Competing contagion processes: Complex contagion triggered by simple contagion

Empirical evidence reveals that contagion processes often occur with competition of simple and complex contagion, meaning that while some agents follow simple contagion, others follow complex contagion. Simple contagion refers to spreading processes induced by a single exposure to a contagious entity while complex contagion demands multiple exposures for transmission. Inspired by this observation, we propose a model of contagion dynamics with a transmission probability that initiates a process of complex contagion. With this probability nodes subject to simple contagion get adopted and trigger a process of complex contagion. We obtain a phase diagram in the parameter space of the transmission probability and the fraction of nodes subject to complex contagion. Our contagion model exhibits a rich variety of phase transitions such as continuous, discontinuous, and hybrid phase transitions, criticality, tricriticality, and double transitions. In particular, we find a double phase transition showing a continuous transition and a following discontinuous transition in the density of adopted nodes with respect to the transmission probability. We show that the double transition occurs with an intermediate phase in which nodes following simple contagion become adopted but nodes with complex contagion remain susceptible.Comment: 9 pages, 4 figure

Competition and dual users in complex contagion processes

We study the competition of two spreading entities, for example innovations, in complex contagion processes in complex networks. We develop an analytical framework and examine the role of dual users, i.e. agents using both technologies. Searching for the spreading transition of the new innovation and the extinction transition of a preexisting one, we identify different phases depending on network mean degree, prevalence of preexisting technology, and thresholds of the contagion process. Competition with the preexisting technology effectively suppresses the spread of the new innovation, but it also allows for phases of coexistence. The existence of dual users largely modifies the transient dynamics creating new phases that promote the spread of a new innovation and extinction of a preexisting one. It enables the global spread of the new innovation even if the old one has the first-mover advantage.Comment: 9 pages, 4 figure

Multilayer coevolution dynamics of the nonlinear voter model

We study a coevolving nonlinear voter model on a two-layer network. Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer. The plasticity parameter p measures the relative time scale of the evolution of the states of the nodes and the evolution of the network by link rewiring. Nonlinearity of the interactions is taken into account through a parameter q that describes the nonlinear effect of local majorities, being q = 1 the marginal situation of the ordinary voter model. Finally the connection between the two layers is measured by a degree of multiplexing `. In terms of these three parameters, p, q and ` we find a rich phase diagram with different phases and transitions. When the two layers have the same plasticity p, the fragmentation transition observed in a single layer is shifted to larger values of p plasticity, so that multiplexing avoids fragmentation. Different plasticities for the two layers lead to new phases that do not exist in a coevolving nonlinear voter model in a single layer, namely an asymmetric fragmented phase for q > 1 and an active shattered phase for q 1, we can find two different transitions by increasing the plasticity parameter, a first absorbing transition with no fragmentation and a subsequent fragmentation transition

Towards real-world complexity: an introduction to multiplex networks

Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system's structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.Comment: 20 pages, 10 figure

Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models

We survey the coevolutionary dynamics of network topology and group interactions in opinion formation, grounded on a coevolving nonlinear voter model. The coevolving nonlinear voter model incorporates two mechanisms: group interactions implemented through nonlinearity in the voter model and network plasticity demonstrated as the rewiring of links to remove connections between nodes in different opinions. We show that the role of group interactions, implemented by the nonlinearity can significantly impact both the dynamical outcomes of nodes' state and the network topology. Additionally, we review several variants of the coevolving nonlinear voter model considering different rewiring mechanisms, noise of flipping nodes' state, and multilayer structures. We portray the various aspects of the coevolving nonlinear voter model as an example of network coevolution driven by group interactions, and finally, present the implications and potential directions for future research.Comment: 8 pages, 2 figure

Finding influential spreaders from human activity beyond network location

Most centralities proposed for identifying influential spreaders on social networks to either spread a message or to stop an epidemic require the full topological information of the network on which spreading occurs. In practice, however, collecting all connections between agents in social networks can be hardly achieved. As a result, such metrics could be difficult to apply to real social networks. Consequently, a new approach for identifying influential people without the explicit network information is demanded in order to provide an efficient immunization or spreading strategy, in a practical sense. In this study, we seek a possible way for finding influential spreaders by using the social mechanisms of how social connections are formed in real networks. We find that a reliable immunization scheme can be achieved by asking people how they interact with each other. From these surveys we find that the probabilistic tendency to connect to a hub has the strongest predictive power for influential spreaders among tested social mechanisms. Our observation also suggests that people who connect different communities is more likely to be an influential spreader when a network has a strong modular structure. Our finding implies that not only the effect of network location but also the behavior of individuals is important to design optimal immunization or spreading schemes