Showing papers on "Network theory published in 1982"
Book•
01 Dec 1982
TL;DR: This book, based on the 1981 AMS Short Course on the Mathematics of Networks, introduces most of the basic ideas of network theory and develops some of these ideas considerably, including areas of active research and a wide variety of applications.
Abstract: The theory of networks is a very lively one, both in terms of developments in the theory itself and of the variety of its applications. This book, based on the 1981 AMS Short Course on the Mathematics of Networks, introduces most of the basic ideas of network theory and develops some of these ideas considerably. A number of more specialized topics are introduced, including areas of active research and a wide variety of applications. Frank Boesch gives the basic definitions in the mathematics of networks and in the closely-related topic of graph theory. He discusses two of the most fundamental network problems - the shortest path problem and the minimum spanning tree problem as well as some of their variants.Boesch also gives an interesting presentation in the area of network reliability. Frances Yao considers maximum flows in networks, the problem most often thought of in connection with the mathematics of networks. Richard Karp gives an account of the computational complexity of network problems. Using the case study method, Shen Lin demonstrates the effective use of heuristic algorithms in network design. Four applications of the mathematics of networks are presented by Daniel Kleitman. These include: the design of irrigation systems, the theory of electrical networks, the scheduling of delivery trucks, and the physics of ice. Finally, Nicholas Pippenger presents a chapter on telephone switching networks, an area of network theory that leads to difficult mathematics drawn from such apparently unrelated fields as harmonic analysis.
246 citations
TL;DR: A measure of degree of centrality in a social network which is based on a natural extension of the Banzhaf (1965) index of power in an N -person game is presented in this paper.
77 citations
TL;DR: Network thermodynamic simulation now utilizes pre-existing circuit simulation programs, such as NET2, SPICE2, and ASTEC, which provides a cheap and efficient way to achieve simulations on a digital computer which previously were best done by analog or hybrid computation due to the complexity of the systems being simulated.
12 citations
8 citations
TL;DR: This chapter focuses on the effective extraction of information included in network description in network descriptions and neural spike records, and various aspects of neuronal network synthesis are presented.
Abstract: Publisher Summary This chapter focuses on the effective extraction of information included in network description in network descriptions and neural spike records. It is first emphasized that an axiomatic foundation of network theory is necessary. The components of such a system are related to the wiring and to the language, and the necessity of a language hypothesis is proven by example. The behavior of formal neuronal network and its relation to the size of the net are briefly discussed. Various aspects of neuronal network synthesis are presented, and movement recognizing network synthesis and analysis are described as examples. Neuronal spike records or descriptions of neuronal networks in morphological terms provide two important sources of information of real nervous systems. However, it occurs rarely that these two kinds of data are obtained simultaneously, mainly because of methodical limitations.