1981 volume 8(4) pages 367 – 391
doi:10.1068/b080367

Cite as:
Earl C F, Johnson J H, 1981, "Graph theory and Q-analysis" Environment and Planning B 8(4) 367 – 391

Download citation data in RIS format

Graph theory and Q-analysis

C F Earl, J H Johnson

Received 9 November 1981; in revised form 29 November 1981

Abstract. Structures of graph theory are compared with those of q-analysis and there are many similarities. The graph and simplicial complex defined by a relation are equivalent in terms of the information they represent, so that the choice between graph theory and q-analysis depends on which gives the most natural and complete description of a system. The higher dimensional graphs are shown to be simplicial families or complexes. Although network theory is very successful in those physical science applications for which it was developed, it is argued that Q-analysis gives a better description of human network systems as patterns of traffic on a backcloth of simplicial complexes. The q-nearness graph represents the q-nearness of pairs of simplices for a given q-value. It is concluded that known results from graph theory could be applied to the q-nearness graph to assist in the investigation of q-connectivity, to introduce the notion of connection defined by graph cuts, and to assist in computation. The application of the q-nearness graph to q-transmission and shomotopy is investigated.

Restricted material:

PDF Full-text PDF size: 3100 Kb

Your computer (IP address: 54.226.7.15) has not been recognised as being on a network authorised to view the full text or references of this article. This content is part of our deep back archive. If you are a member of a university library that has a subscription to the journal, please contact your serials librarian (subscriptions information).