A scalable graph generation algorithm to sample over a given shell distribution

Graphs are commonly used to model the relationships between various entities. These graphs can be enormously large and thus, scalable graph analysis has been the subject of many research efforts. To enable scalable analytics, many researchers have focused on generating realistic graphs that support controlled experiments for understanding how algorithms perform under changing graph features. Significant progress has been made on scalable graph generation which preserve some important graph properties (e.g., degree distribution, clustering coefficients). In this paper, we study how to sample a graph from the space of graphs with a given shell distribution. Shell distribution is related to the k-core, which is the largest subgraph where each vertex is connected to at least k other vertices. A k-shell is the subset of vertices that are in k-core but not (k + 1)-core, and the shell distribution comprises the sizes of these shells. Core decompositions are widely used to extract information from graphs and to assist other computations. We present a scalable shared and distributed memory graph generator that, given a shell decomposition, generates a random graph that conforms to it. Our extensive experimental results show the efficiency and scalability of our methods. Our algorithm generates 233 vertices and 237 edges in less than 50 seconds on 384 cores.