相关论文: Graph W*-probability Theory
We give a complete $K$-theoretical description of when an extension of two simple graph $C^{*}$-algebras is again a graph $C^{*}$-algebra.
It is argued that chiral algebras of conformal field theory possess a W-algebra structure. A survey of explicitly known W-algebras and their constructions is given. (Talk given at the XIX International Colloquium on ``Group Theoretical…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…
One deals with r-regular bipartite graphs with 2n vertices. In a previous paper Butera, Pernici, and the author have introduced a quantity d(i), a function of the number of i-matchings, and conjectured that as n goes to infinity the…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
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…
The reliability polynomial of a graph gives the probability that a graph remains operational when all its edges could fail independently with a certain fixed probability. In general, the problem of finding uniformly most reliable graphs…
We describe a natural topological generalization of edge expansion for graphs to regular CW complexes and prove that this property holds with high probability for certain random complexes.
We classify graph C*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph. This is done by a purely graph theoretical calculation of the K-theory and the position of the unit…
\emph{Uncertain Graph} (also known as \emph{Probabilistic Graph}) is a generic model to represent many real\mbox{-}world networks from social to biological. In recent times analysis and mining of uncertain graphs have drawn significant…
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
We consider the problem of determining the maximum induced density of a graph H in any graph on n vertices. The limit of this density as n tends to infinity is called the inducibility of H. The exact value of this quantity is known only for…
This is an introduction to some of the most probabilistic aspects of free probability theory.
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
In this paper, we study a graph parameter that was recently introduced, the burning number, focusing on a few probabilistic aspects of the problem. The original burning number is revisited and analyzed for binomial random graphs G(n,p),…
A factor-graph representation of quantum-mechanical probabilities is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…