[eng] 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, contagion 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 BarabasiAlbert-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.