An Efficient Module Detection Algorithm for Large-Scale Complex Networks

The module detection problem for large-scale complex networks has attracted attention to understand the interactions of nodes as well as the underlying network property. Since the concept of modularity is created to quantify the module property in a network, numerous efforts have been focused on solving the module detection problem via maximizing the modularity of a network. However, due to the NP-complete nature of the modularity maximization problem, existing algorithms, ranging from heuristic methods to greedy algorithms, are computationally demanding. Accordingly, we first reformulate the network module detection problem as Mixed Integer Quadratic Programming (MIQP) problem. Subsequently, an efficient and memory-saving algorithm based on inexact Augmented Lagrangian Method (ALM) is developed to solve MIQPs. By exploiting the special structure and sparsity of the problem settings, simplified and closed form solutions are obtained for subproblems of the inexact ALM. Simulation results from the proposed algorithm and the greedy algorithm using real-world databases are presented.

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