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A weighted directed network (WDN) is a directed graph in which each edge is associated to a unique value called weight. These networks are very suitable for modeling real-world social networks in which there is an assessment of one vertex…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
Social interactions vary in time and appear to be driven by intrinsic mechanisms, which in turn shape the emerging structure of the social network. Large-scale empirical observations of social interaction structure have become possible only…
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…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This paper introduces a class of models for…
Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of…
Using edge weights is essential for modeling real-world systems where links possess relevant information, and preserving this information in low-dimensional representations is relevant for classification and prediction tasks. This paper…
Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
Multidimensional systems coupled via complex networks are widespread in nature and thus frequently invoked for a large plethora of interesting applications. From ecology to physics, individual entities in mutual interactions are grouped in…
Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…
What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents,…
Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a…
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…