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, The Belgian urban regions as developed by Vanderstraeten and Van Hecke (2019)

. .. Bcr,

, A general organisation of the BCR

A. , B. , and C. .. , Partitions detected using different values of ?, multi-scale modularity, p.26

. .. Compactness-of-communities, 26 2.3 Proportion of in-commuters working in the municipality of Brussels (A) and in the municipality of Leuven (B), p.28

. .. , Weighted degree of the municipalities within the former province of Brabant (including self-loops)

, Partitions detected within the former province of Brabant for different value of ?: A = 0

. .. F-=-2,

, Number of times that each partition is detected for different values of ?

, Number of communities detected, internal and external weighted edges for each partition

. .. , 41 2.11 Communities detected by the Louvain Method (A) and by the Infomap algorithm (B), computed for Belgium but presented for the former province of Brabant, Partitions detected in the former province of Brabant (A) with and (B) without self-loops (eight communities)

, Renumbering of the communities for five runs of the Louvain Method

, Belgium (A) with and (B) without selfloops (10 communities)

, Theoretical network of 44 entities

, Anabel method applied to the theoretical network in iteration 32 (high) and 42 (low)

, Louvain Method applied to the theoretical network, p.53

, Comparison of the results for the methods Anabel and Louvain on an imaginary data set

, Residential basins based on the Anabel method -authorized inter cluster aggregation situation after 562 iterations, p.57

, A) Residential basins based on the Anabel method -authorized inter cluster aggregation after 290 iterations -B) Residential basins based on the Anabel method -authorized inter cluster aggregation after 536 iterations

, A) Communities detected using the Louvain Method (absolute date and ? = 1) -B) Communities detected using the Louvain Method (relative data and ? = 1.25)

, Comparison of partitions from the Louvain Method and Anabel, vol.60

. Blondel, ) regional city, (2) major city , (3) provincial border, Phone basins based on cell phones billing addresses, 2010.

, 2 Variation of Information (VI) versus ? values for commuting movements between municipalities

, Proportion of internal and external edges and number of communities for different values of ? for the 2011 commuting movements (at municipality level)

, Optimal partition in communities when nodes are municipalities (A -? = 0.9) and statistical sectors (B -? = 1.0) -2011 commuting data

, Square matrix of commuting movements appearing in Belgium, p.76

, Commuting communities for different values of ? (A = 0,7 -B = 0,8 -C = 1,0 -D = 2,0)

, Migration communities when ? = 1.0. Hatched municipalities are those where the robustness is < 90%

, Hatched municipalities are those where the robustness is < 90%. 80 4.10 Communities based on commutes to and from the workplace in 2011, on the scale of the statistical sectors for ? = 1 (A) and municipalities for ? = 1 (B), Migration communities when ? = 3.0 (A) and ? = 8.0 (B)

. .. , 2 (Brussels) and all of the other Belgian communities (a), Flow of commutes between communities 1 (Leuven), p.83

, Principal commuting movements appearing in the former province of Brabant

, Square matrix of commuting movements appearing in the former province of Brabant

, Optimal division into communities (? = 1), based on residential migration data from, vol.87, 2011.

. .. , Railway network versus travel-demand network (cities and travel flows symbols proportional to their size/volume; the colour of each train station represents its community), p.93

, 2 (a) Belgium administrative and urban structure, and (b) location of the train stations

, Rank -size distribution of the iRail requests by (a) origins and (b) destinations

. .. , Communities in the iRail dataset for the (a) General and (b) No Brussels subsets (in legend: O = Other communities, with less than 5 nodes; N = Not present in the data set), p.100

. .. , Communities detected in the iRail dataset during (a) Weekdays and (b) Weekends (in legend: O = Other communities, with less than 5 nodes; N = Not present in the data set), p.103

, Dutch and in (b) French (in legend: O = Other communities, with less than 5 nodes; N = Not present in the data set), Communities in the iRail dataset for the requests made in (a), p.106

, Chorematic representation of the travel demand by train in Belgium

, 9 robustness of the communities by subset of the iRail data set (number of times, over the 1,000 iterations that a node is affected to its final community, in %)

