Information processing in homophilic and heterophilic social networks: simple vs. complex contagion

Complex networks are the skeleton upon which many social interactions occur. It is well known that the structure of the network strongly influences the dynamics on it. In this Master’s thesis, one particular class of dynamical processes will be studied; namely, conta- gion processes. These processes share many similarities with disease spreading through networks, so many mathematical tools developed for the latter can be applied to the former. This Master thesis will focus on the effects that homophily (the tendency of nodes to connect with other nodes similar to them) and heterophily (the tendency of nodes to connect with others different from them) has on contagion processes. To study this, so-called Barabasi- Albert-homophily networks (BAh networks) will be simulated and compared to random and scale-free networks. As opposed to Erdos-Renyi and Barabasi-Albert networks, in BAh networks, two classes of nodes are present and an homophily parameter h determines the probability of homophilic and heterophilic interactions. An important point of this work will be to determine if and how the novel structural properties of BAh networks affect the contagion process and its transition points.
On the other hand, it is known that the diffusion of innovations, although similar to epidemics, is not governed by the same rules. Thus, we will compare the predictions of the so-called simple contagion (a framework often used in modelling disease spreading) with the ones of complex contagion (a different class of models more suitable to treat social contagion processes). The influence of the target node will be shown to be different depending on the model: the target’s nature is relevant for simple contagion but not for complex contagion. Furthermore, the critical values of the control parameters will depend on the homophily parameter, indicating that homophily and heterophily can change the impact of the contagion process.
Finally, we study a combined model of simple and complex contagion. This ”hybrid contagion” will exhibit novel behaviours such as contagion at the maximum value of the threshold parameter or asymmetrical propagation of the information. Additionally, the transition between a phase with negligible contagion and a phase with no contagion will show a more complex behaviour, with a suspected double transition.