Related papers: Voter model on heterogeneous directed networks
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…
Collective decision making processes lie at the heart of many social, political and economic challenges. The classical voter model is a well-established conceptual model to study such processes. In this work, we define a new form of…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are…
Approximate master equations are derived for the two-state $q$-voter model with independence on signed random graphs, with negative and positive weights of links corresponding to antagonistic and reinforcing interactions, respectively.…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
In this paper, we provide a theoretical analysis for nonlinear discontinuous consensus protocols in networks of multiagents over weighted directed graphs. By integrating the analytic tools from nonsmooth stability analysis and graph theory,…
Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in…
We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of…
In majority dynamics, agents located at the vertices of an undirected simple graph update their binary opinions synchronously by adopting those of the majority of their neighbors. On infinite unimodular transitive graphs (e.g., Cayley…
In this paper, we study consensus problem in multi-agent system with directed topology by event-triggered feedback control. That is, at each agent, the diffusion coupling feedbacks are based on the information from its latest observations…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
In this work we present novel results to the problem of the Hegselmann-Krause dynamics in networks obtained by an extensive study of the behavior of the standard order parameter sensitive to the onset of consensus: the normalized size of…
In the latent voter model, which models the spread of a technology through a social network, individuals who have just changed their choice have a latent period, which is exponential with rate $\lambda$, during which they will not buy a new…
Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated…
We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is…
We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter $k \ge 0$, in addition to its $+$ or $-$ opinion state. The evolution of the…