ZMDS: Visualizing Structural Entropy in Queried Network Sub-Graphs

The large magnitudes of information in many scale free network datasets makes them difficult to analyze, plot, and visualize. Sacrifices often must be made on the plot’s representational veracity or representational completeness. This paper discusses a method for exploring query based sub-graphs of a larger network using a method based on multidimensional scaling. Since the basis for the network data is a query, certain characteristics of node connections can be compared across the sub-graph and the original network. In this method, node weight data can be represented as a function of its global and local characteristics, exposing the negative entropy the node has in the given neighborhood. According to this scheme, a small sub graph of a larger network structure is analyzed as a modified and weighted Laplacian matrix. A z-score weighting scheme is used to modify each node’s connection strengths in the neighborhood against its total number of connections in the original network, and the dimensionality of these weighted connection strengths is reduced to create a low dimensional embedding suitable for visualization and analysis. The motivation, methods, and example results are all discussed, and potential application methods are offered.