A Viral Spreading Model in Signed Networks

In a business network, a company may be encouraged to utilise a new technique when either its cooperators or its competitors have made their adoption. Nevertheless, its willingness can be reduced as more of its competitors start applying the new technique. Inspired by the this scenario, in this thesis we proposed a viral spreading model in signed networks, in which each link is allocated with a positive or negative sign, representing, e.g. the cooperative or competitive relation between two companies. We introduce a dynamic infection rate to capture the influence of negative links into viral spreadings and explore the performance of our proposed model with respect to the following influential factors: the relative infection rate of negative links with respect to positive links (relative negative-link infection rate), the correlation between positive and negative degrees, and the degree distributions of the positive and negative links respectively. To provide analytical explanations, we develop an Individual-Based Mean Field Approximation (IBMFA) method. We show that IBMFA is a feasible theoretical tool that can well approximate the observations in Monte-Carol simulations. Our results show that, contrary to our intuition, when positive degree and negative degree of nodes are less correlated in scale-free networks, a larger relative negative-link infection rate does not always results in more nodes being infected. In addition, compared to networks with only positive links, viral propagation via negative links can lead to a higher fraction of infected nodes at small infection rate; whereas the overall spreading starts being suppressed in signed networks as the infection rate becomes larger than a certain value. We find that this certain infection rate, at which signed and unsigned networks share the same fraction of infected nodes, is approximately linearly correlated to the relative negative-link infection rate. Corresponding to the scenario mentioned at the beginning, our findings indicate that: (1) Adopting a new technique at a high rate from competitors does not always lead to a larger percentage of adoption among companies; (2) Compared to networks with only cooperative relations, the competitive relations between companies may sometimes facilitate a higher percentage of adoption, especially when every company accepts a new technique at a low rate.