Efficient algorithms for assortative edge switch in large labeled networks

An assortative edge switch is an operation on a labeled network, where two edges are randomly selected and the end vertices are swapped with each other if the labels of the end vertices of the edges remain invariant. Assortative edge switch has important applications in studying the mixing pattern and dynamic behavior of social networks, modeling and analyzing dynamic networks, and generating random networks. In this paper, we present an efficient sequential algorithm and a distributed-memory parallel algorithm for assortative edge switch. To our knowledge, they are the first efficient algorithms for this problem. The dependencies among successive assortative edge switch operations, the requirement of maintaining the assortative coefficient invariant, keeping the network simple, and balancing the computation loads among the processors pose significant challenges in designing a parallel algorithm. Our parallel algorithm achieves a speedup of 68 -- 772 with 1024 processors for a wide variety of networks.