Section: New Results

Diffusion and dynamic of complex networks

Participants : Márton Karsai [correspondant] , Éric Fleury, Christophe Crespelle.

Time varying networks and the weakness of strong ties

We analyse a mobile call dataset and find a simple statistical law that characterize the temporal evolution of users' egocentric networks. We encode this observation in a reinforcement process defining a time-varying network model that exhibits the emergence of strong and weak ties. We study the effect of time-varying and heterogeneous interactions on the classic rumor spreading model in both synthetic, and real-world networks. We observe that strong ties severely inhibit information diffusion by confining the spreading process among agents with recurrent communication patterns. This provides the counterintuitive evidence that strong ties may have a negative role in the spreading of information across networks.

Complex contagion process in spreading of online innovation [8] .

Here we analyse a dataset recording the spreading dynamics of the world's largest Voice over Internet Protocol service to empirically support the assumptions behind models of social contagion. We show that the rate of spontaneous service adoption is constant, the probability of adoption via social influence is linearly proportional to the fraction of adopting neighbors, and the rate of service termination is time-invariant and independent of the behavior of peers. By implementing the detected diffusion mechanisms into a dynamical agent-based model, we are able to emulate the adoption dynamics of the service in several countries worldwide. This approach enables us to make medium-term predictions of service adoption and disclose dependencies between the dynamics of innovation spreading and the socio-economic development of a country.

The role of endogenous and exogenous mechanisms in the formation of R&D networks [10] .

Here we propose a general modeling framework that includes both endogenous and exogenous mechanisms of in link formations in networks with tunable relative importance. The model contains additional ingredients derived from empirical observations, such as the heterogeneous propensity to form alliances and the presence of circles of influence, i.e. clusters of firms in the network. We test our model against the Thomson Reuters SDC Platinum dataset, one of the most complete datasets available nowadays, listing cross-country R&D alliances from 1984 to 2009. Interestingly, by fitting only three macroscopic properties of the network, this framework is able to reproduce a number of microscopic measures characterizing the network topology, including the distributions of degree, local clustering, path length and component size, and the emergence of network clusters. Furthermore, by estimating the link probabilities towards newcomers and established firms from the available data, we find that endogenous mechanisms are predominant over the exogenous ones in the network formation. This quantifies the importance of existing network structures in selecting partners for R&D alliances.

Controlling Contagion Processes in Time-Varying Networks [9] .

In this project we derive an analytical framework for the study of control strategies specifically devised for time-varying networks. We consider the removal/immunization of individual nodes according the their activity in the network and develop a block variable mean-field approach that allows the derivation of the equations describing the evolution of the contagion process concurrently to the network dynamic. We derive the critical immunization threshold and assess the effectiveness of the control strategies. Finally, we validate the theoretical picture by simulating numerically the information spreading process and control strategies in both synthetic networks and a large-scale, real-world mobile telephone call dataset.

Data-driven spreading for the detection of weak ties [24] .

In this work we propose a new method to infer the strength of social ties by using new data-driven simulation techniques. We qualify links by the importance they play during the propagation of information in the social structure. We apply data-driven spreading processes combined with a river-basin algorithmic method to identify links, which are the responsible to bring the information to large number of nodes. We investigate the correlations of the new importance measure with other conventional characteristics and identify their best combination through a percolation analysis to sophisticate further the assignment of social tie strengths. Finally we explore the role of the identified high importance links in control of globally spreading processes through data-driven SIR model simulations. These results point out that the size of infected population can be reduced considerably by weakening interactions through ties with high importance but zero overlap compared to strategies based on dyadic communications.

Dynamic Contact Network Analysis in Hospital Wards [18] .

We analyse a huge and very precise trace of contact data collected during 6 months on the entire population of a rehabilitation hospital. We investigate the graph structure of the average daily contact network. Our main results are to unveil striking properties of this structure in the considered hospital, and to present a methodology that can be used for analyzing any dynamic complex network where nodes are classified into groups.