Ventajas

Blondel et al. (2010) use mobile phone call data from Belgium to find regions in a network of municipalities. The network is formed by aggregating the individual level interactions, as discovered from six months of mobile phone call logs, to the billing address municipality of each customer. Two different measures of interaction are used to produce two separate directed networks. In the first case the ‘relative frequency’ is used where the weight of the edge from municipality A to B is given by WAB

PAPB where WAB is the number of calls made by

customers in A to those in B and PAis the number of customers in municipality

pairs of municipalities even if the pairs of municipalities have different sizes and if the market shares of the provider in the municipalities are different”. In the second case the network is constructed using the average duration of calls from A to B.

Community detection on both of these networks using the Louvain al- gorithm results in surprisingly spatially contiguous regions despite the fact that the method makes no assumptions about community composition based on spatial distance. In the first case using the relative frequency the method finds 17 distinct communities or regions while in the second case using average duration it finds only two regions. Interestingly in the second case the regions correspond very closely to the two distinct linguistic regions of the country. In this case only 2% of all communications are between customers in different regions.

The authors acknowledge that the results may depend on the ordering of the edges in the input to the method. They check the robustness of the method by running the algorithm on 100 random permutations of the edge order for each network. For the first network they find that 91% of municipalities remain in the same communities and those that move are always the ones on the borders between communities. For the network based on average call duration they find that there is no variation of the communities found. Furthermore they note that moving any municipality from its assigned community to any other community reduces the modularity.

Ratti et al. (2010) use landline phone call logs in a similar manner to identify regions in Britain by using “the network’s characteristics to partition the geographic space underneath the network’s topology”. One month of data is used in this study to create a network of interactions aggregated to 3042 square spatial units of 9.5km by 9.5km. The edge weights in this network are defined using the total call time between nodes A and B in an effort to take into

account local population density. The authors apply spectral optimisation of modularity to this network and initially identify a partition of 23 communities with a modularity of 0.58. 13 of these communities are spatially contiguous while the others are scattered individual pixels. After applying Kernighan-Lin steps and enforcing spatial contiguity the modularity increases to 0.60 with 14 contiguous regions. The authors assert that the results show “that not only population distribution in space but also regional boundaries affect the patterns of communication”.

They acknowledge the finding of Good et al. (2010) that modularity has many local maxima and that these are likely to be structurally different to each other. In order to identify alternative local maxima they apply five variations of modularity optimisation techniques to the same network and compare the results. Each result has between 12 and 14 spatially contiguous communit- ies and modularities between 0.606 and 0.613. The authors note that there is some variation along the boundaries but the regions are always spatially contiguous and centred around the same geographic locations. However if we look closely at the mapped outputs of each of these five methods we see that there is significant variation in the community sizes and boundaries between the results. This is even true for the best three results which have practically insignificantly different modularity scores of 0.611474 0.611636 and 0.613114. As a final output the authors take the intersection of the results of all five methods to identify 11 core regions where the nodes are always clustered to- gether. These 11 cores contain 85% of the total population. The authors of this study also acknowledge the resolution limit that affects modularity optim- isation but claim their analysis does not suffer because they are interested in detecting large regions.

Calabrese et al. (2011a) use the same modularity optimisation method as in the previous study to detect communities in network of counties in the USA

using one month of CDR data. In this study separate networks are created using for calls and SMS to investigate the difference in the effect of distance on both modes of communication. As with the previous study, the total call time is used for the edge weights between counties for the first network while the number of messages between counties is used in the second network but each of these values is first normalised to account for differing market shares in different counties. The edge weight for counties A and B is given as WAB_CPA_ACPB_B

where PA is the population of county A and CA is the number of customers

in county A. The method finds 26 communities for the call time network and 28 communities for the SMS network. While a number of the borders and aggregations of counties do change for the two modes of communication it is questionable as to whether these changes are significant or merely represent two local maxima of the modularity for similar networks.

In (Walsh & Pozdnoukhov, 2011) this author uses the Louvain method in conjunction with the tracking method of (Greene et al., 2010) in an attempt to investigate the dynamics of spatial communities Dublin. In this case the cell tower is used as the unit of spatial aggregation with each call creating a link between the towers used by the caller and callee at the time of the call. A series of network snapshots are created by aggregating over two hour periods in five weekdays of data with the Louvain method applied independently to each of these snapshots. The tracking method is then used to identify the change in each community over time. While this study appears to show that these communities do indeed change over the course of the day it unfortunately suffers from the problems described in Section 4.2.7. Later analysis has shown that the different community structure detected in each snapshot is entirely due to the Louvain method finding local optimum solutions. This is confirmed by the fact that there is actually a single partition that has the highest modularity on all network snapshots.