Related papers: Testing properties of graphs and functions
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…
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…
Recently, Goldreich introduced the notion of property testing of bounded-degree graphs with an unknown distribution. We propose a slight modification of his idea: the Radon-Nikodym Oracles. Using these oracles any reasonable graph property…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Query answering routinely employs knowledge graphs to assist the user in the search process. Given a knowledge graph that represents entities and relationships among them, one aims at complementing the search with intuitive but effective…
We give a construction for a self-test for any connected graph state. In other words, for each connected graph state we give a set of non-local correlations that can only be achieved (quantumly) by that particular graph state and certain…
Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the…
We initiate the study of quantum property testing in sparse directed graphs, and more particularly in the unidirectional model, where the algorithm is allowed to query only the outgoing edges of a vertex. In the classical unidirectional…
We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…
We consider properties of edge-colored vertex-ordered graphs, i.e., graphs with a totally ordered vertex set and a finite set of possible edge colors. We show that any hereditary property of such graphs is strongly testable, i.e., testable…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.