Distributed computing of distance‐based graph invariants for analysis and visualization of complex networks

We present a new framework for analysis and visualization of complex networks based on structural information retrieved from their distance k-graphs and B-matrices. The construction of B-matrices for graphs with more than 1 million edges requires massive Breadth-First Search (BFS) computations and is facilitated using new software prepared for distributed environments. Our framework benefits from data parallelism inherent to all-pair shortest-path problem and extends Cassovary, an open-source in-memory graph processing engine, to enable multinode computation of distance k-graphs and related graph descriptors. We also introduce a new type of B-matrix, constructed using clustering coefficient vertex invariant, which can be generated with a computational effort comparable with the one required for a previously known degree B-matrix, while delivering an additional set of information about graph structure. Our approach enables efficient generation of expressive, multidimensional descriptors useful in graph embedding and graph mining tasks. The experiments showed that the new framework is scalable and for specific all-pair shortest-path task provides better performance than existing generic graph processing frameworks. We further present how the developed tools helped in the analysis and visualization of real-world graphs from Stanford Large Network Dataset Collection. Copyright (c) 2016 John Wiley & Sons, Ltd.