Related papers: Sparse Maximum-Entropy Random Graphs with a Given …
Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
We consider events over the probability space generated by the degree sequences of multiple independent Erd\H{o}s-R\'enyi random graphs, and consider an approximation probability space where such degree sequences are deemed to be sequences…
The shift-enabled property of an underlying graph is essential in designing distributed filters. This article discusses when a random graph is shift-enabled. In particular, popular graph models ER, WS, BA random graph are used, weighted and…
The structure of a network is an unlabeled graph, yet graphs in most models of complex networks are labeled by meaningless random integers. Is the associated labeling noise always negligible, or can it overpower the network-structural…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
We consider sufficient conditions for the existence of $k$-th powers of Hamiltonian cycles in $n$-vertex graphs $G$ with minimum degree $\mu n$ for arbitrarily small $\mu>0$. About 20 years ago Koml\'os, Sark\"ozy, and Szemer\'edi resolved…
In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
In this work, we study the maximum matching problem from the perspective of sensitivity. The sensitivity of an algorithm $A$ on a graph $G$ is defined as the maximum Wasserstein distance between the output distributions of $A$ on $G$ and on…
Exponential-family Random Graph Models (ERGMs) constitute a large statistical framework for modeling sparse and dense random graphs, short- and long-tailed degree distributions, covariates, and a wide range of complex dependencies. Special…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is…
Deep generative models (DGMs) for graphs achieve impressively high expressive power thanks to very efficient and scalable neural networks. However, these networks contain non-linearities that prevent analytical computation of many standard…
We consider the random graph $G_{n, {\bf d}}$ chosen uniformly at random from the set of all graphs with a given sparse degree sequence ${\bf d}$. We assume ${\bf d}$ has minimum degree at least 4, at most a power law tail, and place one…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
This work has two contributions. The first one is extending the Large Deviation Principle for uniform hyper-graphons from Lubetzky and Zhao \cite{lubetzky2015replica} to the multi-relational setting where each hyper-graphon can have…