Related papers: A generalized inverse for graphs with absorption
During routine state space circuit analysis of an arbitrarily connected set of nodes representing a lossless LC network, a matrix was formed that was observed to implicitly capture connectivity of the nodes in a graph similar to the…
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…
Some data analysis problems require the computation of (regularised) inverse traces, i.e. quantities of the form $\Tr (q \bI + \bL)^{-1}$. For large matrices, direct methods are unfeasible and one must resort to approximations, for example…
In this paper, we introduce a generalized concept of vertex transitivity in graphs called generalized vertex transitivity. We put forward a new invariant called transitivity number of a graph. The value of this invariant in different…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for…
A complex unit gain graph is a graph where each orientation of an edge is given a complex unit, which is the inverse of the complex unit assigned to the opposite orientation. We extend some fundamental concepts from spectral graph theory to…
We devise methods for finding approximations of the generalized inverse of the graph Laplacian matrix, which arises in many graph-theoretic applications. Finding this matrix in its entirety involves solving a matrix inversion problem, which…
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of…
We study the inverse problem of determining a finite weighted graph $(X,E)$ from the source-to-solution map on a vertex subset $B\subset X$ for heat equations on graphs, where the time variable can be either discrete or continuous. We prove…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
We generalize the notion of an inverse sequence of graph covers from the zero-dimensional dynamical systems to any dynamical system.
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
Distance well-defined graphs consist of connected undirected graphs, strongly connected directed graphs and strongly connected mixed graphs. Let $G$ be a distance well-defined graph, and let ${\sf D}(G)$ be the distance matrix of $G$.…
Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory,…
In previous works the group inverse of a network obtained by some perturbations, as the deletion of a vertex, the addition of a new vertex, contraction of an edge, etc. is obtained in terms of the group inverse of the original network. In…
A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix $(\bb L^+)$ of a simple, undirected graph is proposed. % The nature of the underlying sub-problems is studied in detail…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic substructure. The locally graphic behaviors are formalized in…
We give new general formulas for the asymptotics of the number of spanning trees of a large graph. A special case answers a question of McKay (1983) for regular graphs. The general answer involves a quantity for infinite graphs that we call…