Distance closures on complex networks

Distance closures on complex networks

To expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs. Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties. For instance, the All Pairs Shortest Paths (APSP) problem, based on the Dijkstra algorithm, is equivalent to a metric ...

Graph distance for complex networks

Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in th...

Distance-sum heterogeneity in graphs and complex networks

Distance entropy cartography characterises centrality in complex networks

We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated for a variety of synthetic network models. By coupling distance entropy information with closeness centrality, we introduce a network cartography which allow...

Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance

Thorsten Emmerich,1 Armin Bunde,1 Shlomo Havlin,2 Guanliang Li,3 and Daqing Li4 1Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany 2Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel 3Center for Polymer Studies, Department of Physics, Boston University, Boston, Massachusetts 02215, USA 4School of Reliability and Systems Engineering, Bei...