Feature evolutionary relationship discovery based on tree structure pattern mining and spatial co-location in cliques aims to combine algorithm find data relationships of features these cliques. This allows for a deeper analysis possible causal between features, predicting the occurrence other certain or summarizing general laws. For clique, appearance one feature may lead another feature, whic...

Recently Chase determined the maximum possible number of cliques size in a graph on vertices with given degree. Soon afterward, Chakraborti and Chen answered version this question which we ask that have edges fixed degree (without imposing any constraint vertices). In paper address these problems hypergraphs. For -graphs issues arise do not appear case. instance, for general can assign degrees ...

A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for various graph classes. For example, the maximum number of cliques in a planar graph with n vertices is 8(n − 2).

Mining for cliques in networks provides an essential tool for the discovery of strong associations among entities. Applications vary, from extracting core subgroups in team performance data arising in sports, entertainment, research and business; to the discovery of functional complexes in high-throughput gene interaction data. A challenge in all of these scenarios is the large size of real-wor...

This paper proposes and investigates a framework for clique gossip protocols. As complete subnetworks, the existence of cliques is ubiquitous in various social, computer, and engineering networks. By clique gossiping, nodes interact with each other along a sequence of cliques. Clique-gossip protocols are defined as arbitrary linear node interactions where node states are vectors evolving as lin...

Cliques are commonly used for social network analysis tasks, as they are a good representation of close-knit groups of people. For this reason (as well as for others), the problem of enumerating, i.e., finding, all maximal cliques in a graph has received extensive treatment. However, considering only complete subgraphs is too restrictive in many real-life scenarios where “almost cliques” may be...

We show that the number of potential maximal cliques for an arbitrary graph G on n vertices is O∗(1.8135n), and that all potential maximal cliques can be listed in O∗(1.8899n) time. As a consequence of this results, treewidth and minimum fill-in can be computed in O∗(1.8899n) time.