126,562 research outputs found

    The diameter of the world wide web

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    Despite its increasing role in communication, the world wide web remains the least controlled medium: any individual or institution can create websites with unrestricted number of documents and links. While great efforts are made to map and characterize the Internet's infrastructure, little is known about the topology of the web. Here we take a first step to fill this gap: we use local connectivity measurements to construct a topological model of the world wide web, allowing us to explore and characterize its large scale properties.Comment: 5 pages, 1 figure, updated with most recent results on the size of the ww

    Deterministic Small-World Networks

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    Many real life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two nodes). These networks have been characterized as small-world networks and modeled by the addition of randomness to regular structures. We show that small-world networks can be constructed in a deterministic way. This exact approach permits a direct calculation of relevant network parameters allowing their immediate contrast with real-world networks and avoiding complex computer simulations.Comment: 6 pages, 1 figur

    Optimal Scale-Free Small-World Graphs with Minimum Scaling of Cover Time

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    The cover time of random walks on a graph has found wide practical applications in different fields of computer science, such as crawling and searching on the World Wide Web and query processing in sensor networks, with the application effects dependent on the behavior of cover time: the smaller the cover time, the better the application performance. It was proved that over all graphs with NN nodes, complete graphs have the minimum cover time NlogNN\log N. However, complete graphs cannot mimic real-world networks with small average degree and scale-free small-world properties, for which the cover time has not been examined carefully, and its behavior is still not well understood. In this paper, we first experimentally evaluate the cover time for various real-world networks with scale-free small-world properties, which scales as NlogNN\log N. To better understand the behavior of the cover time for real-world networks, we then study the cover time of three scale-free small-world model networks by using the connection between cover time and resistance diameter. For all the three networks, their cover time also behaves as NlogNN\log N. This work indicates that sparse networks with scale-free and small-world topology are favorable architectures with optimal scaling of cover time. Our results deepen understanding the behavior of cover time in real-world networks with scale-free small-world structure, and have potential implications in the design of efficient algorithms related to cover time

    Self-similarity of complex networks

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    Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks \cite{ab-review,mendes,vespignani,newman,amaral}. A large number of real networks are called ``scale-free'' because they show a power-law distribution of the number of links per node \cite{ab-review,barabasi1999,faloutsos}. However, it is widely believed that complex networks are not {\it length-scale} invariant or self-similar. This conclusion originates from the ``small-world'' property of these networks, which implies that the number of nodes increases exponentially with the ``diameter'' of the network \cite{erdos,bollobas,milgram,watts}, rather than the power-law relation expected for a self-similar structure. Nevertheless, here we present a novel approach to the analysis of such networks, revealing that their structure is indeed self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a finite self-similar exponent. These fundamental properties, which are shown for the WWW, social, cellular and protein-protein interaction networks, help to understand the emergence of the scale-free property in complex networks. They suggest a common self-organization dynamics of diverse networks at different scales into a critical state and in turn bring together previously unrelated fields: the statistical physics of complex networks with renormalization group, fractals and critical phenomena.Comment: 28 pages, 12 figures, more informations at http://www.jamlab.or

    Detonation Database

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    Welcome to the GALCIT Explosion Dynamics Laboratory Detonation Database. The goal of this project is to compile, catalog and present experimental data on gaseous detonations. These data currently include cell width, critical tube diameter, initiation energy, and minimum tube diameter. They are formatted in tables and summary graphs, with citations to the original references. A printed version and a World Wide Web version have been prepared. The purpose of this database is to facilitate explosion hazards evaluations and comparisons with numerical simulations of detonation behavior

    Potential Networks, Contagious Communities, and Understanding Social Network Structure

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    In this paper we study how the network of agents adopting a particular technology relates to the structure of the underlying network over which the technology adoption spreads. We develop a model and show that the network of agents adopting a particular technology may have characteristics that differ significantly from the social network of agents over which the technology spreads. For example, the network induced by a cascade may have a heavy-tailed degree distribution even if the original network does not. This provides evidence that online social networks created by technology adoption over an underlying social network may look fundamentally different from social networks and indicates that using data from many online social networks may mislead us if we try to use it to directly infer the structure of social networks. Our results provide an alternate explanation for certain properties repeatedly observed in data sets, for example: heavy-tailed degree distribution, network densification, shrinking diameter, and network community profile. These properties could be caused by a sort of `sampling bias' rather than by attributes of the underlying social structure. By generating networks using cascades over traditional network models that do not themselves contain these properties, we can nevertheless reliably produce networks that contain all these properties. An opportunity for interesting future research is developing new methods that correctly infer underlying network structure from data about a network that is generated via a cascade spread over the underlying network.Comment: To Appear in Proceedings of the 22nd International World Wide Web Conference(WWW 2013

    Let Your CyberAlter Ego Share Information and Manage Spam

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    Almost all of us have multiple cyberspace identities, and these {\em cyber}alter egos are networked together to form a vast cyberspace social network. This network is distinct from the world-wide-web (WWW), which is being queried and mined to the tune of billions of dollars everyday, and until recently, has gone largely unexplored. Empirically, the cyberspace social networks have been found to possess many of the same complex features that characterize its real counterparts, including scale-free degree distributions, low diameter, and extensive connectivity. We show that these topological features make the latent networks particularly suitable for explorations and management via local-only messaging protocols. {\em Cyber}alter egos can communicate via their direct links (i.e., using only their own address books) and set up a highly decentralized and scalable message passing network that can allow large-scale sharing of information and data. As one particular example of such collaborative systems, we provide a design of a spam filtering system, and our large-scale simulations show that the system achieves a spam detection rate close to 100%, while the false positive rate is kept around zero. This system has several advantages over other recent proposals (i) It uses an already existing network, created by the same social dynamics that govern our daily lives, and no dedicated peer-to-peer (P2P) systems or centralized server-based systems need be constructed; (ii) It utilizes a percolation search algorithm that makes the query-generated traffic scalable; (iii) The network has a built in trust system (just as in social networks) that can be used to thwart malicious attacks; iv) It can be implemented right now as a plugin to popular email programs, such as MS Outlook, Eudora, and Sendmail.Comment: 13 pages, 10 figure

    Error and attack tolerance of complex networks

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    Many complex systems, such as communication networks, 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 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, Internet, social networks or a cell, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However, error tolerance comes at a high price: these networks are extremely vulnerable to attacks, i.e. to the selection and removal of a few nodes that play the most important role in assuring the network's connectivity.Comment: 14 pages, 4 figures, Late

    Four Degrees of Separation, Really

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    We recently measured the average distance of users in the Facebook graph, spurring comments in the scientific community as well as in the general press ("Four Degrees of Separation"). A number of interesting criticisms have been made about the meaningfulness, methods and consequences of the experiment we performed. In this paper we want to discuss some methodological aspects that we deem important to underline in the form of answers to the questions we have read in newspapers, magazines, blogs, or heard from colleagues. We indulge in some reflections on the actual meaning of "average distance" and make a number of side observations showing that, yes, 3.74 "degrees of separation" are really few
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