Redundancy and Robustness of the AS-level Internet topology and its models

A comparison between the topological properties of the measured Internet topology, at the autonomous system level (AS graph), and the equivalent graphs generated by two different power law topology generators is presented. Only one of the synthetic generators reproduces the tier connectivity of the AS graph

Modal makeup of transmission eigenchannels

Transmission eigenchannels and quasi-normal modes are powerful bases for describing wave transport and controlling transmission and energy storage in disordered media. Here we elucidate the connection between these approaches by expressing the transmission matrix (TM) at a particular frequency as a sum of TMs for individual modes drawn from a broad spectral range. The wide range of transmission eigenvalues and correlation frequencies of eigenchannels of transmission is explained by the increasingly off-resonant excitation of modes contributing to eigenchannels with decreasing transmission and by the phasing between these contributions

The Rich-Club Phenomenon In The Internet Topology

We show that the Internet topology at the Autonomous System (AS) level has a rich--club phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The rich--club is a core tier that we measured using the rich--club connectivity and the node--node link distribution. We obtained this core tier without any heuristic assumption between the ASes. The rich--club phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured rich--club of the AS graph with networks obtained using the Barab\'asi--Albert (BA) scale--free network model, the Fitness BA model and the Inet--3.0 model.Comment: To be appeared in the IEEE Communications Letter

Accurately modeling the Internet topology

Based on measurements of the Internet topology data, we found out that there are two mechanisms which are necessary for the correct modeling of the Internet topology at the Autonomous Systems (AS) level: the Interactive Growth of new nodes and new internal links, and a nonlinear preferential attachment, where the preference probability is described by a positive-feedback mechanism. Based on the above mechanisms, we introduce the Positive-Feedback Preference (PFP) model which accurately reproduces many topological properties of the AS-level Internet, including: degree distribution, rich-club connectivity, the maximum degree, shortest path length, short cycles, disassortative mixing and betweenness centrality. The PFP model is a phenomenological model which provides a novel insight into the evolutionary dynamics of real complex networks.Comment: 20 pages and 17 figure