In the framework of graph transformation systems with Negative Application Conditions (NACs) the classical notion of switch equivalence of derivations is extended to permutation equivalence, because there are intuitively equivalent derivations which are not switch-equivalent if NACs are considered. By definition, two derivations are permutation-equivalent, if they respect the NACs and disregard...

A graph is a block if its blocks are all cliques. In this paper, we study the average eccentricity of graphs from perspective order sequences. An equivalence relation established under sequence and used to prove lower upper bounds on graphs. The result that 1 1n?34n2?12n?, respectively, where n graph. Finally, devise linear time algorithm calculate sequence.

We define Ak-moves for embeddings of a finite graph into the 3-sphere for each natural number k. Let Ak-equivalence denote an equivalence relation generated by Ak-moves and ambient isotopy. Ak-equivalence implies Ak−1-equivalence. Let F be an Ak−1-equivalence class of the embeddings of a finite graph into the 3-sphere. Let G be the quotient set of F under Ak-equivalence. We show that the set G ...

Introduction. In a paired comparison experiment n judges give a preference in some or all of the (~) pairs of t items. Frequently the purpose of the experiment is to test the null hypothesis that every preference is equally likely against a vaguely defined alternative of consistency. Our purpose is to study several of the tests used, from the point of view of a natural equivalence relation whic...

The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the definition and analysis of one such search space. We use a theoretically motivated neighbourhood, the inclusion boundary, and represent equivalence classes by essential graphs. We show that this se...

We study three mixing properties of a graph: large algebraic connectivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk on the graph. We prove equivalence of this properties (in some sense). We give estimates for the probability for a random graph to satisfy these properties....

We define an out-degree for F -coalgebras and show that the coalgebras of outdegree at most κ form a covariety. As a subcategory of all F coalgebras, this class has a terminal object, which for many problems can stand in for the terminal F -coalgebra, which need not exist in general. As examples, we derive structure theoretic results about minimal coalgebras, showing that, for instance minimiza...

This paper discusses the expressive power of a graph rewriting model of concurrent processes with higherorder communication. As we reported before, it is difficult to represent the scopes of names using models based on process algebra. Then we presented a model of concurrent systems based on graph rewriting. The model makes it possible to represent the scopes of names precisely. We defined an e...

Edges in a social graph may represent private information that needs to be protected. Due to their graph partition schemes, existing edge anonymization methods have several drawbacks, such as high utility loss and high computational overhead. In this paper, we present a new edge anonymization method, which partitions a graph using a new vertex equivalence relation called the neighbor-set equiva...

We study computability theoretic properties of 01 and 0 1 equivalence structures and how they di er from computable equivalence structures or equivalence structures that belong to the Ershov di erence hierarchy. This includes the complexity of isomorphisms between 01 equivalence structures and between 01 equivalence structures. Any 0 1 equivalence structure A with in nitely many in nite equival...