相关论文: Loop clusters on complete graphs

The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…

We study a discrete dynamic on weighted bipartite graphs on a torus, analogous to dimer integrable systems in Goncharov-Kenyon 2013. The dynamic on the graph is an urban renewal together with shrinking all 2-valent vertices, while it is a…

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.

This paper investigates the Poisson geometry of cluster algebras and the corresponding ideal theory of quantum cluster algebras. We then show how our approach can be applied to the ring theory of quantized coordinate rings. We give a new…

Problems of existence, construction and estimation of parameters of interval colorings of complete k-partite graphs K_{n}^{k} are investigated.

We explore graph theoretical properties of minimal prime graphs of finite solvable groups. In finite group theory studying the prime graph of a group has been an important topic for the past almost half century. Recently prime graphs of…

Graph clustering is the process of grouping vertices into densely connected sets called clusters. We tailor two mathematical programming formulations from the literature, to this problem. In doing so, we obtain a heuristic approximation to…

This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm, and the assumption that the vertices…

Graph clustering is widely used in many data analysis applications. In this paper we propose several parallel graph clustering algorithms based on Monte Carlo simulations and expectation maximization in the context of stochastic block…

We have generalised the concept of graph states to what we have called mixed graph states, which we define in terms of mixed graphs, that is graphs with both directed and undirected edges, as the density matrix stabilized by the associated…

Recently there has been growing interest in discrete homotopies and homotopies of graphs beyond treating graphs as 1-dimensional simplicial spaces. One such type of homotopy is $\times$-homotopy. Recent work by Chih-Scull has developed a…

We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…

A book embedding of a complete graph is a spatial embedding whose planar projection has the vertices located along a circle, consecutive vertices are connected by arcs of the circle, and the projections of the remaining "interior" edges in…

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…

A classification is given of all the countable homogeneous ordered bipartite graphs.

We consider the problem of partitioning the edge set of a graph $G$ into the minimum number $\tau(G)$ of edge-disjoint complete bipartite subgraphs. We show that for a random graph $G$ in $G(n,p)$, for $p$ is a constant no greater than…

Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…

A graph $G=(V,E)$ is a {\it unipolar graph} if there exits a partition $V=V_1 \cup V_2$ such that, $V_1$ is a clique and $V_2$ induces the disjoint union of cliques. The complement-closed class of {\it generalized split graphs} are those…

Motivated by the problem of deformation quantization we introduce and study directed graph complexes with oriented loops and wheels. We develop some technique for computing cohomology of such graph complexes and apply it to several concrete…

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…