Enumeration of Maximal Cliques from an Uncertain Graph

Equations , Maximal Cliques , and Graph Isomorphism

We present a new energy-minimization framework for the graph isomorphism problem which is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feat...

Mining λ-Maximal Cliques from a Fuzzy Graph

The depletion of natural resources in the last century now threatens our planet and the life of future generations. For the sake of sustainable development, this paper pioneers an interesting and practical problem of dense substructure (i.e., maximal cliques) mining in a fuzzy graph where the edges are weighted by the degree of membership. For parameter 0 ≤ λ ≤ 1 (also called fuzzy cut in fuzzy...

The Enumeration of Maximal Cliques of Large Graphs

Replicator Equations, Maximal Cliques, and Graph Isomorphism

We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive featu...

Large Maximal Cliques Enumeration in Large Sparse Graphs

Identifying communities in social networks is a problem of great interest. One popular type of community is where every member of the community knows all others, which can be viewed as a clique in the graph representing the social network. In several real life situations, finding small cliques may not be interesting as they are large in number and low in information content. Hence, in this pape...