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Structural information content of networks: graph entropy based on local vertex functionals |
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| Authors: | Dehmer Matthias Emmert-Streib Frank |
| Affiliation: | aInstitute of Discrete Mathematics and Geometry, Vienna University of Technology, TU Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria bUniversity of Washington, Department of Biostatistics, 1705 NE Pacific St, Box 355065, Seattle, WA 98195, USA cUniversity of Washington, Department of Genome Sciences, 1705 NE Pacific St, Box 355065, Seattle, WA 98195, USA |
| Abstract: | In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating j-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties. |
| Keywords: | Structural information content Graph entropy Information theory Gene networks Chemical graph theory |
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