Comfortability of a Team in Social Networks

TL;DR

This paper introduces the new social network analysis index 'comfortability', defines core comfortable teams using graph theory, proves the problem's NP-Completeness, and offers polynomial-time approximation algorithms with performance guarantees.

Contribution

It defines the novel 'comfortability' index, proves the NP-Completeness of forming core comfortable teams, and provides efficient approximation algorithms with performance bounds.

Findings

NP-Completeness of core comfortable team formation

Polynomial-time approximation algorithms with O(ln Δ) ratio

Algorithms perform well on scale-free networks

Abstract

There are many indexes (measures or metrics) in Social Network Analysis (SNA), like density, cohesion, etc. We have defined a new SNA index called "comfortability". In this paper, core comfortable team of a social network is defined based on graph theoretic concepts and some of their structural properties are analyzed. Comfortability is one of the important attributes (characteristics) for a successful team work. So, it is necessary to find a comfortable and successful team in any given social network. It is proved that forming core comfortable team in any network is NP-Complete using the concepts of domination in graph theory. Next, we give two polynomial-time approximation algorithms for finding such a core comfortable team in any given network with performance ratio O(ln \Delta), where \Delta is the maximum degree of a given network (graph). The time complexity of the algorithm is proved to be O(n^{3}), where n is the number of persons (vertices) in the network (graph). It is also proved that the algorithms give good results in scale-free networks.