Related papers: Premagic and Ideal Flow Matrices
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
Causal loop and stock and flow diagrams are broadly used in System Dynamics because they help organize relationships and convey meaning. Using the analytical work of Schoenberg (2019) to select what to include in a compressed model, this…
We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We…
In this paper, we introduce a matrix for a mixed graph, called the integrated adjacency matrix. This matrix uniquely determines a mixed graph, as long as the indices of the matrix are specified. Additionally, we associate an (undirected)…
We study three mixing properties of a graph: large algebraic connectivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk…
The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…
We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…
Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework that employs a graph neural network-based transformer to learn a velocity field over graph representations with…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
Consider a finite inhomogeneous random graph running in continuous time, where each vertex has a mass, and the edge that links any pair of vertices appears with a rate equal to the product of their masses. The simultaneous…
We provide a sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models based on the structure of their transition matrix. If the observed states of the chain form a zero forcing set of…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…
We consider the ergodicity and consensus problem for a discrete-time linear dynamic model driven by random stochastic matrices, which is equivalent to studying these concepts for the product of such matrices. Our focus is on the model where…
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…
Global Markov properties in mixed graphs are usually formulated in terms of the path-oriented m-separation or by use of augmented graphs (similar to moral graphs in the case of directed acyclic graphs). We provide an alternative…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones.…