Degree and connectivity of the Internet's scale-free topology

In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization constant of the degree distribution p(k). We develop a mathematics model of the Internet's scale-free topology. On this model we theoretically get the formulas of the average degree, the ratios of the kmin-degree (minimum degree) nodes and the kmax-degree (maximum degree) nodes, the fraction of the degrees (or links) in the hands of the richer (top best-connected) nodes. We find the average degree is larger for smaller power-law exponent {\lambda} and larger minimum or maximum degree. The ratio of the kmin-degree nodes is larger for larger {\lambda} and smaller kmin or kmax. The ratio of the kmax-degree ones is larger for smaller {\lambda} and kmax or larger kmin. The richer nodes hold most of the total degrees of the AS-level Internet topology. In addition, we reveal the ratio of the kmin-degree nodes or the rate of the increase of the average degree has power-law decay with the increase of the kmin. The ratio of the kmax-degree nodes has power-law decay with the increase of the kmax, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% (the '73/27 rule'). At last, we empirically calculate, based on empirical data extracted from BGP, the average degree and the ratio and fraction using our method and other methods, and find that our method is rigorous and effective for the AS-level Internet topology.Comment: 22 pages, 8 figure

Generating Representative ISP Technologies From First-Principles

Understanding and modeling the factors that underlie the growth and evolution of network topologies are basic questions that impact capacity planning, forecasting, and protocol research. Early topology generation work focused on generating network-wide connectivity maps, either at the AS-level or the router-level, typically with an eye towards reproducing abstract properties of observed topologies. But recently, advocates of an alternative "first-principles" approach question the feasibility of realizing representative topologies with simple generative models that do not explicitly incorporate real-world constraints, such as the relative costs of router configurations, into the model. Our work synthesizes these two lines by designing a topology generation mechanism that incorporates first-principles constraints. Our goal is more modest than that of constructing an Internet-wide topology: we aim to generate representative topologies for single ISPs. However, our methods also go well beyond previous work, as we annotate these topologies with representative capacity and latency information. Taking only demand for network services over a given region as input, we propose a natural cost model for building and interconnecting PoPs and formulate the resulting optimization problem faced by an ISP. We devise hill-climbing heuristics for this problem and demonstrate that the solutions we obtain are quantitatively similar to those in measured router-level ISP topologies, with respect to both topological properties and fault-tolerance

Emergent topological and dynamical properties of a real inter-municipal commuting network - perspectives for policy-making and planning

A variety of phenomena can be explained by means of a description of the features of their underlying network structure. In addition, a large number of scientists (see the reviews, eg. Barabasi, 2002; Watts, 2003) demonstrated the emergence of large-scale properties common to many different systems. These various results and studies led to what can be termed as the “new science of complex networks” and to emergence of the new “age of connectivity”. In the realms of urban and environmental planning, spatial analysis and regional science, many scientists have shown in the past years an increasing interest for the research developments on complex networks. Their studies range from theoretical statements on the need to apply complex network analysis to spatial phenomena (Salingaros, 2001) to empirical studies on quantitative research about urban space syntax (Jiang and Claramunt, 2004). Concerning transportation systems analysis, interesting results have been recently obtained on subway networks (Latora and Marchiori, 2002; Gastner and Newman, 2004) and airports (Barrat et al, 2004). In this paper, we study the inter-municipal commuting network of Sardinia (Italy). In this complex weighted network, the nodes correspond to urban centres while the weight of the links between two municipalities represents the flow of individuals between them. Following the analysis developed by Barrat et al. (2004), we investigate the topological and dynamical properties of this complex weighted network. The topology of this network can be accurately described by a regular small-world network while the traffic structure is very rich and reveals highly complex traffic patterns. Finally, in the perspective of policy-making and planning, we compare the emerging network behaviors with the geographical, social and demographical aspects of the transportation system.

Using graph concepts to understand the organization of complex systems

Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the topologies of different systems. Attempts to explain these similarities have led to the ongoing development and refinement of network models and graph-theoretical analysis techniques with which to characterize and understand complexity. In this tutorial, we demonstrate through illustrative examples, how network measures and models have contributed to the elucidation of the organization of complex systems.Comment: v(1) 38 pages, 7 figures, to appear in the International Journal of Bifurcation and Chaos v(2) Line spacing changed; now 23 pages, 7 figures, to appear in the Special Issue "Complex Networks' Structure and Dynamics'' of the International Journal of Bifurcation and Chaos (Volume 17, Issue 7, July 2007) edited by S. Boccaletti and V. Lator

Urban geography of digital networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 2003.Includes bibliographical references.This dissertation examines the development of digital network infrastructure in the world's great cities at the turn of the 20th century. Drawing upon the concept of cities as information systems and techniques of communications geography, it analyzes how the physical components of digital networks were deployed in major urban areas during the 1990s. It finds that historical processes and pre-existing differences between places shaped the evolution of this infrastructure at multiple spatial scales; global, metropolitan, and neighborhood. As a result, rather than bringing about the "death of distance", digital network infrastructure actually reinforced many of the pre-existing differences between connected and disconnected places. With the telecom bust of 2000-2002, these differences were likely to persist for a decade or more. Yet just as the development of wired digital network infrastructure slowed, wireless technologies emerged as a more flexible, intuitive, and efficient form of connecting users to networks in everyday urban settings. As a result, an untethered model for digital networks emerged which combining the capacity and security of wired networks over long distances with the flexibility and mobility of wireless networks over short distances. This new hybrid infrastructure provided the technology needed to begin widespread experimentation with the creation of digitally mediated spaces, such as New York City's Bryant Park Wireless Network.by Anthony M. Townsend.Ph.D

A model to study cyber attack mechanics and denial-of-service exploits over the internet\u27s router infrastructure using colored petri nets

The Internet‟s router infrastructure, a scale-free computer network, is vulnerable to targeted denial-of-service (DoS) attacks. Protecting this infrastructure‟s stability is a vital national interest because of the dependence of economic and national security transactions on the Internet. Current defensive countermeasures that rely on monitoring specific router traffic have been shown to be costly, inefficient, impractical, and reactive rather than anticipatory. To address these issues, this research investigation considers a new paradigm that relies on the systemic changes that occur during a cyber attack, rather than individual router traffic anomalies. It has been hypothesized in the literature that systemic knowledge of cyber attack mechanics can be used to infer the existence of an exploit in its formative stages, before severe network degradation occurs. The study described here targeted DoS attacks against large-scale computer networks. To determine whether this new paradigm can be expressed though the study of subtle changes in the physical characteristics of the Internet‟s connectivity environment, this research developed a first of its kind Colored Petri Net (CPN) model of the United States AT&T router connectivity topology. By simulating the systemic affects of a DoS attack over this infrastructure, the objectives of this research were to (1) determine whether it is possible to detect small subtle changes in the connectivity environment of the Internet‟s router connectivity infrastructure that occur during a cyber attack; and (2) if the first premise is valid, to ascertain the feasibility of using these changes as a means for (a) early infrastructure attack detection and (b) router infrastructure protection strategy development against these attacks. Using CPN simulations, this study determined that systemic network changes can be detected in the early stages of a cyber attack. Specifically, this research has provided evidence that using knowledge of the Internet‟s connectivity topology and its physical characteristics to protect the router infrastructure from targeted DoS attacks is feasible. In addition, it is plausible to use these techniques to detect targeted DoS attacks and may lead to new network security tools