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In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
The dynamics of competing opinions in social network play an important role in society, with many applications in diverse social contexts as consensus, elections, morality and so on. Here we study a model of interacting agents connected in…
Humans and other animals often follow the decisions made by others because these are indicative of the quality of possible choices, resulting in `social response rules': observed relationships between the probability that an agent will make…
Social movements, neurons in the brain or even industrial suppliers are best described by agents evolving on networks with basic interaction rules. In these real systems, the connectivity between agents corresponds to the a critical state…
In a social group its members are caled here agents. Any two agents from the group may interact. The interaction consists of the exchange of information and it costs some energy. There exist subgroups of interacting agents which are…
Many networks do not live in isolation but are strongly interacting, with profound consequences on their dynamics. Here, we consider the case of two interacting social networks and, in the context of a simple model, we address the case of…
The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and…
We introduce a probabilistic pairwise \emph{attraction--repulsion} model for opinion dynamics on multilayer social networks, in which agents hold layer-specific states and interact through random matchings that couple multiple, time-varying…
In this work we investigate how future actions are influenced by the previous ones, in the specific contexts of scientific collaborations and friendships on social networks. We are not interested in modeling the process of link formation…
This paper investigates causal influences between agents linked by a social graph and interacting over time. In particular, the work examines the dynamics of social learning models and distributed decision-making protocols, and derives…
An agent-based model is proposed for analyzing the dynamics that arise from interactions within social networks, analyzing the individual behavior of each profile. Said model considers a simplified construction of a social network while…
In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The…
The number of common friends (or connections) in a graph is a commonly used measure of proximity between two nodes. Such measures are used in link prediction algorithms and recommendation systems in large online social networks. We obtain…
Interactions between humans give rise to complex social networks that are characterized by heterogeneous degree distribution, weight-topology relation, overlapping community structure, and dynamics of links. Understanding such networks is a…
We study how the opinions of a group of individuals determine their spatial distribution and connectivity, through an agent-based model. The interaction between agents is described by a Potts-like Hamiltonian in which agents are allowed to…
Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social…
We consider a nonlinear dynamical system on a signed graph, which can be interpreted as a mathematical model of social networks in which the links can have both positive and negative connotations. In accordance with a concept from social…
Many socioeconomic phenomena, such as technology adoption, collaborative problem-solving, and content engagement, involve a collection of agents coordinating to take a common action, aligning their decisions to maximize their individual…