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An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
Graphs are commonly used to model various complex systems, including social networks, power grids, transportation networks, and biological systems. In many applications, the connectivity of these networks can be expressed through the Mean…
Causal discovery aims to recover graphs that represent causal relations among given variables from observations, and new methods are constantly being proposed. Increasingly, the community raises questions about how much progress is made,…
We introduce Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks. It is based on a Markovian latent space dynamic: consecutive latent points are sampled on the Euclidean Sphere using an unknown Markov…
Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
Many applications in networked control require intermittent access of a controller to a system, as in event-triggered systems or information constrained control applications. Motivated by such applications and extending previous work on…
We propose an improved algorithm for counting the number of Hamiltonian cycles in a directed graph. The basic idea of the method is sequential acceptance/rejection, which is successfully used in approximating the number of perfect matchings…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We study Markov processes where the "time" parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
Approximating the graph diameter is a basic task of both theoretical and practical interest. A simple folklore algorithm can output a 2-approximation to the diameter in linear time by running BFS from an arbitrary vertex. It has been open…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
After a brief review of the key theorems concerning recurrent sequences, we give an explicit computation of the inverse of the Vandermonde matrix. This will then be used to derive sub-exponential decay error terms in the ergodic theorem of…
In a graph, a community may be loosely defined as a group of nodes that are more closely connected to one another than to the rest of the graph. While there are a variety of metrics that can be used to specify the quality of a given…