Impact on the topology of power-law networks from anisotropic and localized access to information

Abstract

Preferential attachment is a popular candidate mechanism for generating power-law networks. However, incoming nodes require global information about existing nodes' connectivities before connecting, whereas such information access within real-world networks may be only anisotropic and localized. Here we investigate how anisotropic and localized information access affect the resulting network topology. We find that anisotropy impacts the power-law exponent significantly but has only a weak influence on the clustering coefficient. By contrast, we find that locality influences the clustering coefficient significantly but has only weak influence on the power-law exponent. We show that this generalized network-generation mechanism is capable of generating networks with a broad range of power-law exponents and clustering coefficients. Our findings contribute to the debate about why so many real-world networks have degree distributions that crudely resemble power laws, even if this resemblance doesn't survive strict statistical testing procedures.