Wspólnotowy Serwis Informacyjny Badan i Rozwoju - CORDIS

New model for scale-free networks

New Models for Scale-free Networks

Modeling the Internet and other networks is a fundamental step toward their better understanding and, in the case of technological networks, their possible improvement. Indeed, since large scale experiments on the real world are seldom possible, we must resort to synthetic graphs to study the behavior of real networks, their susceptibility to external and internal interventions and the results of improvement attempts.

Possible models must of course take into account some characterization of the microscopic mechanisms that are likely to be at work in shaping real networks. Such mechanisms are of different kinds, from technological (bandwidth requirements) to economical (providers competing for users), political (governmental regulations), physical (protein-protein interaction strengths) and others. These detailed mechanisms are unfortunately largely unknown and we must therefore mimic them by simplified model rules that have to take into account the network growth by addition of new nodes (the Internet has been growing exponentially; there are more genes and proteins in higher, more evolved organisms than in less evolved ones) and the linking mechanisms between them. During COSIN we have developed various different scale-free models with the goal of exploring how different ingredients contribute at reproducing the topological patterns observed in real networks.

One of the most important models that we have introduced tries to describe how the intrinsic properties of the nodes of the network, captured at a cartoon level by a single real variable, govern the way nodes link with each other. The results have a broad range of applicability: in the Internet, where it as been suggested that the scale-free nature of the Internet graph could be due to the scale-free size of Autonomous Systems, in turn related to the well known Zipf's law of company sizes; in protein interaction networks, where protein interactions can be detected only if they are stronger than a minimal threshold, and where the strength of a protein-protein interaction is due to the intrinsic properties of the two partners.

In the next future we plan to use this model to model in more detail the protein-protein interaction discovery process, so to understand whether the scale-free nature of the corresponding networks is real or only a distortion introduced by the experimental setup on the real network. This is a most important issue since there is growing evidence for many networks that their real structures could be different from the observed ones because of systematic errors in the measurement technique. Another, related result of COSIN is that although in some cases the scale-free nature of networks is real, the measurement process can change the perceived exponent values: besides quantifying the extent of this effect, we have also shown how to avoid it in the case of the Internet.

We have also been able to reproduce the assortativeness of social networks (peers are likely to be connected) by introducing a social-distance dependent modification of the classical "preferential attachment" rule, a further insight that reliable models for scale-free networks do need to better take into account the microscopic properties of the systems under scrutiny. More generally, we hope to have improved the awareness about some methodological problems affecting complex network research (insufficient characterization of the measurement methods and unsatisfying understanding of the system's microscopic behavior), and we plan in the next few years, to call for more effort in such direction from the community.

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