Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real

How does a ‘normal ’ computer (or social) network look like? How can we spot ‘abnormal ’ sub-networks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal money-laundering rings), forecasting, and simulations (“how will a computer virus spread?”). The heart of the problem is finding the properties of real graphs that seem to persist over multiple disciplines. We list such “laws ” and, more importantly, we propose a simple, parsimonious model, the “recursive matrix ” (R-MAT) model, which can quickly generate realistic graphs, capturing the essence of each graph in only a few parameters. Contrary to existing generators, our model can trivially generate weighted, directed and bipartite graphs; it subsumes the celebrated Erdős-Rényi model as a special case; it can match the power law behaviors, as well as the deviations from them (like the “winner does not take it all ” model of Pennock et al. [21]). We present results on multiple, large real graphs, where we show that our parameter fitting algorithm (AutoMAT-fast) fits them very well. 1

Web caches, content distribution networks, peer-to-peer file sharing networks, distributed file systems, and data grids all have in common that they involve a community of users who generate requests for shared data. In each case, overall system performance can be improved significantly if we can first identify and then exploit interesting structure within a community's access patterns. To this end, we propose a novel perspective on file sharing based on the study of the relationships that form among users based on the files in which they are interested. We propose a new structure that captures common user interests in data---the data-sharing graph--- and justify its utility with studies on three data-distribution systems: a high-energy physics collaboration, the Web, and the Kazaa peer-to-peer network. We find small-world patterns in the data-sharing graphs of all three communities. We analyze these graphs and propose some probable causes for these emergent small-world patterns. The significance of smallworld patterns is twofold: it provides a rigorous support to intuition and, perhaps most importantly, it suggests ways to design mechanisms that exploit these naturally emerging patterns.

Abstract. A lot of recent research on content-based P2P searching for filesharing applications has focused on exploiting semantic relations between peers to facilitate searching. To the best of our knowledge, all methods proposed to date suggest reactive ways to seize peers ’ semantic relations. That is, they rely on the usage of the underlying search mechanism, and infer semantic relations based on the queries placed and the corresponding replies received. In this paper we follow a different approach, proposing a proactive method to build a semantic overlay. Our method is based on an epidemic protocol that clusters peers with similar content. It is worth noting that this peer clustering is done in a completely implicit way, that is, without requiring the user to specify his preferences or to characterize the content of files he shares. 1

This paper introduces the newscast model of computation for large-scale computing on the Internet. The engine realizing this model is a lazy fully distributed information propagation protocol among the participants which is responsible for membership management and communication. It maintains a constantly changing communication graph over the participants. This graph has useful emergent properties like small diameter and sufficiently random structure without deploying special purpose protocols to achieve these properties. For adding a new participant only the address of an arbitrary member is needed and for removal no action is necessary. We provide theoretical and empirical evidence that besides being simple and lightweight our newscast computing engine is extremely scalable and robust. We also suggest some interesting application areas including information dissemination, monitoring of large systems, resource sharing and efficient multicasting.

this paper we advocate the benefits of exploiting emergent patterns in self-configuring networks specialized for scientific data-sharing collaborations. We speculate that a P2P scientific collaboration network will exhibit small-world topology, as do a large number of social networks for which the same pattern has been documented

Abstract not found

We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the node-normalized cut (also called cut ratio) and the edge-normalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to these criteria.

We consider the problem of positioning data collecting base stations in a sensor network. We show that in general, the choice of positions has a marked influence on the data rate, or equivalently, the power efficiency, of the network. In our model, which is partly motivated by an experimental environmental monitoring system, the optimum data rate for a fixed layout of base stations can be found by a maximum flow algorithm. Finding the optimum layout of base stations, however, turns out to be an NP-complete problem, even in the special case of homogeneous networks. Our analysis of the optimum layout for the special case of the regular grid shows that all layouts that meet certain constraints are equally good. We also consider two classes of random graphs, chosen to model networks that might be realistically encountered, and empirically evaluate the performance of several base station positioning algorithms on instances of these classes. In comparison to manually choosing positions along the periphery of the network or randomly choosing them within the network, the algorithms tested find positions which significantly improve the data rate and power efficiency of the network.

Abstract. Performing efficient decentralized search is a fundamental problem in Peer-to-Peer (P2P) systems. There has been a significant amount of research recently on developing robust self-organizing P2P topologies that support efficient search. In this paper we discuss four structured and unstructured P2P models (CAN, Chord, PRU, and Hypergrid) and three characteristic search algorithms (BFS, k-Random Walk, and GAPS) for unstructured networks. We report on the results of simulations of these networks and provide measurements of search performance, focusing on search in unstructured networks. We find that the proposed models produce small-world networks, and yet none exhibit power-law degree distributions. Our simulations also suggest that random graphs support decentralized search more effectively than the proposed unstructured P2P models. We also find that on these topologies, the basic breadth-first search algorithm and its simple variants have the lowest search cost. 1