer than blue k-cliques. We show that the number of red k-cliques is always less than ckn , where ck ∈ (0, 1) is the unique root of the equation z = (1 − z) + kz(1 − z)k−1. On the other hand, we construct a coloring in which there are at least ckn k −O(nk−1) red k-cliques and at least the same n...

Considering a clique as a conservative definition of community structure, we examine how partitioning algorithms interact with cliques. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across different partitions by popular algorithms. We examine the largest connected component of the subgraph formed by retaining only edges in ...

NP-complicated problems have been described in the graph theory. An example is the extracting of all maximal cliques from a graph. Many algorithms for solving this problem have been described. However, complexity is linear to the number of maximal cliques. This paper discusses a new approach for extracting maximal cliques, based on the monotone system theory. The complexity of the presented alg...

In social networking analysis, there exists a fundamental problem called maximal cliques enumeration(MCE), which has been extensively investigated in many fields, including social networks, biological science, etc. As a matter of fact, the formation principle of maximal cliques that can help us to speed up the detection of maximal cliques from social networks is often ignored by most existing r...

A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect in exactly p vertices. A graph G is said to have a p-regular k-clique cover if there is a p-regular family H of k-cliques of G such that each edge of G belongs to a clique in H. Such a p-regular kclique cover is separable if the complete subgraphs of order p that arise as intersections of pairs o...

In this paper, we propose a super-pixels clique based tracking algorithm to perform track task, meanwhile it can robustly handle the appearance change of target object and heavy occlusion. By two stage adaptive appearance modeling method, we propose the method of learning the target-background appearance framework ,which is based on super pixels principle histogram bins cluster method. The proc...

This work provides a structural characterisation of hereditary graph classes that do not contain star forest, several graphs obtained from forests by subset complementation, union cliques, and the complement cliques as induced subgraphs. provides, for instance, results containing matching complements matching. In terms speed classes, our imply all such have at most factorial growth.

For a given graph G of n vertices and m edges, a clique S of size k is said to be c-isolated if there are at most ck outgoing edges from S. It is shown that this parameter c is an interesting measure which governs the complexity of finding cliques. In particular, if c is a constant, then we can enumerate all c-isolated maximal cliques in linear time, and if c = O(log n), then we can enumerate a...