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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
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