Beyond Node Degree: Evaluating AS Topology Models

This is the accepted version of 'Beyond Node Degree: Evaluating AS Topology Models', archived originally at arXiv:0807.2023v1 [cs.NI] 13 July 2008.Many models have been proposed to generate Internet Autonomous System (AS) topologies, most of which make structural assumptions about the AS graph. In this paper we compare AS topology generation models with several observed AS topologies. In contrast to most previous works, we avoid making assumptions about which topological properties are important to characterize the AS topology. Our analysis shows that, although matching degree-based properties, the existing AS topology generation models fail to capture the complexity of the local interconnection structure between ASs. Furthermore, we use BGP data from multiple vantage points to show that additional measurement locations significantly affect local structure properties, such as clustering and node centrality. Degree-based properties, however, are not notably affected by additional measurements locations. These observations are particularly valid in the core. The shortcomings of AS topology generation models stems from an underestimation of the complexity of the connectivity in the core caused by inappropriate use of BGP data

Power Grid Network Evolutions for Local Energy Trading

The shift towards an energy Grid dominated by prosumers (consumers and producers of energy) will inevitably have repercussions on the distribution infrastructure. Today it is a hierarchical one designed to deliver energy from large scale facilities to end-users. Tomorrow it will be a capillary infrastructure at the medium and Low Voltage levels that will support local energy trading among prosumers. In our previous work, we analyzed the Dutch Power Grid and made an initial analysis of the economic impact topological properties have on decentralized energy trading. In this paper, we go one step further and investigate how different networks topologies and growth models facilitate the emergence of a decentralized market. In particular, we show how the connectivity plays an important role in improving the properties of reliability and path-cost reduction. From the economic point of view, we estimate how the topological evolutions facilitate local electricity distribution, taking into account the main cost ingredient required for increasing network connectivity, i.e., the price of cabling

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

Hypersparse Neural Network Analysis of Large-Scale Internet Traffic

The Internet is transforming our society, necessitating a quantitative understanding of Internet traffic. Our team collects and curates the largest publicly available Internet traffic data containing 50 billion packets. Utilizing a novel hypersparse neural network analysis of "video" streams of this traffic using 10,000 processors in the MIT SuperCloud reveals a new phenomena: the importance of otherwise unseen leaf nodes and isolated links in Internet traffic. Our neural network approach further shows that a two-parameter modified Zipf-Mandelbrot distribution accurately describes a wide variety of source/destination statistics on moving sample windows ranging from 100,000 to 100,000,000 packets over collections that span years and continents. The inferred model parameters distinguish different network streams and the model leaf parameter strongly correlates with the fraction of the traffic in different underlying network topologies. The hypersparse neural network pipeline is highly adaptable and different network statistics and training models can be incorporated with simple changes to the image filter functions.Comment: 11 pages, 10 figures, 3 tables, 60 citations; to appear in IEEE High Performance Extreme Computing (HPEC) 201

Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required

On the Geographic Location of Internet Resources

One relatively unexplored question about the Internet's physical structure concerns the geographical location of its components: routers, links and autonomous systems (ASes). We study this question using two large inventories of Internet routers and links, collected by different methods and about two years apart. We first map each router to its geographical location using two different state-of-the-art tools. We then study the relationship between router location and population density; between geographic distance and link density; and between the size and geographic extent of ASes. Our findings are consistent across the two datasets and both mapping methods. First, as expected, router density per person varies widely over different economic regions; however, in economically homogeneous regions, router density shows a strong superlinear relationship to population density. Second, the probability that two routers are directly connected is strongly dependent on distance; our data is consistent with a model in which a majority (up to 75-95%) of link formation is based on geographical distance (as in the Waxman topology generation method). Finally, we find that ASes show high variability in geographic size, which is correlated with other measures of AS size (degree and number of interfaces). Among small to medium ASes, ASes show wide variability in their geographic dispersal; however, all ASes exceeding a certain threshold in size are maximally dispersed geographically. These findings have many implications for the next generation of topology generators, which we envisage as producing router-level graphs annotated with attributes such as link latencies, AS identifiers and geographical locations.National Science Foundation (CCR-9706685, ANI-9986397, ANI-0095988, CAREER ANI-0093296); DARPA; CAID

K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases

We consider the $k$-core decomposition of network models and Internet graphs at the autonomous system (AS) level. The $k$-core analysis allows to characterize networks beyond the degree distribution and uncover structural properties and hierarchies due to the specific architecture of the system. We compare the $k$-core structure obtained for AS graphs with those of several network models and discuss the differences and similarities with the real Internet architecture. The presence of biases and the incompleteness of the real maps are discussed and their effect on the $k$-core analysis is assessed with numerical experiments simulating biased exploration on a wide range of network models. We find that the $k$-core analysis provides an interesting characterization of the fluctuations and incompleteness of maps as well as information helping to discriminate the original underlying structure