Centrality-constrained graph embedding

TL;DR

This paper introduces a centrality-aware graph embedding method that emphasizes node hierarchy and structural properties, suitable for large graphs, by formulating a constrained MDS problem solved with block coordinate descent.

Contribution

It proposes a novel graph embedding approach incorporating centrality constraints and smoothness regularization, with guaranteed convergence and scalability to large graphs.

Findings

Algorithm converges reliably.

Efficient embedding of large graphs.

Reduces edge crossings in 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 a graph embedding approach with centrality considerations to comply with node hierarchy. The problem is formulated 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. Experimental results demonstrate that the algorithm converges, and can be used to efficiently embed large graphs on the order of thousands of nodes.