2014/08/22 by H. Francis Song, Hao Song, Xiao-Jing Wang +1 · 1 citation
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn #cs.SI #physics.soc-ph
paper · pdf · doi:10.1103/physreve.90.062801
published as Phys. Rev. E 90, 062801 (2014) · Added a note about G(n,m) vs. G(n,p) ER networks. Thanks to B. Sonnenschein for pointing this out
arxiv created 2014/08/22 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Small-world networks-complex networks characterized by a combination of high clustering and short path lengths-are widely studied using the paradigmatic model of Watts and Strogatz (WS). Although the WS model is already quite minimal and intuitive, we describe an alternative formulation of the WS model in terms of a distance-dependent probability of connection that further simplifies, both practically and theoretically, the generation of directed and undirected WS-type small-world networks. In addition to highlighting an essential feature of the WS model that has previously been overlooked, namely the equivalence to a simple distance-dependent model, this alternative formulation makes it possible to derive exact expressions for quantities such as the degree and motif distributions and global clustering coefficient for both directed and undirected networks in terms of model parameters.