An algorithm for drawing general undirected graphs
Information Processing Letters
Graph drawing by force-directed placement
Software—Practice & Experience
Drawing graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Graph Visualization and Navigation in Information Visualization: A Survey
IEEE Transactions on Visualization and Computer Graphics
GD '95 Proceedings of the Symposium on Graph Drawing
A Bayesian Paradigm for Dynamic Graph Layout
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Visual unrolling of network evolution and the analysis of dynamic discourse
Information Visualization
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
IEEE Transactions on Visualization and Computer Graphics
Colibri: fast mining of large static and dynamic graphs
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Journal of the American Society for Information Science and Technology
On evolutionary spectral clustering
ACM Transactions on Knowledge Discovery from Data (TKDD)
Drawing graphs by eigenvectors: theory and practice
Computers & Mathematics with Applications
Supervised multidimensional scaling for visualization, classification, and bipartite ranking
Computational Statistics & Data Analysis
Graph drawing by stress majorization
GD'04 Proceedings of the 12th international conference on Graph Drawing
A quantitative comparison of stress-minimization approaches for offline dynamic graph drawing
GD'11 Proceedings of the 19th international conference on Graph Drawing
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Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual representation of the network structure at each time step, the sequence should preserve the mental map between layouts of consecutive time steps to allow a human to interpret the temporal evolution of the network. In this paper, we propose a framework for dynamic network visualization in the on-line setting where only present and past graph snapshots are available to create the present layout. The proposed framework creates regularized graph layouts by augmenting the cost function of a static graph layout algorithm with a grouping penalty, which discourages nodes from deviating too far from other nodes belonging to the same group, and a temporal penalty, which discourages large node movements between consecutive time steps. The penalties increase the stability of the layout sequence, thus preserving the mental map. We introduce two dynamic layout algorithms within the proposed framework, namely dynamic multidimensional scaling and dynamic graph Laplacian layout. We apply these algorithms on several data sets to illustrate the importance of both grouping and temporal regularization for producing interpretable visualizations of dynamic networks.