Knitted Complex Networks

TL;DR

This paper introduces two new classes of complex networks based on paths, explores their properties, and compares them to traditional models, providing insights into their structure and potential real-world applications.

Contribution

The work proposes and characterizes two novel path-based network models, expanding the understanding of complex network structures beyond traditional models.

Findings

PA networks derived from star-path transformations of BA networks.

PN networks constructed by progressive, non-repetitive paths covering all nodes.

Distinct structural properties confirmed through comprehensive measurements.

Abstract

To a considerable extent, the continuing importance and popularity of complex networks as models of real-world structures has been motivated by scale free degree distributions as well as the respectively implied hubs. Being related to sequential connections of edges in networks, paths represent another important, dual pattern of connectivity (or motif) in complex networks (e.g., paths are related to important concepts such as betweeness centrality). The present work proposes a new supercategory of complex networks which are organized and/or constructed in terms of paths. Two specific network classes are proposed and characterized: (i) PA networks, obtained by star-path transforming Barabasi-Albert networks; and (ii) PN networks, built by performing progressive paths involving all nodes without repetition. Such new networks are important not only from their potential to provide theoretical insights, but also as putative models of real-world structures. The connectivity structure of these two models is investigated comparatively to four traditional complex networks models (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz and a geographical model). A series of interesting results are described, including the corroboration of the distinct nature of the two proposed models and the importance of considering a comprehensive set of measurements and multivariated statistical methods for the characterization of complex networks.