We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this state. The solutions for exponential and uniform...

The dynamics of opinion formation based on a majority rule model is studied in a network with the social hierarchical structure as one of its limits. The exit probability is found to change sensitively with the number of nodes in the system, but not with the parameter of homophyly characterizing...

There is much interest in studying evolutionary games in structured populations, in order to understand how cooperation emerges in communities of egoistic agents. In this paper, we consider a new mechanism for cooperation to survive on networks. Agents are designed to reproduce offspring in...

Social networks in communities, markets, and societies self-organise through the interactions of many individuals. In this paper we use a well-known mechanism of social interactions — the balance of sentiment in triadic relations — to describe the development of social networks. Our model...

The detection of community structure has been used to reveal the relationships between individual objects and their groupings in networks. This paper presents a mathematical programming approach to identify the optimal community structures in complex networks based on the maximisation of a...

We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperators and sustainable cooperation. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary...

Networks are commonly observed structures in complex systems with interacting and interdependent parts that self-organize. For nonlinearly growing networks, when the total number of connections increases faster than the total number of nodes, the network is said to accelerate. We propose a...