Related papers: Continuum graph dynamics via population dynamics: …
In [Athreya, den Hollander, R\"ollin; 2021, arXiv:1908.06241] models from population genetics were used to define stochastic dynamics in the space of graphons arising as continuum limits of dense graphs. In the present paper we exhibit an…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…
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…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…
Recent advancements in graph representation learning have shifted attention towards dynamic graphs, which exhibit evolving topologies and features over time. The increased use of such graphs creates a paramount need for generative models…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
Generative models for network time series (also known as dynamic graphs) have tremendous potential in fields such as epidemiology, biology and economics, where complex graph-based dynamics are core objects of study. Designing flexible and…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…
Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
In this paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erd\H{o}s--R\'enyi graph that is resampled every time unit, independently of the previous ones, with `edge existence…
In network science, collective dynamics of complex systems are typically modelled as (nonlinear, often including many-body) vertex-level update rules evolving over a graph interaction structure. In recent years, frameworks that explicitly…
Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In…