Structural properties of urban street patterns and the Multiple Centrality Assessment
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1 Structural properties of urban street patterns and the Multiple Centrality Assessment Alessio Cardillo Department of Physics and Astronomy Università degli studi di Catania Complex Networks - Equilibrium and Vulnerability Analysis with Applications Catania Italy A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 1/17
2 Our Group University of Catania Vito Latora Salvatore Scellato Alessio Cardillo Polytechnic of Milan Sergio Porta Emanuele Strano A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 2/17
3 Outline Structural Properties ; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 3/17
4 Outline Structural Properties ; Multiple Centrality Assessment (MCA); A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 3/17
5 Outline Structural Properties ; Multiple Centrality Assessment (MCA); Relation between Centrality and Commercial Activity; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 3/17
6 Outline Structural Properties ; Multiple Centrality Assessment (MCA); Relation between Centrality and Commercial Activity; Conclusions. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 3/17
7 Complex Networks & Cities Question: How can we map a city into a graph? A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 4/17
8 Complex Networks & Cities Answer: We can follow two ways: 1 A Primal Approach; 2 A Dual Approach. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 4/17
9 Introduction Structural Properties Centrality vs. Comercial Activities Conclusions Complex Networks & Cities Primal Approach A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 4/17
10 Introduction Structural Properties Centrality vs. Comercial Activities Conclusions Complex Networks & Cities Primal Approach Intersections as nodes, streets as edges; Focus on intersection. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 4/17
11 Introduction Structural Properties Centrality vs. Comercial Activities Conclusions Complex Networks & Cities Dual Approach A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 4/17
12 Introduction Structural Properties Centrality vs. Comercial Activities Conclusions Complex Networks & Cities Dual Approach Streets as nodes, intersections as edges; Focus on streets; Not unique (name based, line of sight). A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 4/17
13 From Trees to GT Question: How to compare a graph? A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 5/17
14 From Trees to GT Question: How to compare a graph? Answer: Usually real networks are compared with their randomized version. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 5/17
15 From Trees to GT Question: How to compare a graph? Answer: Usually real networks are compared with their randomized version. Randomization Loss of Planarity; Use of extreme cases: Minimum Spanning Tree (MST); Greedy Triangulation (GT). A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 5/17
16 From Trees to GT An example: the city of Savannah A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 5/17
17 From Trees to GT Definition The minimum spanning tree (MST) is the shortest tree which connects every node into a single connected component. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 5/17
18 From Trees to GT Definition The greedy triangulation (GT) is the planar graph with the highest number of edges K max, and that minimize the total length. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 5/17
19 From Trees to GT A. Cardillo, S. Scellato, V. Latora, S. Porta, Phys. Rev. E 73 (2006) S. Scellato, A. Cardillo, V. Latora, S. Porta, Eur. Phys. Journ. B 50 (2006) 221. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 5/17
20 Topological Properties Fractal Dimension d BOX A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
21 Topological Properties Fractal Dimension d BOX Local Properties A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
22 Topological Properties Fractal Dimension d BOX Local Properties Degree k; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
23 Topological Properties Fractal Dimension d BOX Local Properties Degree k; Meshedness M; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
24 Topological Properties Fractal Dimension d BOX Local Properties Degree k; Meshedness M; Motifs; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
25 Topological Properties Fractal Dimension d BOX Local Properties Degree k; Meshedness M; Motifs; Global Properties A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
26 Topological Properties Fractal Dimension d BOX Local Properties Degree k; Meshedness M; Motifs; Global Properties Cost W ; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
27 Topological Properties Fractal Dimension d BOX Local Properties Degree k; Meshedness M; Motifs; Global Properties Cost W ; Global Efficiency E(G). A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 6/17
28 Local Properties Meshedness Coefficient The Meshedness Coefficient M is more general measures of the structure of cycles than the clustering coeficient. M = { f 0 if G is a tree, = f max 1 if G is a complete planar graph. where f =m n + 1, f max =2n 5. J. Buhl et.al. Eur. Phys. J. B 42, (2004) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 7/17
29 Local Properties An example of Meshedness: f =m n + 1 = = 0 0 M = = 0 3 = 0 f =m n + 1 = = 3 3 M = = 3 3 = 1 A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 7/17
30 Local Properties A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 7/17
31 Local Properties A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 7/17
32 Local Properties Motifs In order to evaluate the complexity of graph inner structure one could count the number of cycles of length three (triangles), four (squares) and five (pentagons). A motif is significant if its number is higher than the number found in an equivalent random graph. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 7/17
33 Local Properties A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 7/17
34 Global Properties Cost To take into account the ammount of resources needed to build a street one could consider several functional forms. The simplest one is the Euclidean distance between start and arrival node. This is the so called Cost. W ij = (x j x i ) 2 (y j y i ) 2 ; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 8/17
