Solving maximum fuzzy clique problem with neural networks and its applications

Abstract

The maximum clique problem is an important problem in graph theory. Many real-life problems are still being mapped into this problem for their effective solutions. A natural extension of this problem that has emerged very recently in many real-life networks, is its fuzzification. The problem of finding the maximum fuzzy clique has been formalized on fuzzy graphs and subsequently addressed in this paper. It has been shown here that the problem reduces to an unconstrained quadratic 0-1 programming problem. Using a maximum neural network, along with mutation capability of genetic adaptive systems, the reduced problem has been solved. Empirical studies have been done by applying the method on stock flow graphs to identify the collusion set, which contains a group of traders performing unfair trading among themselves. Additionally, it has been applied on a gene co-expression network to find out significant gene modules and on some benchmark graphs.

Network-Based Study Reveals Potential Infection Pathways of Hepatitis-C Leading to Various Diseases

“…Before describing the proposed methods, here we first define a few terms to help subsequent discussions 21 , 22 .…”

Finding Maximum Clique in Stochastic Graphs Using Distributed Learning Automata

“…Pullan et al 37 proposed a cooperating local search as a parallelized hyper heuristic for MC problem and resented an application to desktop multi core computers. Bhattacharyya et al 38 addressed the fuzzy version of maximum clique problem in fuzzy graph and solve it with neural networks. MC problem has many practical applications in wide spread of areas such as machine vision, 39 online shopping recommendation, 40 data clustering, 41 timetabling 42 and wireless sensor networks.…”