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1 year ago

# arXiv:1604.04722v2

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## degree distribution 10 4

degree distribution 10 4 10 0 10 1 10 2 10 3 10 4 10 3 frequency 10 2 10 1 10 0 degree Figure 2: Degree distribution of the city network node. It turns out that cities in the global network of interlocking directorates are interconnected with an average distance of only 2.83. The distribution of average distances shown in Figure 3 indicates that the global city network is relatively well connected through interlocking directorates; it is indeed a smallworld network (Kleinberg, 2000). A next step is to consider those cities that are most central in this global city network. Table 1 shows the distribution of the eccentricity values. On the rightmost end of the eccentricity spectrum there are the cities that are least well connected. The largest eccentricity score is 7, meaning that those cities are 7 steps away of at least one other city in the network. We can say these cities form the periphery. There are only 37 nodes in this periphery, which upon manual inspection appears to mainly consist of smaller businesses in rural areas of Russia and the United States. More interesting in Table 1 is the lowest value of eccentricity in the network. This value is called the radius, and the set of nodes with an eccentricity distance distribution 10 8 10 7 10 6 10 9 0 1 2 3 4 5 6 7 frequency 10 5 10 4 10 3 10 2 10 1 10 0 distance Figure 3: Distance distribution of the city network 12

Table 1: Eccentricity distribution of the city network Eccentricity value 4 5 6 7 Frequency 409 20782 3519 37 value equal to this this radius are in the center of the network. The cities in the center of the network have an eccentricity of 4, meaning that they can reach all other cities in at most four steps. This group consists of 409 cities: 1.65% of the nodes in the city network. Figure 4 shows the network between this set of central cities. For visibility reasons, we have chosen to only show edges when two cities are connected by more than 20 board interlocks. One observation clearly stands out: London is right in the center of this group of central cities. It is the most central city in the global board interlock network by both degree and betweenness measures (see Table 2). It is followed by high degree centrality cities Paris, Madrid, Brussels, Milano, Luxembourg and Barcelona. Sao Paulo and Moscow score among the top five cities ranked by betweenness centrality, since they connect their emerging markets Figure 4: Visualization of the center (eccentricity value 4) of the city network 13

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