Related papers: Path Weights in Concentration Graphs
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
Graph classification plays a pivotal role in various domains, including pathology, where images can be represented as graphs. In this domain, images can be represented as graphs, where nodes might represent individual nuclei, and edges…
Let ${\cal G}=(G,w)$ be a weighted simple finite connected graph, that is, let $G$ be a simple finite connected graph endowed with a function $w$ from the set of the edges of $G$ to the set of real numbers. For any subgraph $G'$ of $G$, we…
For the first time proposed: a method for representing the projections of a graph in computer memory and a description based on it of a quick search for shortest paths in unweighted dynamic graphs. The spatial complexity of the projection…
A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to…
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…
An important step for any causal inference study design is understanding the distribution of the treated and control subjects in terms of measured baseline covariates. However, not all baseline variation is equally important. In the…
The paper considers the behaviour of the number of paths of length $N$ on graphs with two heavy roots. Such vertices can be entropic traps. Numerical analysis is carried out for graphs with different degrees of root vertices. In the…
A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…
Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…
Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…
We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…
Many natural, technological, and social systems incorporate multiway interactions, yet are characterized and measured on the basis of weighted pairwise interactions. In this article, I propose a family of models in which pairwise…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the…
We consider the following "multiway cut packing" problem in undirected graphs: we are given a graph G=(V,E) and k commodities, each corresponding to a set of terminals located at different vertices in the graph; our goal is to produce a…
A random graph evolution rule is considered. The graph evolution is based on interactions of three vertices. The weight of a clique is the number of its interactions. The asymptotic behaviour of the weights is described. It is known that…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…