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We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with 1…
Zero-range processes, in which particles hop between sites on a lattice, are closely related to equilibrium networks, in which rewiring of links take place. Both systems exhibit a condensation transition for appropriate choices of the…
An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the…
When a link is occupied to restrict the growth of large clusters using the size information of a finite number of finite clusters, so-called local information, an abrupt but continuous transition is exhibited. We report here that a hybrid…
We investigate the dynamics of an epidemiological susceptible-infected-susceptible (SIS) model on an adaptive network. This model combines epidemic spreading (dynamics on the network) with rewiring of network connections (topological…
In adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of…
Complex networks often exhibit co-evolutionary dynamics, meaning that the network topology and the state of nodes or links are coupled, affecting each other in overlapping time scales. We focus on the co-evolutionary dynamics of online…
We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological…
We investigate the role of connection density in an adaptive network model of chaotic units that dynamically rewire based on their internal states and local coherence. By systematically varying the network's connectivity density, we uncover…
We investigate a nonlinear version of coevolving voter models, in which node states and network structure update as a coupled stochastic dynamical process. Most prior work on coevolving voter models has focused on linear update rules with…
Social fragmentation caused by widening differences among constituents has recently become a highly relevant issue to our modern society. Theoretical models of social fragmentation using the adaptive network framework have been proposed and…
Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch…
We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating…
We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework, we provide a detailed analysis of the stationary…
We present a new model of the evolutionary dynamics and the growth of on-line social networks. The model emulates people's strategies for acquiring information in social networks, emphasising the local subjective view of an individual and…
We study the contact process on layered networks in which each layer is unidirectionally coupled to the next layer. Each layer has elements sitting on i) Erd{\"o}s-R{\'e}yni network, ii) a $d$-dimensional lattice. The layer at the top which…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…