Related papers: Continuum graph dynamics via population dynamics: …

Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions. In this work, we propose a unified framework that explicitly models graph data as a mixture of…

Learning graph representations is a fundamental task aimed at capturing various properties of graphs in vector space. The most recent methods learn such representations for static networks. However, real world networks evolve over time and…

Numerous social, medical, engineering and biological challenges can be framed as graph-based learning tasks. Here, we propose a new feature based approach to network classification. We show how dynamics on a network can be useful to reveal…

In this paper we investigate the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way. Apart from the typical rates of growth, i.e. exponential or polynomial, we identify…

Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…

The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov processes and associated boundaries, analysis of path-space,…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…

We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite…

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…

Social networks have a small number of large hubs, and a large number of small dense communities. We propose a generative model that captures both hub and dense structures. Based on recent results about graphons on line graphs, our model is…

State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are…

In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at…

Sampling random graphs is essential in many applications, and often algorithms use Markov chain Monte Carlo methods to sample uniformly from the space of graphs. However, often there is a need to sample graphs with some property that we are…

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…

Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…

This paper proposes a framework to ensure the existence of dynamical system trajectories in the state space of labeled, weighted, and attributed graphs. The evolution of such a system exhibits hybrid behavior: discrete jumps affecting the…

Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of…

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…

Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. Two standard algorithms -- label propagation and graph neural networks -- both operate by repeatedly passing information along edges,…