Efficient Algorithm for Maximal Clique Size Evaluation

Ubaida Fatima,Saman Hina

doi:10.14569/ijacsa.2019.0100761

Abstract

A large dataset network is considered for computation of maximal clique size (MC). Additionally, its link with popular centrality metrics to decrease uncertainty and complexity and for finding influential points of any network has also been investigated. Previous studies focus on centrality metrics like degree centrality (DC), closeness centrality (CC), betweenness centrality (BC) and Eigenvector centrality (EVC) and compare them with maximal clique size however, in this study Katz centrality measure is also considered and shows a pretty robust relation with maximal clique size (MC). Secondly, maximal clique size (MC) algorithm is also revised for network analysis to avoid complexity in computation. Association between MC and five centrality metrics has been evaluated through recognized methods that are Pearson’s correlation coefficient (PCC), Spearman’s correlation coefficient (SCC) and Kendall’s correlation coefficient (KCC). The strong strength of association between them is seen through all three correlation coefficients measure.

Highlights

This Network analysis has become a crucial tool in studying the patterns involved in branched systems and graphs
The outcome of the Kendall‟s correlation coefficient (KCC) is given by equation (26) that arrows positive link between maximal clique size (MC) and degree centrality (DC) that is of amount 0.4
The complete work of this paper addressed an amount of modularity and use of improved method of maximal clique size (MC) in large network datasets

Summary

INTRODUCTION

This Network analysis has become a crucial tool in studying the patterns involved in branched systems and graphs. From its initial journey of solving bridges by Euler all the way back in 1735, network analysis and graph theory have greatly evolved and found applications in nearly every area of study. Since, these analyses involving the exchange of information/resources between „actors‟ (nodes) fields like big data science, health care, finance, computer science, social sciences, etc. In networks which are highly linked and have complex interactions, this maximum size of a clique can help identify whether a node in particular is of importance in a community or not based on its modular score.

LITERATURE REVIEW

NETWORK GRAPH AND IMPORTANT METRICS IN NETWORK ANALYSIS

AMAZON PRODUCT NETWORK DATA

CONCLUSION