Scaling of Directed Dynamical Small-World Networks with Random Responses

2003/12/07 by Chen-Ping Zhu, Shi-Jie Xiong, Shi‐Jie Xiong +5
Physics and Astronomy · Psychology · #Complex Network Analysis Techniques #Mental Health Research Topics #Opinion Dynamics and Social Influence #cond-mat.dis-nn

paper · pdf · doi:10.1103/physrevlett.92.218702

4 pages, 6 Figures

arxiv created 2003/12/07 · openalex publication_date 2004/05/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A dynamical model of small-world networks, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of sites to the input message are introduced to simulate real systems. The interplay of these ingredients results in the collective dynamical evolution of a spinlike variable S(t) of the whole network. The global average spreading length ⟨L⟩_s and average spreading time ⟨T⟩_s are found to scale as p^\ensuremath-\ensuremathαlnN with different exponents. Meanwhile, S(t) behaves in a duple scaling form for N\ensuremath≫N^*: S\ensuremath∼f(p^\ensuremath-\ensuremathβq^\ensuremathγ\stackrel\texttildelowt), where p and q are rewiring and external parameters, \ensuremathα, \ensuremathβ, and \ensuremathγ are scaling exponents, and f(\stackrel\texttildelowt) is a universal function. Possible applications of the model are discussed.

Citations

• Food-web structure and network theory: The role of connectance and size
• Relaxation properties of small-world networks
• Statistical mechanics of complex networks
• Evolution of networks
• The large-scale organization of metabolic networks
• Simple models of small-world networks with directed links