This paper presents a tool CCGA-BN Constructor for learning Bayesian network that uses cooperative co-evolutionary genetic algorithm to learn Bayesian network structure from data. The problem has been broken down into two sub-problems: (a) to find the optimal nodes'ordering and (b) to find the optimal adjacency matrix of the graph. Both the sub-problems' solutions are then combined to...

Ordering of subclasses of trees by algebraic connectivity is a very active area of research. Let G = (V,E) be a simple undirected graph on n vertices. The Laplacian matrix of G is the n × n matrix L (G) = D (G) − A (G) where A (G) is the adjacency matrix and D (G) is the diagonal matrix of vertex degrees. It is well known that L (G) is a positive semidefinite matrix and that (0, e) is an eigenp...

The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCS-ordering of a graph is an ordering of the vertices that can be generated by the Maximum Cardinality Search algorithm. The visited degree of a vertex v in an MCS-ordering is the number of neighb...

A key step in the probabilistic analysis of combinatorial algorithms is often that of establishing that certain conditioning introduced by the operation so far of the algorithm either helps or at least does not hurt too much. In this note we consider a conditioning problem that arises from searching adjacency lists, and which occurs for example in the analysis of algorithms for finding Hamilton...

A graph is integral if the spectrum (of its adjacency matrix) consists entirely of integers. The problem of determining all non-regular bipartite integral graphs with maximum degree four which do not have ±1 as eigenvalues was posed in K.T. Balińska, S.K. Simić, K.T. Zwierzyński: Which nonregular bipartite integral graphs with maximum degree four do not have ±1 as eigenvalues? Discrete Math., 2...

Time series can be transformed into graphs called horizontal visibility graphs (HVGs) in order to gain useful insights. Here, the maximum eigenvalue of the adjacency matrix associated to the HVG derived from several time series is calculated. The maximum eigenvalue methodology is able to discriminate between chaos and randomness and is suitable for short time series, hence for experimental resu...

Let X be k-regular graph on v vertices and let τ denote the least eigenvalue of its adjacency matrix A(X). If α(X) denotes the maximum size of an independent set in X, we have the following well known bound: α(X) ≤ v 1− k τ . It is less well known that if equality holds here and S is a maximum independent set in X with characteristic vector x, then the vector

In this paper, we apply a measure, exemplar adjacency number, which complements and extends the well-studied breakpoint distance between two permutations, to measure the similarity between two genomes (or in general, between any two sequences drawn from the same alphabet). For two genomes G andH drawn from the same set of n gene families and containing gene repetitions, we consider the correspo...