Algebraic approach to small-world network models

Michael Rudolph (1, 2) , Lyle Muller (1, 2)

1 UNIC - Unité de Neurosciences Information et Complexité [Gif sur Yvette]
2 INAF - Institut de Neurobiologie Alfred Fessard

We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.

Domaines: Neurobiologie; Psychologie et comportements; Sciences cognitives

Michael Rudolph, Lyle Muller. Algebraic approach to small-world network models. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89 (1), pp.012812. ⟨10.1103/PhysRevE.89.012812⟩. ⟨hal-02425372⟩