Related papers: Community Correlations and Testing Independence Be…
The large amount of work on community detection and its applications leaves unaddressed one important question: the statistical validation of the results. In this paper we present a methodology able to clearly detect if the community…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The…
We consider the problem of recovering a binary rating matrix as well as clusters of users and items based on a partially observed matrix together with side-information in the form of social and item similarity graphs. These two graphs are…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
We develop a Bayesian hierarchical model to identify communities in networks for which we do not observe the edges directly, but instead observe a series of interdependent signals for each of the nodes. Fitting the model provides an…
Inferring brain connectivity network and quantifying the significance of interactions between brain regions are of paramount importance in neuroscience. Although there have recently emerged some tests for graph inference based on…
Graph theory has drawn a lot of attention in the field of Neuroscience during the last decade, mainly due to the abundance of tools that it provides to explore the interactions of elements in a complex network like the brain. The local and…
The assumption that data samples are independent and identically distributed (iid) is standard in many areas of statistics and machine learning. Nevertheless, in some settings, such as social networks, infectious disease modeling, and…
In this paper we present results from a method of community detection using label propagation in undirected, unweighted graphs which incorporates elements of neural computing and spike-based data. Using a fully connected, edge-weighted…
Conditional Independence (CI) graphs are a type of probabilistic graphical models that are primarily used to gain insights about feature relationships. Each edge represents the partial correlation between the connected features which gives…
We consider the problem of detecting whether a power-law inhomogeneous random graph contains a geometric community, and we frame this as an hypothesis testing problem. More precisely, we assume that we are given a sample from an unknown…
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produced by the neurons at an instant of time is a binary state on…
We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…
The Web is a typical example of a social network. One of the most intriguing features of the Web is its self-organization behavior, which is usually faced through the existence of communities. The discovery of the communities in a Web-graph…
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…
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…