Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, $(SGD)^2$

TL;DR

This paper introduces $(SGD)^2$, a flexible, scalable graph drawing method that optimizes multiple readability criteria simultaneously using differentiable functions, improving layout quality for large graphs.

Contribution

The paper presents a novel stochastic gradient descent-based approach that can optimize multiple graph readability criteria concurrently, including new criteria not previously addressed in such frameworks.

Findings

Effectively balances multiple readability criteria in graph layouts.

Scales to large graphs with efficient runtime.

Provides both quantitative and qualitative validation.

Abstract

Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically optimize one such criterion, usually at the expense of others. We propose a layout approach, Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, $(SGD)^2$, that can handle multiple readability criteria. $(SGD)^2$ can optimize any criterion that can be described by a differentiable function. Our approach is flexible and can be used to optimize several criteria that have already been considered earlier (e.g., obtaining ideal edge lengths, stress, neighborhood preservation) as well as other criteria which have not yet been explicitly optimized in such fashion (e.g., node resolution, angular resolution, aspect ratio). The approach is scalable and can handle large graphs. A variation of the underlying approach can also be used to optimize many desirable properties in planar graphs, while maintaining planarity. Finally, we provide quantitative and qualitative evidence of the effectiveness of $(SGD)^2$: we analyze the interactions between criteria, measure the quality of layouts generated from $(SGD)^2$ as well as the runtime behavior, and analyze the impact of sample sizes. The source code is available on github and we also provide an interactive demo for small graphs.