Drawing Large Graphs by Multilevel Maxent-Stress Optimization

TL;DR

This paper introduces a multilevel, parallel algorithm for large graph visualization that efficiently optimizes a combined stress-entropy metric, significantly outperforming previous methods in speed while maintaining quality.

Contribution

It presents a novel multilevel, parallel optimization approach for graph drawing based on maxent-stress, avoiding traditional linear solvers and enabling faster computation.

Findings

30x faster than previous sequential maxent-stress optimizer

Maintains comparable layout quality

Effective for dynamic graph visualization

Abstract

Drawing large graphs appropriately is an important step for the visual analysis of data from real-world networks. Here we present a novel multilevel algorithm to compute a graph layout with respect to a recently proposed metric that combines layout stress and entropy. As opposed to previous work, we do not solve the linear systems of the maxent-stress metric with a typical numerical solver. Instead we use a simple local iterative scheme within a multilevel approach. To accelerate local optimization, we approximate long-range forces and use shared-memory parallelism. Our experiments validate the high potential of our approach, which is particularly appealing for dynamic graphs. In comparison to the previously best maxent-stress optimizer, which is sequential, our parallel implementation is on average 30 times faster already for static graphs (and still faster if executed on one thread) while producing a comparable solution quality.