Related papers: Multistable binary decision making on networks
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
Two of the main factors shaping an individual's opinion are social coordination and personal preferences, or personal biases. To understand the role of those and that of the topology of the network of interactions, we study an extension of…
We study a model of network with clustering and desired node degree. The original purpose of the model was to describe optimal structures of scientific collaboration in the European Union. The model belongs to the family of exponential…
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…
Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…
Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a…
We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…
Compared to pure fluids, binary mixtures display a very diverse phase behavior, which depends sensitively on the parameters of the microscopic potential. Here we investigate the phase diagrams of simple model mixtures by use of a…
Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary…
In public opinion studies, the relationships between opinions on different topics are likely to shift based on the characteristics of the respondents. Thus, understanding the complexities of public opinion requires methods that can account…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective…
Signed networks capture the polarity of relationships between nodes, providing valuable insights into complex systems where both supportive and antagonistic interactions play a critical role in shaping the network dynamics. We propose a…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication…
Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness-of-fit for a given random graph model. In this paper we introduce goodness-of-fit tests for two classes of models.…
The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited…