Deterministic weighted scale-free small-world networks

Abstract

We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the coevolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks, we suggest a recursive algorithm to generate the network, which restricts the traffic fluctuations on it effectively during the evolutionary process. we provide a relatively complete view of topological structure and weight dynamics characteristics of the networks: weight and strength distribution; degree correlations; average clustering coefficient and degree-cluster correlations; as well as the diameter.

Small-World Propensity and Weighted Brain Networks

“…However, the generalizability of these methods has been hampered by the lack of a theoretical model to construct weighted small-world networks and to study the transition in and out of the small-world regime. (Although, see Zhang et al 47 for a method to generate weighted scale-free small-world networks.) Our work directly fills this gap in the field of neuroscience, allowing the creation of weighted small-world networks with varied degrees of SWP that can be used to compare and contrast network behavior and dynamics throughout the small-world regime.…”

Weighted Fractal Networks

“…In recent years we observed an increasing number of papers were authors proposed models of deterministic (pseudo) fractal networks [30][31][32][33][34][35][36][37][38][39] exhibiting scale-free and hierarchical structures. In a limited number of cases, models presented also a stochastic component [40][41][42][43].…”

Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs

“…Our solutions can also be easily extended to several weighted or delayed models, such as weighted scale-free small-world graphs [33] and delayed pseudofractal graphs [34].…”