Gossiping (via mobile?) in social networks

The study of information dissemination in social networks is an important endeavour, encompassing a variety of questions ranging from the purely technological to the spread of viruses and the diffusion of ideas in human communities. In order to gain insight into these and other related questions, research has proceeded on two fronts. On the one hand, empirical studies have produced a precious data mining activity that has been able to enucleate several important properties of social networks. The advent of the web has made possible sociological studies on a scale that is unprecedented. While Milgram's famous studies on six degrees of separation involved a thousand people, modern replicas with LiveJournal, Email or Instant Messenger involve up to hundreds of millions of people, possibly heralding a new era in the social sciences [11,13,12,10]. A second front of scientific investigation concerns sophisticated mathematical modeling. A lot of activity has been devoted to developing and studying stochastic generative models for social networks that are capable to reproduce some of their salient features. In particular, the so-called preferential attachment model (henceforth PA model), intuitively introduced by Barabasi and Alberts [1] and later precisely formalized and analized by Bollobas et al. [7], is a good representation of social networks in many respects. In this model nodes arrive one after the other. Roughly speaking, when a new node arrives, m nodes are chosen randomly as neighbours, with probability proportional to their degree. The model exhibits the so-called rich-get-richer effect -- if a node has high degree now it is likely to enjoy an even higher degree in the future.

The PA model has been the object of a great deal of rigorous study by a number of authors [2,3,4,6,7,8,9]. It is known that its degree distribution follows a power-law, that its diameter is small (i.e. Θ(log n / log log n), for m ≥ 2), and that its cover time is Θ(n log n). These are all properties enjoyed by social networks. Social networks are likely to play an important role in networking and especially mobile networking in the near future. The advent of high quality mobile devices is expected to turn them into the preferred mode of accessing of the Web-- another momentous development with wide-ranging implications at the technological and societal level. Not only established social networks will be accessed via mobile devices, but new, genuinely mobile applications are likely to sprout. Thus, it seems worthwhile to study how fundamental primitives of information dissemination behave in social networks. This might bring a better understanding at various levels. From a purely networking point of view it might be possible to take advantage of the special structure of social networks and come up with simple and yet highly performing protocols. Gossiping is one of the most fundamental information diffusion primitives. Its simple, basic character makes it useful as a protocol and interesting theoretically, for one can hope to gain insight on more complex phenomena by studying it. This question can be tackled at the experimental level for instance by simulating it on various snapshots of real social networks [14].