Related papers: Doeblin Trees
In this work, the topologies of networks constructed from time series from an underlying system undergo a period doubling cascade have been explored by means of the prevalence of different motifs using an efficient computational motif…
Let $G$ be a finite tree with root $r$ and associate to the internal vertices of $G$ a collection of transition probabilities for a simple nondegenerate Markov chain. Embedd $G$ into a graph $G^\prime$ constructed by gluing finite linear…
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 give a deterministic algorithm to construct a graph with no loops (a tree or a forest) whose vertices are the points of a d-dimensional stationary Poisson process S, subset of R^d. The algorithm is independent of the origin of…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space and randomness complexities of such samplers. In the standard…
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
The number of observable degrees of freedom is typically limited in experiments. Here, we consider discrete Markov networks in which an observer has access to a few visible transitions and the waiting times between these transitions.…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
The switching model is a Markov chain approach to sample graphs with fixed degree sequence uniformly at random. The recently invented Curveball algorithm for bipartite graphs applies several switches simultaneously (`trades'). Here, we…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…
We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…
We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the…