Chinese Internet AS-level Topology

We present the first complete measurement of the Chinese Internet topology at the autonomous systems (AS) level based on traceroute data probed from servers of major ISPs in mainland China. We show that both the Chinese Internet AS graph and the global Internet AS graph can be accurately reproduced by the Positive-Feedback Preference (PFP) model with the same parameters. This result suggests that the Chinese Internet preserves well the topological characteristics of the global Internet. This is the first demonstration of the Internet's topological fractality, or self-similarity, performed at the level of topology evolution modeling.Comment: This paper is a preprint of a paper submitted to IEE Proceedings on Communications and is subject to Institution of Engineering and Technology Copyright. If accepted, the copy of record will be available at IET Digital Librar

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

Understanding the internet topology evolution dynamics

The internet structure is extremely complex. The Positive-Feedback Preference (PFP) model is a recently introduced internet topology generator. The model uses two generic algorithms to replicate the evolution dynamics observed on the internet historic data. The phenomenological model was originally designed to match only two topology properties of the internet, i.e. the rich-club connectivity and the exact form of degree distribution. Whereas numerical evaluation has shown that the PFP model accurately reproduces a large set of other nontrivial characteristics as well. This paper aims to investigate why and how this generative model captures so many diverse properties of the internet. Based on comprehensive simulation results, the paper presents a detailed analysis on the exact origin of each of the topology properties produced by the model. This work reveals how network evolution mechanisms control the obtained topology properties and it also provides insights on correlations between various structural characteristics of complex networks.Comment: 15 figure

Ricci Curvature of the Internet Topology

Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core congestion and route reliability. In this work we analyze the discrete Ricci curvature of the Internet, defined by Ollivier, Lin, etc. Ricci curvature measures whether local distances diverge or converge. It is a more local measure which allows us to understand the distribution of curvatures in the network. We show by various Internet data sets that the distribution of Ricci cuvature is spread out, suggesting the network topology to be non-homogenous. We also show that the Ricci curvature has interesting connections to both local measures such as node degree and clustering coefficient, global measures such as betweenness centrality and network connectivity, as well as auxilary attributes such as geographical distances. These observations add to the richness of geometric structures in complex network theory.Comment: 9 pages, 16 figures. To be appear on INFOCOM 201

Modeling the Internet's Large-Scale Topology

Network generators that capture the Internet's large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet's evolution. By combining the most extensive data on the time evolution, topology and physical layout of the Internet, we identify the universal mechanisms that shape the Internet's router and autonomous system level topology. We find that the physical layout of nodes form a fractal set, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently employed exponential laws. The universal parameters that we extract significantly restrict the class of potentially correct Internet models, and indicate that the networks created by all available topology generators are significantly different from the Internet

Topology Adaption for the Quantum Internet

In the quantum repeater networks of the quantum Internet, the varying stability of entangled quantum links makes dynamic topology adaption an emerging issue. Here we define an efficient topology adaption method for quantum repeater networks. The model assumes the random failures of entangled links and several parallel demands from legal users. The shortest path defines a set of entangled links for which the probability of stability is above a critical threshold. The scheme is utilized in a base-graph of the overlay quantum network to provide an efficient shortest path selection for the demands of all users of the network. We study the problem of entanglement assignment in a quantum repeater network, prove its computational complexity, and show an optimization procedure. The results are particularly convenient for future quantum networking, quantum-Internet, and experimental long-distance quantum communications.Comment: 17 pages, Journal-ref: Quant. Inf. Proc. (2018