Network Size Reduction Preserving Optimal Modularity and Clique Partition
|Článek ve sborníku
|Lecture Notes in Computer Science
|Fakulta / Pracoviště MU
|Network size reduction Clustering Community detection Modularity Clique partitioning problem Exact solution
|Graph clustering and community detection are significant and actively developing topics in network science. Uncovering community structure can provide essential information about the underlying system. In this work, we consider two closely related graph clustering problems. One is the clique partitioning problem, and the other is the maximization of partition quality function called modularity. We are interested in the exact solution. However, both problems are NP-hard. Thus the computational complexity of any existing algorithm makes it impossible to solve the problems exactly for the networks larger than several hundreds of nodes. That is why even a small reduction of network size can significantly improve the speed of finding the solution to these problems. We propose a new method for reducing the network size that preserves the optimal partition in terms of modularity score or the clique partitioning objective function. Furthermore, we prove that the optimal partition of the reduced network has the same quality as the optimal partition of the initial network. We also address the cases where a previously proposed method could provide incorrect results. Finally, we evaluate our method by finding the optimal partitions for two sets of networks. Our results show that the proposed method reduces the network size by 40% on average, decreasing the computation time by about 54%.