This paper describes how the maximum potential number of edges of an encapsulated graph varies as the graph is transformed, that is, as nodes are created and modified. The equations governing these changes of maximum potential number of edges caused by the transformations are derived and briefly analysed.

In this paper it is shown that the spectrum of a nested interval graph has a very simple structure. From this result a formula is derived to the number of spanning trees in a nested interval graph; this is a generalization of the Cayley formula.

We show that the Gaussian random fields and harmonic energy minimizing function framework for semi-supervised learning can be viewed in terms of Gaussian processes, with covariance matrices derived from the graph Laplacian. We derive hyperparameter learning with evidence maximization, and give an empirical study of various ways to parameterize the graph weights.

We address the problem of generating a minimal state graph from a program, without building the whole state graph. Minimality is considered here with respect to bisimulation. A generation algorithm is derived and illustrated. Applications concern program veri cation and control synthesis in reactive program compilation.

In this paper, we present a graph model which is powerful in classifying and compiling linear recursive formulas in deductive databases. The graph model consists of two kinds of graphs: I-graph and Resolution Graph. We can extract essential properties of a recursive formula from its I-graph and can easily figure out the compiled formula and the query evaluation plan of the recursive formula fro...

The graph construction procedure essentially determines the potentials of those graph-oriented learning algorithms for image analysis. In this paper, we propose a process to build the so-called directed l1-graph, in which the vertices involve all the samples and the ingoing edge weights to each vertex describe its l1-norm driven reconstruction from the remaining samples and the noise. Then, a s...

This paper describes Graph Investigator, the application intended for analysis of complex networks. A rich set of application functions is briefly described including graph feature generation, comparison, visualization and edition. The program enables to analyze global and local structural properties of networks with the use of various descriptors derived from graph theory. Furthermore, it allo...

New lower bounds for eigenvalues of a simple graph are derived. Upper and lower bounds for eigenvalues of bipartite graphs are presented in terms of traces and degree of vertices. Finally a non-trivial lower bound for the algebraic connectivity of a connected graph is given.

We address the problem of generating a minimal state graph from a program, without building the whole state graph. Minimality is considered here with respect to bisimulation. A generation algorithm is derived and illustrated. Applications concern program veriication and control synthesis in reactive program compilation.

Graph analysis is a promising tool to quantify brain connectivity. However, an essential requirement is that the graph measures are reproducible and robust. We have studied the reproducibility and robustness of various graph measures in group based and in individual binary and weighted networks derived from a task fMRI experiment during explicit associative-semantic processing of words and pict...