Comfortability of a Team in Social Networks

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 NPComplete 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∆), where ∆ is the maximum degree of a given network (graph). The time complexity of the algorithm is proved to be O(n), 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.