In this paper‎, ‎we define two $n$-square upper Hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph‎. ‎We investigate relations between permanents and determinants of these upper Hessenberg matrices‎, ‎and sum formulas of the well-known Pell and Jacobsthal sequences‎. ‎Finally‎, ‎we present two Maple 13 procedures in order to calculate permanents of t...

Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. Spectral graph theory seeks to relate the eigenvectors and eigenvalues of matrices corresponding to a Graph to the combinatorial properties of the graph. While generally the theorems are designed for unweighted and undirected graphs they can be extended to the weighted graph case and (less co...

Main talks 1. Simeon Ball, On subsets of a finite vector space in which every subset of basis size is a basis 2. Simon Blackburn, Honeycomb arrays 3. Gàbor Korchmàros, Curves over finite fields, an approach from finite geometry 4. Cheryl Praeger, Basic pregeometries 5. Bernhard Schmidt, Finiteness of circulant weighing matrices of fixed weight 6. Douglas Stinson, Multicollision attacks on itera...

After summarizing the harmonic approach to topological coordinates and the null space embedding of graphs, three-coordinated tiling of the plane by hexagons, pentagons, and heptagons are presented and used for the construction of tubular, toroidal, and helical carbon structures. Physically realistic 3D geometries are formed from the corresponding adjacency matrices, and the final structure was ...

Graph ranking algorithms such as PageRank and HITS share the common idea of calculating eigenvectors of graph adjacency matrices. This paper shows that the power method usually used to calculate eigenvectors is also present in a spreading activation search. In addition, we empirically show that spreading activation algorithm is able to converge on periodic graphs, where power method fails. Furt...

Visualizing social networks presents challeges for both nodelink and adjacency matrix representations. Social networks are locally dense, which makes node-link displays unreadable. Yet, main analysis tasks require following paths, which is difficult on matrices. This article presents MatLink, a hybrid representation with links overlaid on the borders of a matrix and dynamic topological feedback...

In this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern-space. We adopt a graph-spectral approach. We use the leading eigenvectors of the graph adjacency matrix to de0ne eigenmodes of the adjacency matrix. For each eigenmode, we compute vectors of spectral properties. These include the eigenmode perimeter, eigenmode volume, Cheeger number, inter-mode ...

We analyze the largest eigenvalue and eigenvector for the adjacency matrices of sparse random graph. Let λ1 be the largest eigenvalue of an n-vertex graph, and v1 be its corresponding normalized eigenvector. For graphs of average degree d log n, where d is a large enough constant, we show λ1 = d log n + 1 ± o(1) and 〈1, v1〉 = √ n ( 1−Θ ( 1 logn )) . It shows a limitation of the existing method ...

An output measure is an image of a uniform Bernoulli measure on finitely many states. We discuss “generalized Bernoulli” measures of [F-J], and answer several questions posed in that paper, in particular we establish a condition when such a measure is a finitary output measure. Answering D. Goldstein’s question, we characterize output measures via block codes in terms of walks on labeled graphs...

NodeTrix representations are a popular way to visualize clustered graphs; they represent clusters as adjacency matrices and intercluster edges as curves connecting the matrix boundaries. We study the complexity of constructing NodeTrix representations focusing on planarity testing problems, and we show several NP-completeness results and some polynomial-time algorithms. Building on such algorit...