Marshall, Stephen;
(2015)
Line Structure Interpretation of Networks: Relationships, Matrices and Properties.
(CASA working paper
204).
UCL Centre for Advanced Spatial Analysis (CASA): London, UK.
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Abstract
This working paper sets out an interpretation of the line structure as a device for representing network structure. First, the line structure S# is briefly introduced with reference to Euclidean and Cartesian geometry. Then its relation to the primal graph (G’) and dual graph (G’’) are set out, demonstrated using an intermediate form, the hypergraph H#. A series of point matrices X ̇ and line matrices X ̅ for specifying the line structure are set out, from which line structural properties such as continuity and connectivity are derived.
| Type: | Working / discussion paper |
|---|---|
| Title: | Line Structure Interpretation of Networks: Relationships, Matrices and Properties |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://www.ucl.ac.uk/bartlett/casa/case-studies/2... |
| Language: | English |
| Additional information: | This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Line structure, graph theory, networks, geometry, matrices |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > The Bartlett School of Planning |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1472820 |
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