Section: New Results

Network Science

Participants : Eitan Altman, Konstantin Avrachenkov, Mahmoud El Chamie, Julien Gaillard, Philippe Nain, Giovanni Neglia, Marina Sokol.

Epidemic models of propagation of content

In [15] , E. Altman and P. Nain, in collaboration with Y. Xu (Maestro member at the time of submission) and A. Shwartz (Technion, Israel), focus on the propagation of content in peer-to-peer (P2P) networks. They first study the transient behavior of some P2P networks whenever information is replicated and disseminated according to epidemic-like dynamics. They then use the insight gained from the previous analysis in order to predict how efficient could measures taken against P2P networks be. They first introduce a stochastic model which extends a classical epidemic model, and characterize the P2P swarm behavior in presence of free riding peers. They then study a second model in which a peer initiates a contact with another peer chosen randomly. In both cases the network is shown to exhibit phase transitions: a small change in the parameters causes a large change in the behavior of the network. The authors show, in particular, how phase transitions affect measures of content providers against P2P networks that distribute non-authorized music, books or articles, and what is the efficiency of counter-measures. In addition, this analytic framework can be generalized to characterize the heterogeneity of cooperative peers.

The design of recommendation systems (RS) for social networks

Recommendation systems take advantage of products and users information in order to propose items to targeted consumers. In [50] , J. Gaillard, E. Altman, M. El Bèze and E. Ethis (both from Univ. Avignon) propose a framework to overcome the usual scalability issues of nowadays systems. The system includes a dynamic adaptation to enhance the accuracy of rating predictions by applying a new similarity measure. They perform several experiments on films data from Vodkaster, showing that systems incorporating dynamic adaptation improve significantly the quality of recommendations compared to static ones.

In [51] the same authors propose new modifications of the recommendation algorithm that allow not only to present a recommendation but also to propose a list of words which appeared frequently in recommendations of other people who watched that film and who have been identified to have similar preferences, according to their opinions on common movies.

Network centrality measures

A class of centrality measures called betweenness centralities reflects degree of participation of edges or nodes in communication between different parts of the network. The original shortest-path betweenness centrality is based on counting shortest paths which go through a node or an edge. One of shortcomings of this metric is that it ignores the paths that might be one or two hops longer than the shortest paths, while the edges on such paths can be important for communication processes in the network. To rectify this shortcoming a current flow betweenness centrality has been proposed. Similarly to the shortest-path betweenness, it has prohibitive complexity for large size networks. In [42] K. Avrachenkov, N. Litvak (Univ. of Twente, the Netherlands), V. Medyanikov (St. Petersburg State Univ., Russia) and M. Sokol propose and analyze two regularizations of the current flow betweenness centrality, $\alpha$-current flow betweenness and truncated $\alpha$-current flow betweenness, which can be computed fast and correlate well with the original current flow betweenness. In particular, the new centrality measures indicate well vulnerability of a network.

Average consensus protocols

Information can flow in a network through communication links connecting the nodes. Not all the links have the same importance and it is common in complex networks to distinguish “weak” links/ties and “strong” ones. Depending on the specific network, the strength of a link connecting two nodes can be quantified by its transmission capacity, the inter-meeting rate between the two nodes, the level of mutual trust of the two nodes, etc.. The topology of connections and the strength of the links are two factors that affect the speed of spread of information in the network. In [63] , M. El Chamie and G. Neglia in collaboration with L. Severini (student at Univ. of Nice Sophia Antipolis, France) have shown that the topology can have stronger effect on the information spread than the strength of the links. In particular, they have considered an iterative belief propagation process as in average consensus protocols where each node in the network has a certain belief (a real number) that is updated iteratively by the weighted average of the nodes' belief and the ones they connected to. They have shown by simulations on random graphs that a topological optimization can have a significant faster spread of beliefs than any weight selection optimization techniques. They have also given a 2-hop message averaging that performs faster convergence than standard algorithms.

The activity on “Reducing communication overhead of average consensus protocols”, described in Maestro 's 2012 activity report has lead to the publication [49] .