Related papers: An isomorphism theorem for random interlacements
We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree…
We explore an identity between two branching graphs and propose a physical meaning in the context of the gauge-gravity correspondence. From the mathematical point of view, the identity equates probabilities associated with $\mathbb{GT}$,…
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps.…
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…
We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development…
We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…
This is a preliminary study of the equation of motion of Euclidean classical gravity on a graph, based on the Lin-Lu-Yau Ricci curvature on graphs. We observe that the constant edge weights configuration gives the unique solution on an…
Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.
Sampling uniform simple graphs with power-law degree distributions with degree exponent $\tau\in(2,3)$ is a non-trivial problem. We propose a method to sample uniform simple graphs that uses a constrained version of the configuration model…
The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called…
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show…
We get central limit type theorems for the total number of edges in the generalized random graphs with random vertex weights under different moment conditions on distributions of the weights.
We investigate random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the…
We present a rigorous proof of the convergence theorem for the Feynman graphs in arbitrary massive Euclidean quantum field theories on non-commutative R^d (NQFT). We give a detailed classification of divergent graphs in some massive NQFT…
Berry and Wang [Phys. Rev. A {\bf 83}, 042317 (2011)] show numerically that a discrete-time quantum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…