Foreword. Category theory is well known as a high-level polymorphic framework suitable for specifying complex structures and formalisms. Quite unexpectedly, however, it turned out that even elementary category theory notions can be valuable in practice of software engineering (see JD93, DDJ93, CD95, CD96]), and in the summer of 1994 we wrote a manifesto ((CD94], the rst version of the present o...

In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network analysis plays an important role in these domains. A powerful and widespread class of network analysis methods is based on algebraic graph theory, i.e., repre...

In this paper we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are una...

Acknowledgments First of all, I would like to thank my supervisor Jacobo Torán for his support and guidance during my research on this work. I am grateful to Thomas Thierauf for refereeing my thesis. His invaluable discussions and suggestions have been reflected in many places in this research. Thanks to Jens Bolte for reading the whole thesis and refereeing it. My thanks go also to Martin Bade...

Graph transformation systems are widely recognized as a powerful formalism for the specification of concurrent and distributed systems. Therefore, the need emerges naturally of developing formal concurrent semantics for graph transformation systems allowing for a suitable description and analysis of their computational properties. The aim of this chapter is to review and compare various concurr...

In this paper, we propose a new approach to inheritance and abstraction in the context of algebraic graph transformation by providing a suitable categorial framework which reflects the semantics of class-based inheritance in software engineering. Inheritance is modelled by a type graph T that comes equipped with a partial order. Typed graphs are arrows with codomain T which preserve graph struc...

We introduce a pair of natural, equivalent models for random threshold graphs and use these models to deduce a variety of properties of random threshold graphs. Specifically, a random threshold graph G is generated by choosing n IID values x1, . . . , xn uniformly in [0, 1]; distinct vertices i, j of G are adjacent exactly when xi + x j > 1. We examine various properties of random threshold gra...

The algebraic connectivity ofG is the second smallest eigenvalue of its Laplacianmatrix. Let Un be the set of all unicyclic graphs of order n. In this paper, wewill provide the ordering of unicyclic graphs inUn up to the last seven graphs according to their algebraic connectivities when n ≥ 13. This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphswith the sma...