Community core detection in transportation networks

This work analyzes methods for the identification and the stability under perturbation of a territorial community structure with specific reference to transportation networks. We considered networks of commuters for a city and an insular region. In both cases, we have studied the distribution of commuters’ trips (i.e., home-to-work trips and vice versa). The identification and stability of the communities’ cores are linked to the land-use distribution within the zone system, and therefore their proper definition may be useful to transport planners.

Figure 1

This picture (a) describes the situation in which the modularity of a network has been maximized. Starting from this state it is possible to determine the list of negative $dQ$ values associated to each node assuming to move it in every other community. As a matter of fact, if a node (in this picture we consider as example the node “a”) would change its belonging to the community in which has been placed during the modularity optimization, the modularity of the network would obviously decrease, as shown in (b) and (c). This negative variation is related to the fact that, for each change in the partition, like the ones depicted in (b) and (c), the total number of links internal to the communities is always smaller with respect to the one associated to (a).

Figure 2

$dQ$ frequency plots relative to four communities detected for the city of Atlanta, GA. The correlation coefficients of the exponential fits are (from top right to bottom left, respectively) 0.956, 0.946, 0.937, and 0.933. In general, these distributions are the typical $dQ$ frequency distribution inside a community (provided there are enough nodes to perform an exponential fit).

Figure 3

Cores detected for the city of Atlanta, GA, using a threshold equal to double the typical length of the exponential distribution of the $dQ$ frequencies.

Figure 4

Geographical versus topologic representation of the the Sardinian intermunicipal commuting network (SMCN): the nodes (red points) correspond to the towns, while the links to a flow value larger than 50 commuters between two towns.

Figure 5

Extension of the zone system in the ARC model. Only the links with a weight greater than 250 have been shown. Each point is a centroid of a TAZ.

Figure 6

Gradient plot for population in the ARC model.

Figure 7

Gradient plot for employment in the ARC model.

Figure 8

$dQ$ plot for the network related to employment in the SMCN network.

Figure 9

A comparison between the current provincial division (CA $=$ Cagliari, CI $=$ Carbonia-Iglesias, VS $=$ Medio Campidano, OR $=$ Oristano, OG $=$ Ogliastra, NU $=$ Nuoro, SS $=$ Sassari, and OT $=$ Olbia-Tempio) of the Sardinia region, Italy, and the result of the community detection.

Figure 10

$dQ$ plot for the ARC network.

Figure 11

$dQ$ and community boundary plot for the ARC network.

Figure 12

The correlation between $dQ$ and in-strength is equal to 0.78.