Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to ...

Let G denote a graph, and KV(G) represent a set of target vertices. Assume that the non-target vertices of G fail independently with given probabilities. The K-terminal reliability of G is defined as the probability that all target vertices in K are connected. Computing K-terminal reliability is #P-complete for general graphs, yet solvable in polynomial time for interval graphs. This work prop...

We present a notion of convergence for sequences of finite graphs {Gn} that can be seen as a generalization of the Benjamini-Schramm convergence notion for bounded degree graphs, regarding the distribution of r-neighbourhoods of the vertices, and the left-convergence notion for dense graphs, regarding, given any finite graph F , the limit of the probabilities that a random map from V (F ) to V ...

We establish several discrepancy and isoperimetric inequalities for directed graphs by considering the associated random walk. We show that various isoperimetric parameters, as measured by the stationary distribution of the random walks, including the Cheeger constant and discrepancy, are related to the singular values of the normalized probability matrix and the normalized Laplacian. Further, ...

In this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graph G, each pair of vertices are joined by an edge with a probability p, where p is a constant between 0 and 1. We show that, a maximum independent set in a random graph that contains n vertices can be computed in expected computation time 2 2 2 . Using te...

A Hamilton cycle in a digraph is a cycle passes through all the vertices, where all the arcs are oriented in the same direction. The problem of finding Hamilton cycles in directed graphs is well studied and is known to be hard. One of the main reasons for this, is that there is no general tool for finding Hamilton cycles in directed graphs comparable to the so called Posá ‘rotationextension’ te...

We consider the classical rumor spreading problem, where a piece of information must be disseminated from a single node to all n nodes of a given network. We devise two simple push-based protocols, in which nodes choose the neighbor they send the information to in each round using pairwise independent hash functions, or a pseudo-random generator, respectively. For several wellstudied topologies...

This paper focuses on the probability density function of the Euclidean distance between node pairs in rectangular random graphs. As the main achievement of the paper, a closed analytic formula of the probability density function of the Euclidean distance between node pairs in rectangular random graphs was obtained basing on combinatorial theory and asymptotic concept. Some lemmas, such as numb...

We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. The probability distribution of graphs of this kind is shown to depend on the symmetries of these graphs, which are reflected in the equilibrium distribution of the Markov chain. We prove that the algorithm is ergodic and proceed to estimate t...

This paper deals with the construction of a computation tree (hypertree) for interacting systems modeled using graphs (hypergraphs) that preserve the marginal probability of any vertex of interest. Local message passing equations have been used for some time to approximate the marginal probabilities in graphs but it is known that these equations are incorrect for graphs with loops. In this pape...