Section: New Results

Dynamic network analysis

During the last decade, the study of large scale complex networks has attracted a substantial amount of attention and works from several domains: sociology, biology, computer science, epidemiology. This emerging domain has proposed a large set of tools that can be used on any complex network in order to get a deep insight on its properties and to compare it to other networks. Such fundamental properties are used as characterization parameters in the study of various problems such as virus spreading in the epidemiology context, or information / innovation diffusion for instance. Whereas most of such complex networks are inherently dynamic, this aspect has less been studied. Most approaches consider growing models , such as the preferential attachment model or analyze the aggregation of all interactions. Both approaches may miss the real dynamic behavior while there is a strong need for dynamic network models in order to sustain protocol performance evaluations and fundamental analyzes.

In [10] , we address the description and the simulation of sensor mobility networks (interaction networks like the one we'll need to analyze within the MOSAR context). The proposed methods come from various research domains (signal processing, graph theory and data mining). This emphasizes the necessity of interdisciplinary research since dynamic networks are becoming a central point of interest, not only for engineers and computer scientists but also for people in many other fields.

We introduce some simple methods to describe the network dynamics and propose models of dynamic networks :

1. We study graph properties as function of time to provide an empirical statistical characterization of the dynamics.

2. We also compute global indicators from the dynamics of the network (connected components, triangles, and communities).

3. We propose models to perform random dynamic networks simulations.

The descriptive analysis show that link (or edge) creation and deletion processes is mostly independent of other graph properties and that such networks exhibit a large number of possible configurations, from sparse to dense. From those observations, we propose simple yet accurate models that allow to generate random mobility graphs with similar temporal behavior as the one observed in experimental data.

In [11] we study another dynamic complex network comming from community shared bicycle systems, namely the Vélo'v program launched in Lyon in May 2005. Such a network is a public transportation programs that can be studied as a complex system composed of interconnected stations that exchange bicycles. They generate digital footprints that reveal the activity in the city over time and space, making possible a quantitative analysis of people's movements. A careful study relying on nonstationary statistical modeling and data mining is done to first model the time evolution of the dynamics of movements with V´elo'v, that is mostly cyclostationary over the week with nonstationary evolutions over larger time-scales, and second to disentangle the spatial patterns to understand and visualize the flows of V´elo'v bicycles in the city. This study gives insights about social behaviors of the users of this intermodal transportation system, the objective being to help in designing and planning policy in urban transportation.