Simple Bundles of Complex Networks

Abstract: Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree, shortest paths, and modularity. In the present work, we develop an approach aimed at identifying and characterizing simple bundles of interconnections between pairs of nodes (source and destination) in complex networks. More specifically, simple bundles can be understood as corresponding to the bundle of paths obtained while traveling through successive neighborhoods after departing from a given source node. Because no node appears more than once along a given bundle, these structures have been said to be simple, in analogy to the concept of a simple path. In addition to describing simple bundles and providing a possible methodology for their identification, we also consider how their respective effective width can be estimated in terms of diffusion flow and exponential entropy of transition probabilities. The potential of the concepts and methods described in this work is then illustrated respectively to the characterization and analysis of model-theoretic networks, with several interesting results.