Embedding Graphs under Centrality Constraints for Network Visualization
This work addresses the need for network visualizations that prioritize structural properties over aesthetics, particularly for applications like travel-time maps, though it is incremental as it builds on existing embedding methods.
The paper tackled the problem of visualizing graphs under centrality constraints to reflect node hierarchy, proposing two embedding approaches based on constrained MDS and LLE, which effectively handle large networks with thousands of nodes.
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.