title: Structural information content of networks: graph entropy based on local vertex functionals.
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.
authors.affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, TU Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria. mdehmer@geometrie.tuwien.ac.at
authors.forename: Matthias
authors.initials: M
authors.lastname: Dehmer
authors.forename: Frank
authors.initials: F
authors.lastname: Emmert-Streib
mesh_terms: D000465:Algorithms; D002627:Chemistry, Physical / Q000379:methods* / Q000706:statistics & numerical data; D003196:Computer Graphics; D019277:Entropy; D008956:Models, Chemical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*