Geography in a Scale-Free Network Model

TL;DR

This paper introduces a scale-free network model with geographic structure, showing it has a nonzero percolation threshold, which impacts disease spread and immunization strategies.

Contribution

It presents a lattice-based scale-free network model with geography, demonstrating a nonzero percolation threshold unlike traditional models.

Findings

Nonzero percolation threshold for alpha>2

Geography influences disease spread thresholds

Small-world links do not eliminate thresholds

Abstract

We offer an example of an network model with a power law degree distribution, P(k) ~ k^{-alpha}, for nodes but which nevertheless has a well-defined geography and a nonzero threshold percolation probability for alpha>2, the range of real-world contact networks. This is different from the p_c=0 for alpha<3 results for well-mixed scale-free networks. In our lattice-based scale-free network, individuals link to nearby neighbors on a lattice. Even considerable additional small-world links do not change our conclusion of nonzero thresholds. When applied to disease propagation, these results suggest that random immunization may be more successful in controlling human epidemics than previously suggested if there is geographical clustering.