Gautier Krings

Urban gravity: a model for inter-city telecommunication flows

We analyze the anonymous communication patterns of 2.5 million customers of a Belgian mobile phone operator. Grouping customers by billing address, we build a social network of cities that consists of communications between 571 cities in Belgium. We show that inter-city communication intensity is characterized by a gravity model: the communication intensity between two cities is proportional to the product of their sizes divided by the square of their distance.

A survey of results on mobile phone datasets analysis

In this paper, we review some advances made recently in the study of mobile phone datasets. This area of research has emerged a decade ago, with the increasing availability of large-scale anonymized datasets, and has grown into a stand-alone topic. We survey the contributions made so far on the social networks that can be constructed with such data, the study of personal mobility, geographical partitioning, urban planning, and help towards development as well as security and privacy issues.

Significant Scales in Community Structure

Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem shows foremost in multi-resolution methods. We here introduce an efficient method for scanning for resolutions in one such method. Additionally, we introduce the notion of “significance” of a partition, based on subgraph probabilities. Significance is independent of the exact method used, so could also be applied in other methods, and can be interpreted as the gain in encoding a graph by making use of a partition. Using significance, we can determine “good” resolution parameters, which we demonstrate on benchmark networks. Moreover, optimizing significance itself also shows excellent performance. We demonstrate our method on voting data from the European Parliament. Our analysis suggests the European Parliament has become increasingly ideologically divided and that nationality plays no role.

Scaling Behaviors in the Communication Network between Cities

Researchers have been unable to predict the large-scale features of aggregate social networks. We analyze the anonymous communications patterns of 2.5 million customers of a Belgian mobile phone operator. With these communications, we construct the social network of the customers, that we call microscopic network. Grouping customers together by billing address city, we obtain a social network of cities, which we call the macroscopic network, is built from 571 towns and cities in Belgium. Using the mobile phone network, we are able to show that the macroscopic network has both a degree distribution and edge weight distribution with lognormal characteristics. We find that inter-city communications can be characterized by a gravity model: the intensity of communication between two cities is proportional to the product of the two populations divided by the square of the distance between them. Furthermore, we observe that intra-urban communications scale superlinearly with city population.

Role of second trials in cascades of information over networks

We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with probability p_{1} after their first contact with the information and with probability p_{2} at all subsequent contacts. The diffusion starts from one random node and leads to a cascade of infection. It is shown that first and subsequent trials play different roles in the propagation and that the size of the cascade depends in a nontrivial way on p_{1} , p_{2} , and on the network structure. Second trials are shown to amplify the propagation in dense parts of the network while first trials are dominant for the exploration of new parts of the network and launching new seeds of infection.

Sensitivity analysis of a branching process evolving on a network with application in epidemiology

We perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the network. We then apply our results to the early stages of an influenza-like epidemic spreading among a set of cities connected by air routes in the United States. We also consider vaccination and analyze the sensitivity of the total size of the epidemic with respect to the fraction of vaccinated people. Our analysis shows that the epidemic growth is more sensitive with respect to transmission rates within cities than travel rates between cities. More generally, we highlight the fact that branching processes offer a powerful stochastic modeling tool with analytical formulas for sensitivity which are easy to use in practice.