Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

https://arxiv.org/pdf/cond-mat/9910332.pdf

Emergence of Scaling in Random Networks

The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

/pdf/statistical-mechanics-of-complex-networks-1zfjpvxipu.pdf

Statistical mechanics of complex networks

The importance of a Web page is an inherently subjective matter, which depends on the readers interests, knowledge and attitudes. But there is still much that can be said objectively about the relative importance of Web pages. This paper describes PageRank, a mathod for rating Web pages objectively and mechanically, effectively measuring the human interest and attention devoted to them. We compare PageRank to an idealized random Web surfer. We show how to efficiently compute PageRank for large numbers of pages. And, we show how to apply PageRank to search and to user navigation.

The PageRank Citation Ranking : Bringing Order to the Web

The network structure of a hyperlinked environment can be a rich source of information about the content of the environment, provided we have effective means for understanding it. We develop a set of algorithmic tools for extracting information from the link structures of such environments, and report on experiments that demonstrate their effectiveness in a variety of context on the World Wide Web. The central issue we address within our framework is the distillation of broad search topics, through the discovery of “authorative” information sources on such topics. We propose and test an algorithmic formulation of the notion of authority, based on the relationship between a set of relevant authoritative pages and the set of “hub pages” that join them together in the link structure. Our formulation has connections to the eigenvectors of certain matrices associated with the link graph; these connections in turn motivate additional heuristrics for link-based analysis.

/pdf/authoritative-sources-in-a-hyperlinked-environment-1p23r698i9.pdf

Authoritative sources in a hyperlinked environment

The authors address the role of marketing in hypermedia computer-mediated environments (CMEs). Their approach considers hypermedia CMEs to be large-scale (i.e., national or global) networked enviro...

/pdf/marketing-in-hypermedia-computer-mediated-environments-2ffhdnb9gv.pdf

Marketing in Hypermedia Computer-Mediated Environments: Conceptual Foundations

To date there have been a number of efforts that attempt to characterize various aspects of the World Wide Web. This paper presents a summary of these efforts, highlighting regularities and insights that have been discovered across the variety of access points available for instrumentation. Characterizations that are derived from client, proxy, and server instrumentation are reviewed as well as efforts to characterize the entire structure of the WWW. Given the dynamic nature of the Web, it may be surprising for some readers to find that many properties of the Web follow regular and predictable patterns that have not changed in form over the Web’s lifetime. Understanding these aspects as well as those that vary is critical to designing a better Web, and as a direct consequence, creating a more enjoyable user experience.

/pdf/summary-of-www-characterizations-3sz2s2h9ji.pdf

Summary of WWW characterizations

A system and method for ranking the results of a search on a collection of linked documents. Documents found on the Web are typically referred to as Web pages. The system utilizes various information relating to the collection of linked documents, including the topology, content and historical usage of the linked collections of documents. The ranking is based on historical patterns and information about the current context of interest (e.g. what the user or group seems to be currently interested in doing). A spreading activation technique is used to identify the frequency of activation of the documents in the search results. Spreading activation techniques are based on representations of Web pages as nodes in graph networks representing usage, content, and hypertext relations among Web pages. After performing the spreading activation based on an initial set defined by the search results, each document from the results may be ranked based on their level of activation.

System for ranking search results from a collection of documents using spreading activation techniques

Five years is not very long on most historical scales, but for the World Wide Web (WWW) it constitutes a lifetime. A question almost as old as the web itself is, "Who is using it, and for what?" One way to answer this question is to use paper surveys, telephone surveys, or diaries which are some of the the same methods used to measure the audiences of other one-way media such as television and radio. However, something interesting happened in early 1994: the implementation of HTML Forms turned the web into a two-way medium which made it possible to contact the audience directly. To test the viability of the web as a survey medium and collect preliminary data on the web population, the first GVU WWW User Survey was conducted in January 1994. Subsequent surveys have been conducted approximately every six months. The collection of responses from over 55,000 Web users over five surveys has given us a unique perspective on the advances in surveying technology and methodology and changes in the web population itself. In the following sections, we discuss what we have learned in each of these areas.

/pdf/surveying-the-territory-gvu-s-five-www-user-surveys-4ymucuqb2r.pdf

Surveying the Territory: GVU's Five WWW User Surveys

A system and method of caching uses quality or value attributes, provided for example, by a recommender system or by a dynamical analysis of site accesses, which are attached to cached information to prioritize items in the cache. Documents are prioritized in the cache according to the relative value of their content. Value data may be provided from a recommender system which provides a value for a document according to user recommendations (using explicit recommendations) or from statistical analysis of site visits from unique users (implicit recommendations) or a combination of the two to identify the higher value documents. The caching method may also be used to improve performance of a recommender system.

System and method for caching

A method and apparatus for predicting document access within a collection of linked documents. The present invention utilizes a predictive technique known as "spreading activation" where document collections are graphically represented as a network. Empirical data is analyzed according to a law of surfing to generate a decay function which is used to dampen the activation as spreads through the network. Activation is applied to a set of focus documents and propagates through the network until a stable pattern of activation is achieved across all documents. From this stable pattern, the desired usage information is extracted. Such a system will provide several practical benefits to users of the World Wide Web. For example, the present invention can be used to identify relevant pages to a set of one or more focus pages or to predict the number of times a document will be accessed in a collection of linked documents. Further, alone or in combination, this information can be used in connection with web site design or re-design.

James E. Pitkow

Papers

Summary of WWW characterizations

System for ranking search results from a collection of documents using spreading activation techniques

Surveying the Territory: GVU's Five WWW User Surveys

System and method for caching

Method and apparatus for predicting document access in a collection of linked documents featuring link proprabilities and spreading activation