Related papers: Testing Dependency of Weighted Random Graphs
In this paper, we investigate the problem of deciding whether two random databases $\mathsf{X}\in\mathcal{X}^{n\times d}$ and $\mathsf{Y}\in\mathcal{Y}^{n\times d}$ are statistically dependent or not. This is formulated as a hypothesis…
This paper analyzes different online algorithms for the problem of assigning weights to edges in a fully-connected bipartite graph that minimizes the overall cost while satisfying constraints. Edges in this graph may disappear and reappear…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
We consider the minimum spanning tree problem in a setting where the edge weights are stochastic from unknown distributions, and the only available information is a single sample of each edge's weight distribution. In this setting, we…
In the first part of this paper, we consider weighted domination in the case where the vertices of the complete graph on~\(n\) vertices are equipped with independent and identically distributed (i.i.d.) weights. We use the probabilistic…
An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
The theory of random graphs is being applied in recent years to model neural interactions in the brain. While the probabilistic properties of random graphs has been extensively studied in the literature, the development of statistical…
Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…
We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph,…
We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some unidentifiable similarity transformations. Our test statistic is…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
For any positive edge density $p$, a random graph in the Erd\H{o}s-Renyi $G_{n,p}$ model is connected with non-zero probability, since all edges are mutually independent. We consider random graph models in which edges that do not share…
We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…
We study the problem of detecting local geometry in random graphs. We introduce a model $\mathcal{G}(n, p, d, k)$, where a hidden community of average size $k$ has edges drawn as a random geometric graph on $\mathbb{S}^{d-1}$, while all…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
Estimation of graph parameters based on a collection of graphs is essential for a wide range of graph inference tasks. In practice, weighted graphs are generally observed with edge contamination. We consider a weighted latent position graph…
Let $G=(V, E)$ be a given edge-weighted graph and let its {\em realization} $\mathcal{G}$ be a random subgraph of $G$ that includes each edge $e \in E$ independently with probability $p$. In the {\em stochastic matching} problem, the goal…
We study the k-wise independent relaxation of the usual model G(N,p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probability p, however, it is only required that the distribution of any…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…