Related papers: Modularity and partially observed graphs
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…
Two models are introduced to investigate graph matching in the presence of corrupt nodes. The weak model, inspired by biological networks, allows one or both networks to have a positive fraction of molecular entities interact randomly with…
Suppose $G$ is a graph with degrees bounded by $d$, and one needs to remove more than $\epsilon n$ of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of $G$ is far from…
Given a sufficiently large and sufficiently dense bipartite graph $G=(A, B; E),$ we present a novel method for decomposing the majority of the edges of $G$ into quasirandom graphs so that the vertex sets of these quasirandom graphs…
Given a graph $G$ and a non trivial partition $(V_1,V_2)$ of its vertex-set, the satisfaction of a vertex $v\in V_i$ is the ratio between the size of it's closed neighborhood in $V_i$ and the size of its closed neighborhood in $G$. The…
Let $\chi'_\subset(G)$ be the least number of colours necessary to properly colour the edges of a graph $G$ with minimum degree $\delta\geq 2$ so that the set of colours incident with any vertex is not contained in a set of colours incident…
Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…
Bipartite testing has been a central problem in the area of property testing since its inception in the seminal work of Goldreich, Goldwasser and Ron [FOCS'96 and JACM'98]. Though the non-tolerant version of bipartite testing has been…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
In high-dimensional graph learning problems, some topological properties of the graph, such as bounded node degree or tree structure, are typically assumed to hold so that the sample complexity of recovering the graph structure can be…
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…
A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Consider a random graph process where vertices are chosen from the interval $[0,1]$, and edges are chosen independently at random, but so that, for a given vertex $x$, the probability that there is an edge to a vertex $y$ decreases as the…
We give a formula for the v-number of a graded ideal that can be used to compute this number. Then we show that for the edge ideal $I(G)$ of a graph $G$ the induced matching number of $G$ is an upper bound for the v-number of $I(G)$ when…
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…