Embedding Graphs under Centrality Constraints for Network Visualization

TL;DR

This paper introduces two novel graph embedding methods that incorporate centrality constraints to improve the visualization of network structures, especially for large graphs, balancing aesthetic and structural fidelity.

Contribution

It proposes two new embedding algorithms that integrate node centrality into graph visualization, with guaranteed convergence and reduced edge crossings.

Findings

Both methods effectively visualize large networks with thousands of nodes.

The approaches preserve node hierarchy and structural properties.

Experimental results show improved clarity and interpretability of network visualizations.

Abstract

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates two graph embedding approaches with centrality considerations to comply with node hierarchy. The problem is formulated first as one of constrained multi-dimensional scaling (MDS), and it is solved via block coordinate descent iterations with successive approximations and guaranteed convergence to a KKT point. In addition, a regularization term enforcing graph smoothness is incorporated with the goal of reducing edge crossings. A second approach leverages the locally-linear embedding (LLE) algorithm which assumes that the graph encodes data sampled from a low-dimensional manifold. Closed-form solutions to the resulting centrality-constrained optimization problems are determined yielding meaningful embeddings. Experimental results demonstrate the efficacy of both approaches, especially for visualizing large networks on the order of thousands of nodes.