The missing links in the BGP-based AS connectivity maps

PAM2003 - The Passive and Active Measurement Workshop(http://www.pam2003.org), San Diego, USA, April 2003PAM2003 - The Passive and Active Measurement Workshop(http://www.pam2003.org), San Diego, USA, April 2003PAM2003 - The Passive and Active Measurement Workshop(http://www.pam2003.org), San Diego, USA, April 2003A number of recent studies of the Internet topology at the autonomous systems level (AS graph) are based on the BGP-based AS connectivity maps (original maps). The so-called extended maps use additional data sources and contain more complete pictures of the AS graph. In this paper, we compare an original map, an extended map and a synthetic map generated by the Barabasi-Albert model. We examine the recently reported rich-club phenomenon, alternative routing paths and attack tolerance. We point out that the majority of the missing links of the original maps are the connecting links between rich nodes (nodes with large numbers of links) of the extended maps. We show that the missing links are relevant because links between rich nodes can be crucial for the network structure

The architecture of complex weighted networks

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity. Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensity of the connections. These features, however, have mainly not been considered in past studies where links are usually represented as binary states, i.e. either present or absent. Here, we study the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network. We define new appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices. This information allows us to investigate for the first time the correlations among weighted quantities and the underlying topological structure of the network. These results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks