Related papers: Dynamical Networks in Function Dynamics
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
The net of N ``physical'' neurons is considered as a dynamical system. These neurons form a complete graph. The state of any neuron is its electric potential. The potential linearly increases until reaches its maximal value. Then it falls…
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…
The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…
Dynamic networks are graphs in which edges are available only at specific time instants, modeling connections that change over time. The dynamic network creation game studies this setting as a strategic interaction where each vertex…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
Networks have been studied mainly using statistical methods. Here I collect some dynamical systems tools which are useful to study both the dynamics on networks and their evolution. They include decomposition of differential dynamics,…
Graphs are a highly expressive abstraction for modeling entities and their relations, such as molecular structures, social networks, and traffic networks. Deep Graph Networks (DGNs) have emerged as a family of deep learning models that can…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
We study a mathematical model of biological neuronal networks composed by any finite number $N \geq 2$ of non necessarily identical cells. The model is a deterministic dynamical system governed by finite-dimensional impulsive differential…
The description of large temporal graphs requires effective methods giving an appropriate mesoscopic partition. Many approaches exist today to detect communities in static graphs. However, many networks are intrinsically dynamical, and need…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
A finite dynamical system (FDS) is a system of multivariate functions over a finite alphabet, that is typically used to model a network of interacting entities. The main feature of a finite dynamical system is its interaction graph, which…
Real-world networks are composed of diverse interacting and evolving entities, while most of existing researches simply characterize them as particular static networks, without consideration of the evolution trend in dynamic networks.…
A dynamic system, which is used in the neural network theory, Ising spin glasses and factor analysis, has been investigated. The properties of the connection matrix, which guarantee the coincidence of the set of the fixed points of the…
Motifs, which have been established as building blocks for network structure, move beyond pair-wise connections to capture longer-range correlations in connections and activity. In spite of this, there are few generative graph models that…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
Temporal networks, defined as sequences of time-aggregated adjacency matrices, sample latent graph dynamics and trace trajectories in graph space. By interpreting each adjacency matrix as a different time snapshot of a scalar field,…