Portraits of Complex Networks

Abstract

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animations. Applications to graph theory are discussed, as are generalizations to weighted networks, real-world network similarity testing, and applicability to the graph isomorphism problem.

6 pages, 9 figures

References in corpus (11)

• Emergence of scaling in random networks
• Community structure in social and biological networks
• Assortative mixing in networks
• The large-scale organization of metabolic networks
• Random graphs with arbitrary degree distributions and their applications
• Classes of behavior of small-world networks
• Scaling and percolation in the small-world network model
• Organization of Growing Random Networks
• Fractal and Transfractal Recursive Scale-Free Nets
• Metric structure of random networks
• Generation of arbitrarily two-point correlated random networks

Cited by in corpus (11)

• An information-theoretic, all-scales approach to comparing networks
• A Framework for Creative-Visualization Opportunities Workshops
• Topology comparison of Twitter diffusion networks effectively reveals misleading information
• embComp: Visual Interactive Comparison of Vector Embeddings
• Self-affine Fractals Embedded in Spectra of Complex Networks
• War pact model of shrinking networks
• Implementation of exponential and parametrized algorithms in the AGAPE project
• Higher-order dissimilarity measures for hypergraph comparison
• The Infinity Mirror Test for Graph Models
• The Census-Stub Graph Invariant Descriptor
• Graffinity: Visualizing Connectivity In Large Graphs