Studies Of An Issue On Community Extraction For Social Networks

According to the community’s intuitive definition, its strength relies on links between its members and links to the rest of the network, not on links between nonmembers; yet the density of the outside world can also indirectly and positively impact the obtainment of the tightest community, which should not be ignored. Based on the community extraction criterion proposed by Zhao et al (2011), we propose a slightly distinct framework that additionally considers the density of the remainder of the network when extracting the tightest community at a time. Taking that extra information of the outside world into consideration, our newly adjusted extraction criterion still perfectly holds the same properties as that by Zhao et al (2011). For the case of the stochastic block model, the asymptotic consistency of estimated node labels is established. Simulations and real data application show that our proposed newly adjusted criterion is not only mildly superior to the counterpart in Zhao et al (2011) in terms of positive predictive value (PPV) criterion, but capable of extracting the "tightest" community with slightly more power in some special cases.