Most social networks exhibit the meso-scale feature of modular organization, i.e., occurrence of communities whose members are more likely to be connected to each other than to members of other communities. In this paper, we look at how the existence of modules in the contact structure of a population affects its adoption of an innovation that is characterized by a given perceived advantage. For this we consider both theoretical models of modular networks as well as the empirical social network of a village in Karnataka. We first use a network generalization of the well-known Bass model of diffusion, which is a variant of the SI compartmental model of contagion propagation, on the empirical network and on an ensemble of degree-preserved randomized surrogates. By comparing the dynamics of the diffusion process in these networks, we see that the modular organization reduces the speed of adoption in the population. However, as there are limitations of the diffusion model, we have also considered an alternative dynamical process based on spin-spin interaction that is inspired by statistical physics. Here, individuals try to coordinate their action with that of neighbors on the contact network, while having randomly distributed thresholds (that measures their inrinsic resistance to adoption). By varying the external field, which is a measure of the perceived advantage of the innovation we observe transitions of the population to a state of complete adoption. While the model network with community organization shows that the occurrence of modularity increases the critical value of perceived advantage at which the transition happens, surprisingly we see that in the empirical network the process of adoption can occur faster than in the corresponding degree-preserved randomized surrogate. We show that by reducing the inter-modular connectivity of the empirical network, the process can indeed be made slower than the corresponding randomized networks. Our results underline th- critical importance of modular organization in social networks in affecting the process of adoption of innovation in society.
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