Distributing information in small-world networks: four social cases of the process of contagion in Spain

Abstract

This case study is part of a research project based in Spain between 2011 and 2014 on the social institutions and affective processes involved in what is normally referred to as social movement. Our purpose is to study how information circulates in small-world networks in which the dynamics are modeled with a stochastic version of Greenberg–Hasting’s excitable model. This is a three-state model in which a node can be in an excited, passive, or susceptible state. Only in the susceptible state does a node interact with its neighbors in the small-world network, and its interaction depends on the probability of contagion. We introduce an infection probability, which is the only parameter in our implementation of Greenberg–Hasting’s model. The small-world network is characterized by a mean connectivity parameter and by a disorder parameter.

The resulting dynamics are characterized by the average activity in the network. We have found transitions from inactive to active collective regimes, and we can induce this transition by varying. We search for different dynamics within small-world networks of citizens’ organizations by going through the following steps: identifying alliance patterns; looking for robust small-world attributes and how they are constructed; and interpreting the three modes of our model.