Parallel Algorithm for Generating Massive Random Networks with a Given Sequence of Expected Degrees

Abstract—Random networks are widely used for modeling and analyzing complex processes. Many mathematical models for random networks have been proposed to capture the diversity of the real-world processes. Capturing the degree distribution is one of the most important aspects of these models. Many of the models can only produce random networks with predefined degree distribution. Chung–Lu model is a general random network model, which can produce networks with any arbitrary degree distribution. The complex systems we deal with are growing larger, and generating random networks with billions of nodes and edges or more has become a necessity. Generation of such massive networks requires efficient and parallel algorithms. In this paper, we present an MPI-based distributed memory parallel algorithm for generating massive random networks using Chung–Lu model with a given expected degree sequence. The main challenge in designing this parallel algorithm is balancing computational load among the processors. We study several load balancing schemes with rigorous theoretical and experimental analysis and present a novel parallel algorithm for load balancing. The proposed parallel algorithm for Chung–Lu model, coupled with the parallel load balancing algorithm, achieves a very good load balancing and scale very well to a large number of processors. It can generate massive networks with 250 billion edges in eight minutes using 1024 processors. Index Terms—massive networks, parallel algorithms, network generato