The popularity of peer-to-peer multimedia file sharing applications such as Gnutella and Napster has created a flurry of recent research activity into peer-to-peer architectures. We believe that the proper evaluation of a peer-to-peer system must take into account the characteristics of the peers that choose to participate. Surprisingly, however, few of the peer-to-peer architectures currently being developed are evaluated with respect to such considerations. In this paper, we remedy this situation by performing a detailed measurement study of the two popular peer-to-peer file sharing systems, namely Napster and Gnutella. In particular, our measurement study seeks to precisely characterize the population of end-user hosts that participate in these two systems. This characterization includes the bottleneck bandwidths between these hosts and the Internet at large, IP-level latencies to send packets to these hosts, how often hosts connect and disconnect from the system, how many les hosts share and download, the degree of cooperation between the hosts, and several correlations between these characteristics. Our measurements show that there is significant heterogeneity and lack of cooperation across peers participating in these systems.

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network [1]. Complex communication networks [2] display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems ’ components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is displayed only by a class of inhomogeneously wired networks, called scale-free networks. We find that scale-free networks, describing a number of systems, such as the World Wide Web (www) [3–5], Internet [6], social networks [7] or a cell [8], display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However,

We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We will illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We will also discuss the threshold function, the giant component, and the evolution of random graphs in this model.

Effective engineering of the Internet is predicated upon a detailed understanding of issues such as the large-scale structure of its underlying physical topology, the manner in which it evolves over time, and the way in which its constituent components contribute to its overall function. Unfortunately, developing a deep understanding of these issues has proven to be a challenging task, since it in turn involves solving difficult problems such as mapping the actual topology, characterizing it, and developing models that capture its emergent behavior. Consequently, even though there are a number of topology models, it is an open question as to how representative the generated topologies they generate are of the actual Internet. Our goal is to produce a topology generation framework which improves the state of the art and is based on the design principles of representativeness, inclusiveness, and interoperability. Representativeness leads to synthetic topologies that accurately reflect many aspects of the actual Internet topology (e.g. hierarchical structure, node degree distribution, etc.). Inclusiveness combines the strengths of as many generation models as possible in a single generation tool. Interoperability provides interfaces to widely-used simulation applications such as ns and SSF and visualization tools like otter. We call such a tool a universal topology generator. Keywords: topology generation, graph models, network topology, growth models, annotated topologies, simulation environments. 1

Despite recent excitement generated by the peer-to-peer (P2P) paradigm and the surprisingly rapid deployment of some P2P applications, there are few quantitative evaluations of P2P systems behavior. The open architecture, achieved scale, and self-organizing structure of the Gnutella network make it an interesting P2P architecture to study. Like most other P2P applications, Gnutella builds, at the application level, a virtual network with its own routing mechanisms. The topology of this virtual network and the routing mechanisms used have a significant influence on application properties such as performance, reliability, and scalability. We have built a “crawler” to extract the topology of Gnutella’s application level network. In this paper we analyze the topology graph and evaluate generated network traffic. Our two major findings are that: (1) although Gnutella is not a pure power-law network, its current configuration has the benefits and drawbacks of a power-law structure, and (2) the Gnutella virtual network topology does not match well the underlying Internet topology, hence leading to ineffective use of the physical networking infrastructure. These findings guide us to propose changes to the Gnutella protocol and implementations that may bring significant performance and scalability improvements. We believe that our findings as well as our measurement and analysis techniques have broad applicability to P2P systems and provide unique insights into P2P system design tradeoffs.

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems

How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification, requires very few parameters (like the “flammability” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.

Despite recent excitement generated by the P2P paradigm and despite surprisingly fast deployment of some P2P applications, there are few quantitative evaluations of P2P systems behavior. Due to its' open architecture and achieved scale, Gnutella is an interesting P2P architecture case study. Gnutella, like most other P2P applications, builds' at the application level a virtual network with its' own routing mechanisms. The topology of this virtual network and the routing mechanisms used have a significant influence on application properties such as performance, reliability, and scalability. We built a 'crawler' to extract the topology of Gnutella's application level network. In this' paper we analyze the topology graph and evaluate generated network traffic. We find that although Gnutella is' not a pure power-law network, its' current configuration has the benefits' and drawbacks' of a power-law structure. These findings lead us to propose changes to Gnutella protocol and implementations that bring significant performance and scalability improvements'.

The study of the web as a graph is not only fascinating in its own right, but also yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution. We report on experiments on local and global properties of the web graph using two Altavista crawls each with over 200 million pages and 1.5 billion links. Our study indicates that the macroscopic structure of the web is considerably more intricate than suggested by earlier experiments on a smaller scale.