The type of business relationships between the Internet autonomous systems (AS) determines the BGP inter-domain routing. Previous works on inferring AS relationships relied on the connectivity information between ASes. In this paper we infer AS relat
ionships by analysing the routing polices of ASes encoded in the BGP attributes Communities and the Locpref. We accumulate BGP data from RouteViews, RIPE RIS and the public Route Servers in August 2010 and February 2011. Based on the routing policies extracted from data of the two BGP attributes, we obtain AS relationships for 39% links in our data, which include all links among the Tier-1 ASes and most links between Tier-1 and Tier-2 ASes. We also reveal a number of special AS relationships, namely the hybrid relationship, the partial-transit relationship, the indirect peering relationship and the backup links. These special relationships are relevant to a better understanding of the Internet routing. Our work provides a profound methodological progress for inferring the AS relationships.
During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid expansion in topology. The size of the Internet becomes enormous, yet the network is very `small in the sense that it is ex
tremely efficient to route data packets across the global Internet. This paper provides a brief review on three fundamental properties of the Internet topology at the autonomous systems (AS) level. Firstly the Internet has a power-law degree distribution, which means the majority of nodes on the Internet AS graph have small numbers of links, whereas a few nodes have very large numbers of links. Secondly the Internet exhibits a property called disassortative mixing, which means poorly-connected nodes tend to link with well-connected nodes, and vice versa. Thirdly the best-connected nodes, or the rich nodes, are tightly interconnected with each other forming a rich-club. We explain that it is these structural properties that make the global Internet so small.
In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the nodes importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e. if two node
s are connected, they tend to have similar node degrees, suggesting that people tend to mix with those of comparable prominence. In this paper, we report the second-order assortative mixing in social networks. If two nodes are connected, we measure the degree correlation between their most prominent neighbours, rather than between the two nodes themselves. We observe very strong second-order assortative mixing in social networks, often significantly stronger than the first-order assortative mixing. This suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same. This is also true if we measure the average prominence of neighbours of the two people. This property is weaker or negative in non-social networks. We investigate a number of possible explanations for this property. However, none of them was found to provide an adequate explanation. We therefore conclude that second-order assortative mixing is a new property of social networks.
The topological structures of the Internet and the Web have received considerable attention. However, there has been little research on the topological properties of individual web sites. In this paper, we consider whether web sites (as opposed to th
e entire Web) exhibit structural similarities. To do so, we exhaustively crawled 18 web sites as diverse as governmental departments, commercial companies and university departments in different countries. These web sites consisted of as little as a few thousand pages to millions of pages. Statistical analysis of these 18 sites revealed that the internal link structure of the web sites are significantly different when measured with first and second-order topological properties, i.e. properties based on the connectivity of an individual or a pairs of nodes. However, examination of a third-order topological property that consider the connectivity between three nodes that form a triangle, revealed a strong correspondence across web sites, suggestive of an invariant. Comparison with the Web, the AS Internet, and a citation network, showed that this third-order property is not shared across other types of networks. Nor is the property exhibited in generative network models such as that of Barabasi and Albert.
