The characteristic polynomial of a graph

AbstractThe present paper is addressed to the problem of determining under what conditions the characteristic polynomial of the adjacency matrix of a graph distinguishes between non-isomorphic graphs. A formula for the coefficients of the characteristic polynomial of an arbitrary digraph is derived, and the polynomial of a tree is examined in depth. It is shown that the coefficients of the polynomial of a tree count matchings. Several recurrence relations are also given for computing the coefficients. An appendix is provided which lists n-node trees (2 ≤ n ≤ 10) together with the coefficients of their polynomials. It should be noted that this list corrects some errors in the earlier table of [1]

On Building a Trans-European Network

This paper explores the social shaping of network-based information systems, drawing on the author’s experience as a participant in a major networking project of the European Commission. The project was undertaken in conjunction with the establishment of a European Monitoring Centre for Drugs and Drug Addiction (EMCDDA). A key function of the EMCDDA is to integrate activities and sources of information (e.g., specialized libraries, documentation centres, statistical databases, etc.) dealing with drug abuse, i.e., possession or use of, or trafficking in illicit drugs. The social and technological complexities of building a trans-European network make it an especially interesting and revealing case to study. This paper examines in the ways in which the EMCDDA project has confronted and resolved the technological and social issues of network design and development

On the market value of information commodities. I. The nature of information and information commodities

This article lays the conceptual foundations for the study of the market value of information commodities. The terms “information” and “commodity” are given precise definitions in order to characterize “information commodity,” and thus to provide a sound basis for examining questions of pricing. Information is used by marketplace actors to make decisions or to control processes. Thus, we define information as the ability of a goal‐seeking system to decide or control. By “decide” we mean choosing one alternative among several that may be executed in pursuit of a well‐defined objective. “Control” means the ordering of actions. Two factors make it possible to turn something into a commodity: (1) appropriability, and (2) valuability. If something cannot be appropriated (i.e., owned), it cannot be traded; moreover, if it cannot be valued, there is no way to determine for what it might be exchanged. We define an information commodity as a commodity whose function it is to enable the user, a goal‐seeking system, to obtain information, i.e., to otain the ability to decide or control. Books, databases, computer programs, and advisory services are common examples of information commodities. Their market value derives from their capacity to furnish information

Relating vertex and global graph entropy in randomly generated graphs

Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of vertex level measures that do not suffer from this pathological computational complexity, but that can be shown to be effective at quantifying graph complexity. In this paper, we consider whether these local measures are fundamentally equivalent to global entropy measures. Specifically, we investigate the existence of a correlation between vertex level and global measures of entropy for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate strong correlation for this subset of graphs and outline how this may arise theoretically

Structural Differentiation of Graphs Using Hosoya-Based Indices

In this paper, we introduce the Hosoya-Spectral indices and the Hosoya information content of a graph. The first measure combines structural information captured by partial Hosoya polynomials and graph spectra. The latter is a graph entropy measure which is based on blocks consisting of vertices with the same partial Hosoya polynomial. We evaluate the discrimination power of these quantities by interpreting numerical results

A Note on Graphs with Prescribed Orbit Structure

This paper presents a proof of the existence of connected, undirected graphs with prescribed orbit structure, giving an explicit construction procedure for these graphs. Trees with prescribed orbit structure are also investigated.publishedVersionPeer reviewe

Cospectral Graphs and Digraphs

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135469/1/blms0321.pd

The Discrimination Power of Structural SuperIndices

In this paper, we evaluate the discrimination power of structural superindices. Superindices for graphs represent measures composed of other structural indices. In particular, we compare the discrimination power of the superindices with those of individual graph descriptors. In addition, we perform a statistical analysis to generalize our findings to large graphs

The Hosoya Entropy of a Graph

This paper demonstrates properties of Hosoya entropy, a quantitative measure of graph complexity based on a decomposition of the vertices linked to partial Hosoya polynomials. Connections between the information content of a graph and Hosoya entropy are established, and the special case of Hosoya entropy of trees is investigated