, Transformation of raw GPS points into trips and Origin-Destination segments

, 2 Number of journeys detected for different duration of stops, p.125

, Appearing and disappearing of the trucks

, Main steps of the detection and correction of inconsistencies, according to the occurrence of errors observed for each ID, p.127

. .. , Trucks in Belgium: average daily traffic, p.130

. .. , Trucks in Belgium: daily averaged connections, p.131

, Absolute daily traffic (a) and relative daily traffic (b) of trucks having the Brussels agglomeration as Origin or Destination, p.134

, Absolute OD (a) and relative (b) of trucks having the Brussels agglomeration as Origin or Destination

, Proportion of GPS points emitted by countries of registration by day

, Daily evolution of the proportion of A) the number of trucks per hour and B) the number of GPS points emitted per hour, for the four defined categories of trucks

, A) general network, B) places visited more than 10 times, C) intra trucks, D) inter trucks, E) Belgian trucks, and, F) foreign trucks

, A) general network, B) places visited more than 10 times, C) intra trucks, D) inter trucks, E) Belgian trucks, and, F) foreign trucks

, 151 7.2 Location of the studied calls within the Former province of Brabant (in % of the total), Number of mobile phone calls per day (A) and per hour on one working day (B)

. .. , Mobile telephony areas on the scale of Thiessen polygons around antennas (A) and on the scale of municipalities (B), p.153

, Day (B), Weekend (C) and Night (D), Mobile phone calls: communities of antennas detected for the four predefined networks: General (A)

, Communities of antennas: uncertainty of the classification of the day (A) and night (B) partitions

, Circular graph and the associated O-D matrix (expressed in %) for all phone calls (General)

, Vrije Universiteit Brussel (VUB), 10. Audi Forest and other industrial areas, 11. Bois de la Cambre, Mobile telephony areas (close-up of the centre of Brussels) during the day (A) and night (B) where locations on the map are: 1. Marché matinal et centre Européen de fruits et de légumes, vol.2

, Temporal variation of phone activity: A: number of calls emitted by four randomly selected antenna, B: cumulated calls emitted by each antenna, for all antennas, C: average cumulated calls for each cluster of antennas

. .. Activity, 161 7.11 Zoom on Brussels (A) and Ottignies Louvain-la-Neuve (B) where locations on the map are: 1 the Ixelles cemetery, 2 is the Eugène Flagey Place, 3 the Grand Place, 4 VW-Audi car factory (Forest), 5 Brussels Airport (Zaventem), 6 and 7 Sport centres, 8 Concert Hall (Forest National), 9 Ottignies, 10 family residential area, 11 student residential area, Clusters of antennas based on logistic curve characteristics of their hourly workday's

, Clusters of statistical sections based on socio-economic variables, vol.164

, Composition of each cluster of the concluding partition mapped in Figure 7

, A concluding partition of the Metropolitan area of Brussels based on the three classifications, vol.170

, Creation of the new BSU based on two different spatial entities. 173 List of Tables

, Weighted degree size-ranked municipalities within the former province of Brabant

. N-m-i, values between partitions resulting from different ?-values. 33 2.3 Compactness of the communities detected in the province of Brabant for different values of ?

. .. , Compactness values of the communities detected with the inclusion of or without self-loops (the number of municipalities within communities is given in brackets), p.40

, Number of entities composing each group (basin/community), according to the method used and the number of groups selected (2 or 3)

, 2 Composition of basins (Anabel) and communities (Louvain Method), p.61

. .. , Index c comparing basins and communities, p.62

, NMI values between pairs of partitions (municipality level), p.81

, Comparing solutions for partitions based on municipalities, p.81

, Descriptive statistics of the subsets

. .. , Average travel distance alongside the railway network (km; between bracket = standard deviation), p.99

, Average value of the spatial contiguity index (between bracket = standard deviation)

. .. , Robustness of the communities (in %; high values = high robustness; between bracket = standard deviation), p.101

. .. , Central node of the communities by betweenness centrality (between bracket = name of the train station), p.114

. .. , 124 LIST OF TABLES 6.2 Retained information after the main filtering, cleaning and validation steps

. .. , NMI measured between pairs of calls network, p.155

, Pearson correlation coefficients between the variables, p.172