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As social networks grow, they become more and more complex, and analyzing them becomes complicated. One way to reduce this complexity is to divide the network into subnets, which are also called communities. Dividing social networks into desirable communities can help analysts and experts to understand the behavior and function of the networks. Community detection in networks is a challenging topic in network science and various methods have been proposed for that. Modularity maximization is one of the state-of-the-art methods suggested for community detection. Modularity maximization is an NP-hard problem meaning that no polynomial-time algorithm exists that could solve the problem optimally unless P=NP. A group of approaches that could solve such problems is approximate algorithms. Identifying the influential nodes has many important applications in social networks. This technique could also be used in community detection. To maximize modularity, in this paper, we propose approximate algorithms based on identifying the influential nodes and their influence domain. We used the concept of scale-free networks to prove the approximate factor. Experiments on real-world networks show that the proposed algorithm can compete with the state-of-the-art methods of community detection algorithms. [ABSTRACT FROM AUTHOR]

Hub location problem is further used in transportation and telecommunication networks (airlines, post delivery services, etc.) so origin-destination pairs, receive or send commodities via special facilities called Hub. Hub median problem with multiple allocation is an NP-hard problem which includes both locating hub facilities and allocating non-hub nodes to hubs as minimizes total transportation and location costs. In this paper, the hub median problem is considered in an environment which network flow varies during the time periods and the capacities of hubs and arcs are unlimited. Also opening and closing hubs in different periods of planning horizon are permitted. The model and the proposed algorithm for this problem were considered to Iran airlines network using real passenger flows data. Computational results state that the dynamic network compared with static model has lower cost and whatever the number of time periods in dynamic case increases, the cost will be reduced as well. [ABSTRACT FROM AUTHOR]