Related papers: Approximating the Statistics of various Properties…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of…
We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…
We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…
We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
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 parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
We consider the problem of finding edges of a hidden weighted graph using a certain type of queries. Let $G$ be a weighted graph with $n$ vertices. In the most general setting, the $n$ vertices are known and no other information about $G$…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
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…