The problem of eecient characterization of inclusion neighbourhood is crucial for some methods of learning (equivalence classes of) Bayesian networks. In this paper, neighbouring equivalence classes of a given equivalence class of Bayesian networks are characterized eeciently by means of the respective essential graph. The characterization reveals hidded internal structure of the inclusion neig...

| This paper suggests a characterization of systems through equivalence classes of the input signals. Two input signals are called equivalent if they are mapped by the system to the same output. The corresponding equivalence classes for linear systems can be described by subspaces of the signal space. For the nonlinear case the description in terms of subspaces is no longer valid. We show how t...

emph{The (undirected) power graph on the conjugacy classes} $mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.

An automaton with concurrency relations A is a labeled transition system with a collection of binary relations indicating when two actions in a given state of the automaton can occur independently of each other. The concurrency relations induce a natural equivalence relation for nite computation sequences. We investigate two graph-theoretic representations of the equivalence classes of computat...

The paper considers an equivalence relation in the set of vertices of a bipartite graph. Some numerical characteristics showing the cardinality of equivalence classes are introduced. A combinatorial identity that is in relationship to these characteristics of the set of all bipartite graphs of the type g = 〈Rg ∪Cg , Eg〉 is formulated and proved, where V = Rg ∪ Cg is the set of vertices, Eg is t...

Circular planar graphs are used to model electrical networks, which arise in classical physics. Associated with such a network is a network response matrix, which carries information about how the network behaves in response to certain potential differences. Circular planar graphs can be organized into equivalence classes based upon these response matrices. In each equivalence class, certain fu...

A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the combinatorial burden of isomorphism testing. Unrolling the graph into a tree at each vertex allows structurally different regular graphs to be discriminated...

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

Bayesian networks are a useful tool in the representation of uncertain knowledge. This paper proposes a new algorithm to learn the structure of a Bayesian network. It does this by conducting a search through the space of equivalence classes of Bayesian networks using Ant Colony Optimization (ACO). To this end, two novel extensions of traditional ACO techniques are proposed and implemented. Firs...