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Modularity Q is an important function for identifying community structure in complex networks. In this paper, we prove that the modularity maximization problem is equivalent to a nonconvex quadratic programming problem. This result provide us a simple way to improve the efficiency of heuristic algorithms for maximizing modularity Q. Many numerical results demonstrate that it is very effective.
We investigate the impact of community structure on information diffusion with the linear threshold model. Our results demonstrate that modular structure may have counter-intuitive effects on information diffusion when social reinforcement is present
Let P_G(q) denote the number of proper q-colorings of a graph G. This function, called the chromatic polynomial of G, was introduced by Birkhoff in 1912, who sought to attack the famous four-color problem by minimizing P_G(4) over all planar graphs G
Recently, many researchers have studied efficiently gathering data in wireless sensor networks to minimize the total energy consumption when a fixed number of data are allowed to be aggregated into one packet. However, minimizing the total energy con
The rapid diffusion of information and the adoption of social behaviors are of critical importance in situations as diverse as collective actions, pandemic prevention, or advertising and marketing. Although the dynamics of large cascades have been ex
The problem of maximizing a non-negative submodular function was introduced by Feige, Mirrokni, and Vondrak [FOCS07] who provided a deterministic local-search based algorithm that guarantees an approximation ratio of $frac 1 3$, as well as a randomiz