In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every $\alpha \gt 0$, there exists a constant $C$ such that for every $n$-vertex digraph of minimum semi-degree at least $\alpha n$, if one adds $Cn$ random edges then asymptotically almost surely the resulting digraph contains a consistently oriented Hamilton cycle. We generalize their result, showing that the hypothesis of this theorem actually asymptotically almost surely ensures the existence of every orientation of a cycle of every possible length, simultaneously. Moreover, we prove that we can relax the minimum semi-degree condition to a minimum total degree condition when considering orientations of a cycle that do not contain a large number of vertices of indegree $1$. Our proofs make use of a variant of an absorbing method of Montgomery.

We study site and bond percolation in simple directed random graphs with a given degree distribution. We derive the percolation threshold for the giant strongly connected component and the fraction of vertices in this component as a function of the percolation probability. The results are obtained for degree sequences in which the maximum degree may depend on the total number of nodes n, being asymptotically bounded by $n^{\frac{1}{9}}$.

We introduce the notion of balanced strong shift equivalence between square non-negative integer matrices, and show that two finite graphs with no sinks are one-sided eventually conjugate if and only if their adjacency matrices are conjugate to balanced strong shift equivalent matrices. Moreover, we show that such graphs are eventually conjugate if and only if one can be reached by the other via a sequence of out-splits and balanced in-splits, the latter move being a variation of the classical in-split move introduced by Williams in his study of shifts of finite type. We also relate one-sided eventual conjugacies to certain block maps on the finite paths of the graphs. These characterizations emphasize that eventual conjugacy is the one-sided analog of two-sided conjugacy.

In this paper we show that every non-cycle finite transitive directed graph has a Cuntz–Krieger family whose WOT-closed algebra is $B(\mathcal {H})$. This is accomplished through a new construction that reduces this problem to in-degree 2-regular graphs, which is then treated by applying the periodic Road Colouring Theorem of Béal and Perrin. As a consequence we show that finite disjoint unions of finite transitive directed graphs are exactly those finite graphs which admit self-adjoint free semigroupoid algebras.

U.S. live cattle markets have experienced dramatic shifts in marketing methods over the past two decades, changing the way live cattle prices are discovered. We identify relationships between prices of the five major live cattle marketing regions using Granger causality and directed graph analysis. The two approaches complement each other and reveal that interweek and intraweek price discovery roles for given markets differ. Evidence indicates that Colorado, though a minor market in terms of relative volume, has become an important source of interweek price information to other markets.

This article examines the impacts of monetary policy on agricultural prices in four Asian economies using time series analysis and graph theory. The estimations clearly show that agricultural prices overshoot their long-run equilibrium values for Korea, Philippines, and Thailand, and the overshooting for agricultural prices is larger than for manufactured prices. Impulse-response functions and variance-decomposition analysis based on directed graphs and causal structures highlight the complex interplay among the variables in the model and how those relationships differ by country. Money supply changes clearly affect real variables and relative prices for all countries either through overshooting or non-neutrality of money.

The Law of One Price (LOP) is important to models of international trade and exchange rate determination. This study investigates a variant of the LOP applied to developed and developing countries. The competing hypotheses are (1) that one price prevails in both developed and developing countries and (2) that one price prevails in developed countries and another single price in developing countries. Using data from an internationally competitive commodity (soybean meal), we found evidence favors the first hypothesis, although two large developing countries under study are active participants in regional trade integration, which may bias them against the first hypothesis.

Let be a finite set of finite tournaments. We will give a necessary and sufficient condition for the -free homogeneous directed graph to be divisible. That is, that there is a partition of into two classes such that neither of them contains an isomorphic copy of .