QUICK INDEX:

• Network Measures
• Internet Resources on Networks
• Outline Input-Output
• Matrix Multiplications | or here
• Matrix Analysis of Networks
• Network Exercise (207)
• Network Exercise (350)

• Direct linkages, Indirect Linkages,
• Connectivity = attribute of a network; measures the effort (minimum number of links) needed to reach all nodes from all other nodes
• Accessibility = attribute of a node: measures the effort needed to reach all or certain nodes from a specific node.
• Path: a set of consecutive links involving different nodes
• Forward and Backward Linkages, Directed Graphs (flows move in one direction only)
• "Fundamental Circuits": are circuits (= closed paths) which do not contain other circuits (such "loops" create redundancies in the network)

• Beta Index: Compares the number of links with the number of nodes in a network
• Gamma Index: Compares the actual number of links with the maximum number
• Alpha Index: compares the number of actual (fundamental) "circuits" with the maximum number of all possible fundamental circuits
• Associated Number (Koenig Number): measures the accessibility (or centrality) of a node by the number of links needed to connect this node with the (topologically) most distant node in the network
• Shimbel Index: Measure of the minimum number of links necessary to connect one node with all nodes in the network
• Diameter of a network: Number of links in the shortest path between the furthest pair of nodes.
  Analytical significance: It is needed to identify the number of matrix multiplications (using the adjacency matrix) needed to fill all the "boxes" in the "solution matrix" (i.e. to assure that all nodes are directly or indirectly linked to each other when assessing the accessibility of the network's nodes; more specifically, the adjacency matrix has to be taken to the power of the diameter).
• Nodal Degree: The sum of the (direct) links which connect a node to adjacent nodes. It can be calculated by summing rows or columns of (direct) connection matrix. Its limitation relates to the lack of consideration of indirect links.

• Network Exercise (Geog.350)

• Graph Theory [in Wicks, Finite Mathematics, Online] [disconnected?]

• Andersson, Ake E., Knowledge and Networks in a Dynamic Economy: Festschrift in Honor of Ake E. Andersson. Edited by Martin J. Beckmann, et al. Heidelberg and New York: Springer, 1998. Pp. ix, 421. ISBN 3-540-64245-5. Twenty papers, in honor of Ake E. Andersson, director of the Institute for Futures Studies and winner of the Japanese Honda Prize in 1995 for his work on dynamical analysis in the fields of regional economics and regional planning, present research into knowledge and networks in the dynamic economy.

• Nicholas Economides, "Economics of Networks," (March 1996)

Literature:

• Campbell, J. (1975) "Application of graph theoretic analysis to interindustry relationships: The example of Washington state," Regional Science and Urban Economics, 5:91-106.
• Degenne, Alain and Michel Forse, Introducing Social Networks. (transl. by Arthur Borges), Sage Publications, 1999. [HM741.D43.1999]
  • Chapter 3: Graph Thoey
  • Chapter 6: Power and Centrality
  • Appendix (pp.211ff.): Matrix Operations

• Garrison, W.L. and D.F. Marble. "Graph Theoretic Concepts," in: Michael E. Eliot Hurst, ed., Transportation Geography: Comments and Readings. NY: McGraw, 1974, pp.58-80.

• Garrison, W.L., "Connectivity of the Interstate Highway System," Papers of the Regional Science association 6 (1960), 121-37 [Reprinted in M.Eliot Hurst, ed., Transportation Geography, 1974, pp.81ff.]

• Goodall, Dictionary of Human Geography;

• Johnston, et al., Dictionary of Human Geography, p.419 + 233-5

  Kansky, K.J. Structure of Transportation Networks: Relationships Between Network Geometry and Regional Characteristics. Chicago: University of Chicago, 1963 [Department of Geography Research Paper #84]. [presents additional network measures and indices]

• Kilkenny, Maureen and Laura Nalbarte, Keystone Sector Identification: A Graph Theory-Social Network Analysis Approach; West Virginia BookWeb of Regional Science, 1999/2000.

• Taaffe & Gauthier, Geography of Transportation. (1973 or 1996 edition)

• West, Douglas B. Introduction to Graph Theory - Second edition Prentice Hall 1996. [xx+588 pages, 1296 exercises, 447 figures, ISBN 0-13-014400-2].

Video:

• Five Forces in the Network Economy [Hal Varian, 1999] Information goods -- from movies and music to software code and stock quotes -- have supplanted industrial goods as the key drivers of world markets.

Clippings:

Cheney knows -- thanks to his connections; Seattle P-I, Saturday, December 1, 2001 By STEWART M. POWELL, SEATTLE POST-INTELLIGENCER WASHINGTON BUREAU