Related papers: Recurrence and transience for non-Archimedean and …
One must add arrows which are forced by transitivity to form the transitive closure of a directed graph. We introduce a construction of a transitive directed graph which is formed by adding vertices instead of arrows and which preserves the…
In a bidirected graph an edge has a direction at each end, so bidirected graphs generalize directed graphs. We generalize the definitions of transitive closure and transitive reduction from directed graphs to bidirected graphs by…
We consider the range of random walks up to time n, R_n, on graphs satisfying a uniform condition. This condition is characterized by potential theory. Not only all vertex transitive graphs but also many non-regular graphs satisfy the…
We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…
We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…
In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…
We study how the recurrence and transience of space-time sets for a branching random walk on a graph depends on the offspring distribution. Here, we say that a space-time set $A$ is recurrent if it is visited infinitely often almost surely…
We study the recurrence behaviour of random walks on partially oriented honeycomb lattices. The vertical edges are undirected while the orientation of the horizontal edges is random: depending on their distribution, we prove a.s. transience…
This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.
We characterise the computational power of recurrent graph neural networks (GNNs) in terms of arithmetic circuits over the real numbers. Our networks are not restricted to aggregate-combine GNNs or other particular types. Generalising…
We survey distributional properties of $\mathbb{R}^d$-valued cocycles of finite measure preserving ergodic transformations (or, equivalently, of stationary random walks in $\mathbb{R}^d$) which determine recurrence or transience.
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We review criteria for transience and weak…
The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length $n$ and edges that are permutations of length $n+1$ in which an edge $a_1\cdots…
In this paper we study the structure of $k$-transitive closures of directed paths and formulate several properties. Concept of $k$-transitive orientation generalize the traditional concept of transitive orientation of a graph.
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
In a directed graph, the imbalance of a vertex is its outdegree minus its indegree. We characterize the sequences that are realizable as the sequence of imbalances of a simple directed graph. Moreover, a realization of a realizable sequence…