35 Global Properties Global Efficiency A measure of the typical separation between two nodes in the graph is given by the average shortest path length, also known as characteristic path length L, defined as: L = 1 N(N 1) i,j G i j d ij ; An alternative approach is to consider the harmonic mean of geodesic lengths, and to define the so-called efficiency of G as: E(G) = 1 N(N 1) i,j G i j 1 d ij ; V. Latora, M. Marchiori, PRL 87, (2001) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 8/17
36 Data Analisys In order to compare different city we used two quantities: Relative Efficiency E rel and Relative Cost W rel defined as: E rel = E E MST E GT E ; W MST rel = W W MST W GT W ; MST A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 9/17
37 Data Analisys A. Cardillo, S. Scellato, V. Latora, S. Porta, Phys. Rev. E73 (2006) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 9/17
38 Multiple Centrality Assessment (MCA) Main Scope Set up a methodology for investigation of spatial systems as complex networks to spot the hot places, the critical components and the central routes of a city. P. Crucitti, V. Latora, S. Porta, Chaos 16 (2006) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 10/17
39 Centrality Indices Question: What does it mean being Central? (Bavelas 1948) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 11/17
40 Centrality Indices It means know many people? Degree Centrality; (Nieminem 1974) k i = N a ij ; j=1 A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 11/17
41 Centrality Indices Or act like a bridge between two nodes? Betweenness Centrality; (Freeman 1977) C B i = 1 (N 1)(N 2) X j,k G j k i n jk (i) n jk ; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 11/17
42 Centrality Indices Or being more close to other nodes? Closeness Centrality; (Sabidussi 1966) Ci C = N 1 ; 1 d ij j G P. Crucitti, V. Latora and S. Porta Phys. Rev. E 73 (2006) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 11/17
43 Centrality Indices Or how much you are in a straight line with others? Straightness Centrality; (Crucitti 2006) Ci S = 1 X dij Eucl. ; N 1 d ij j G j i P. Crucitti, V. Latora and S. Porta Phys. Rev. E 73 (2006) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 11/17
44 Centrality Indices Or how much your removal affect network efficiency Latora (2005)? Information Centrality; (Latora 2007) Ci I = E E = E(G) E(G ), E(G) P i,j G 1 d ij E(G) = N(N 1) ; V. Latora, M. Marchiori, Phys. Rev. E 71 (2005) R. V. Latora, M. Marchiori, New. J. Phys 9 (2007) 188 A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 11/17
45 Centrality Indices Answer: All of these features make you Central!!! S. Porta, P. Crucitti, V. Latora, Environmental and Planning B33 (2006) 705. P. Crucitti, V. Latora, S. Porta, Chaos 16 (2006) A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 11/17
46 Some Example of MCA A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 12/17
47 Some Example of MCA A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 12/17
48 Some Example of MCA A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 12/17
49 Some Example of MCA A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 12/17
50 Relationship Between Centrality and Commerce Retail The Grocer s Mantra Mario runs his business at the street corner just in front of my door. He told me that he spent one week in the street before making the choiche for the location of his grocery The first thing he said is where do the people walk Mario is quite good in his work, he says You have to be central, people are where centrality is. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 13/17
51 Relationship Between Centrality and Commerce Retail Question: Is there empirical evidence of the correlation between street centrality and economic activities? A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 13/17
52 Relationship Between Centrality and Commerce Retail In order to study the relation between centrality and commerce the space has been divided into square cells. Per each cell a Kernel Density Estimator (KDE) function has been calculated. The same operation has been done with centrality. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 13/17
53 Some Results Case study: the city of Bologna Porta S et. al. Street Centrality and Densities of Retails and Services in Bologna, Italy physics/ In press in Env. Plann. B A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 14/17
54 What are we doing Application of MCA to large scale graphs (entire cities); A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 15/17
55 What are we doing Application of MCA to large scale graphs (entire cities); Comparison between city structure and biological systems like leafs ; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 15/17
56 What are we doing Application of MCA to large scale graphs (entire cities); Comparison between city structure and biological systems like leafs ; Elaboration of a city growth model based not only on geometrical costraint but also on centrality and retail. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 15/17
57 Summary Analysis of structural properties of planar graphs based on urban street patterns; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 16/17
58 Summary Analysis of structural properties of planar graphs based on urban street patterns; Elaboration of a method to compare different spatial graphs; A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 16/17
59 Summary Analysis of structural properties of planar graphs based on urban street patterns; Elaboration of a method to compare different spatial graphs; Analysis of city structure based on multiple centrality indices (MCA); A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 16/17
60 Summary Analysis of structural properties of planar graphs based on urban street patterns; Elaboration of a method to compare different spatial graphs; Analysis of city structure based on multiple centrality indices (MCA); Relation between centrality and commercial activities Geomarketing. A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 16/17
61 References A. Cardillo, S. Scellato, V. Latora, S. Porta,Phys. Rev. E 73 (2006) S. Scellato, A. Cardillo, V. Latora, S. Porta, Eur. Phys. Journ. B 50 (2006) 221 P. Crucitti, V. Latora and S. Porta Phys. Rev. E 73 (2006) S. Porta, P. Crucitti, V. Latora, Enviromental and Planning B 33 (2006) 705 P. Crucitti, V. Latora, S. Porta, Chaos 16 (2006) Porta S et. al. Street Centrality and Densities of Retails and Services in Bologna, Italy physics/ In press in Env. Plann. B A. Cardillo Structural properties of urban street patterns and the Multiple Centrality Assessment 17/17
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