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Complex Network Metrology

In order to study some complex networks like the Internet, the Web, social networks or biological networks, one first has to explore them. This gives a partial and biased view of the real object, which is generally assumed to be representative of the whole. However, up to now nobody knows how and how much the measure influences the results. Using the example of the Internet and a rough model of its exploration process, we show that the way a given complex network is explored may strongly influence the observed properties. This leads us to argue for the necessity of developing a science of metrology of complex networks. Its aim would be to study how the partial and biased view of a network relates to the properties of the whole network. Introduction. Some complex networks of high interest can only be known after an exploration process. This is in particular true for the Internet (interconnection of computers), the Web (links between pages), social networks (acquaintance relations for example), and biological networks (brain topology or protein interactions for example). There have been many studies published on these objects, see for instance [3, 6, 8, 10, 16, 17, 19, 21, 22, 23, 26]. Most of them rely on from partial views obtained using various, and often intricate, exploration methods. Until now, the approach generally used is to obtain views as large as possible and then assume that they are (representative of) the whole, see for instance [12, 15, 20, 28]. However, except in a few limited cases [12, 18, 27], nobody has any idea on the bias introduced by the partial exploration methods and the influence it may have on the results. We show here that this bias may be very important, even under some very optimistic assumptions. Using the representative example of the Internet topology, we show how some natural models of the exploration process give very different views of a given network, which proves that the way one explores a complex network has a strong influence of the properties of the obtained view. We therefore insist on the necessity of developing a theory of complex network metrology Its aim would be to study how the partial and biased view of a network relates to the properties of the whole network. Our global approach is the following: we consider a (known) network G, we simulate an exploration of this network to obtain a view G of it, and then we compare the two objects.