Empirical analysis of Internet telephone network: from user ID to phone

In order to study the interaction between different communication networks, in this paper, personal computer (PC)-to-phone log data in the year of 2007 are collected from UUCALL database and described as an ID-to-phone bipartite network (ItPBN). The ItPBN contains one giant component (GC) and a large number of satellitic components (SCs), both of which are carefully analyzed. It is found that the ItPBN has power-law incoming/outgoing degree distributions as well as a power-law clustering function (by proposing a new definition of clustering coefficient) indicating a hierarchical and modular structure of the ItPBN. Furthermore, the fact that most of the weak links always surrounding those ID nodes of large degree in the GC suggests that weak links may be more important to keep the structure of the GC than those strong ones. More interestingly, it is also revealed that there is strong correlation between many statistical properties of different SCs and their size, these extra information may be very useful in modeling the ItPBN in the future.