Architectural planning with graph theory: finding closest places and feasible pathways
N/A
Resumen
In Planning a layout for a city or town one of the most important considerations is allocation of places and buildings in a city efficiently. Architects and Urban Planners strive hard to achieve this efficiency by making these spaces and resources accessible to each and everyone. If the places and buildings in a city could be thought of as nodes and roads as connections between them, then the nodes and connections together could form a spatial network which could be read as a graph. And in any spatial network the proximity of places and buildings will determine the efficiency of the network.
Graph theory is a branch of mathematics which is a study of relationship between vertices(nodes) and edges (lines) and is often used in structural modelling. The spatial network (layout) can be represented as a weighted graph, Eccentricity and Domination set theory; graph theory concepts give the central points of the network. This article presents an innovative technique for pinpointing the nearest location to each point in the network. Results are compared with the results derived by using the new method proposed. Other Centrality measures like Degree of the vertices, betweenness and Closeness also provide the nearest location among the given space networks.
This proposed method gives more accurate results and can be applied to networks of varying sizes, i.e., a network of any number of vertices in the future, using an algorithm that is introduced in this paper for enabling the identification of all feasible pathways between any pair of vertices. As a result, architects can efficiently plan space networks by determining the closest location for each point in the given network and also the algorithm to identify all available pathways. This simplifies the task of locating the nearest point within vast space networks for architects and planners alike.
Descargas
Citas
2.B. Hillier and J. Hanson, The Social Logic of Space, Cambridge University Press, 1984.
3.B. Hillier, Space is the Machine, Cambridge University Press, 1996.
4.C. F. and L. March, Architectural applications of graph theory, 1979.
5.D. A. Bader, S. Kintali, K. Madduri, and M. Mihail, Approximating betweenness centrality, Lecture Notes in Computer Science, 4863 (2007), 124–137.
6.D. J. Klein, Centrality measure in graphs, Journal of Mathematical Chemistry 47 (2010), 1209–1223. DOI: 10.1007/s10910-009-9635-0.
7.D. Nawir, M. D. Bakri, and L. A. Syarif, Central government role in road infrastructure development and economic growth in the form of future study: the case of Indonesia, City, Territory and Architecture 10 (2023), no. 12.
8.E. Estrada and J. A. Rodriguez-Velazquez, Subgraph centrality in complex networks, Physical Review E 71 (2005), 056103.
9.F. R. Pitts, A graph theoretic approach to historical geography, Professional Geographer 17 (1965), no. 5, 15–20.
10.H. Maonsuur and T. Storcken, Centers in connected undirected graphs, Operations Research 52 (2004), 54–64.
11.J. Chamero, Dijkstra’s Algorithm, Discrete Structures and Algorithms, 2006.
12.J. L. Martin and L. J. March (eds.), Urban Space and Structure, Cambridge University Press, 1972.
13.J. P. Steadman, Architectural Morphology, Pion, 1983.
14.J. Zhang and Y. Luo, Degree centrality, betweenness centrality, and closeness centrality in social network, Advances in Intelligent Systems Research 132 (2017), Proc. 2nd International Conference on Modelling, Simulation, and Applied Mathematics, Atlantic Press.
15.L. J. March and J. P. Steadman, The Geometry of Environment, RIBA, 1971.
16.M. Piraveenan, M. Prokopenko, and L. Hossain, Percolation centrality: quantifying graph theoretic impact of nodes during percolation in networks, PLoS ONE 8 (2013), no. 1, e53095. DOI: 10.1371/journal.pone.0053095.
17.M. Wagale and A. P. Singh, Socio-economic impacts of low-volume roads using a mixed-method approach of PCA and Fuzzy-TOPSIS, Int. Rev. Spatial Plann. Sustain. Dev. 9 (2021), no. 2, 112–133.
18.N. Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall of India, 1974
19.N. Napong, The graph geometry for architecture planning, Journal of Asian Architecture and Building Engineering 3 (2004), 157–164.
20.P. Dankelmann, W. Goddard, and C. S. Swart, The average eccentricity of a graph and its subgraphs, Utilitas Mathematica 41 (2004), 41–51.
21.P. Sinclair, Betweenness centralization for bipartite graphs, Journal of Mathematical Sociology 29 (2005), 25–31; erratum, 29 (2005), 263–264.
22.R. Grassi, S. Stefani, and A. Torriero, Some new results on the eigenvector centrality, Journal of Mathematical Sociology 31 (2007), 237–248.
23.R. J. Wilson and L. W. Beineke (eds.), Applications of Graph Theory, Academic Press, London, 1979.
24.S. P. Borgatti and M. G. Everett, A graph-theoretic perspective on centrality, Social Networks 28 (2006), 466–484.
25.S. P. Borgatti, Centrality and network flow, Social Networks 27 (2005), 55–71.
26.U. Akpan and R. Morimoto, An application of multi-attribute utility theory (MAUT) to the prioritization of rural roads to improve rural accessibility in Nigeria, Socio-Econ. Plann. Sci. 82 (2022), Article 101256.
27.V. K. Balakrishnan, Graph Theory: Schaum’s Outlines, McGraw-Hill, 1997.
Y. E. Kalay, Modeling Objects and Environment, John Wiley & Sons, 1987.
Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
