Diffusion of innovations in finite networks: Effects of heterogeneity, clustering, and bilingual option on the threshold in the contagion game model

Abstract

The contagion threshold for diffusion of innovations is defined and calculated in finite graphs (two-dimensional regular lattices, regular random networks (RRNs), and two kinds of scale-free networks (SFNs)) with and without the bilingual option. Without the bilingual option, degree inhomogeneity and clustering enhance the contagion threshold in non-regular networks except for those with an unrealistically small average degree. It is explained by the friendship paradox and detour effect. We found the general boundary of the cost that makes the bilingual option effective. With a low-cost bilingual option, among regular lattices, SFNs, and RRNs, the contagion threshold is largest in regular lattices and smallest in RRNs. The contagion threshold of regular random networks is almost the same as that of the regular trees, which is the minimum among regular networks. We show that the contagion threshold increases by clustering with a low-cost bilingual option.