Professor Barabási's talk described how the tools of network science can help understand the Web's structure, development and weaknesses. The Web is an information network, in which the nodes are documents (at the time of writing over one trillion of them), connected by links. Other well-known network structures include the Internet, a physical network where the nodes are routers and the links are physical connections, and organizations, where the nodes are people and the links represent communications.

The growth of the Web has required us to think about the design of information systems in which large-scale computational and social feedback effects are simultaneously at work. At the same time, the data generated by Web-scale systems—recording the ways in which millions of participants create content, link information, form groups and communicate with one another—have made it possible to evaluate long-standing theories of social interaction, and to formulate new theories based on what we observe. These developments have created a new level of interaction between computing and the social sciences, enriching the perspectives of both of these disciplines. We discuss some of the observations, theories and conclusions that have grown from the study of Web-scale social interaction, focusing on issues including the mechanisms by which people join groups, the ways in which different groups are linked together in social networks and the interplay of positive and negative interactions in these networks.

We introduce the concepts of closed sets and closure operators as mathematical tools for the study of social networks. Dynamic networks are represented by transformations. It is shown that under continuous change/transformation, all networks tend to "break down" and become less complex. It is a kind of entropy. The product of this theoretical decomposition is an abundance of triadically closed clusters which sociologists have observed in practice. This gives credence to the relevance of this kind of mathematical analysis in the sociological context.

The structure of a large network (graph) can often be revealed by partitioning it into smaller and possibly more dense sub-networks that are easier to handle. One of such decompositions is based on “

In contrast to many other scientific disciplines, computer science considers conference publications. Conferences have the advantage of providing fast publication of papers and of bringing researchers together to present and discuss the paper with peers. Previous work on knowledge mapping focused on the map of all sciences or a particular domain based on ISI published Journal Citation Report (JCR). Although this data cover most of the important journals, it lacks computer science conference and workshop proceedings, which results in an imprecise and incomplete analysis of the computer science knowledge. This paper presents an analysis on the computer science knowledge network constructed from all types of publications, aiming at providing a complete view of computer science research. Based on the combination of two important digital libraries (DBLP and CiteSeerX), we study the knowledge network created at journal/conference level using citation linkage, to identify the development of sub-disciplines. We investigate the collaborative and citation behavior of journals/conferences by analyzing the properties of their co-authorship and citation subgraphs. The paper draws several important conclusions. First, conferences constitute social structures that shape the computer science knowledge. Second, computer science is becoming more interdisciplinary. Third, experts are the key success factor for sustainability of journals/conferences.

Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these traditional methods often do not capture well the underlying structural information, clustering, and neighborhoods. In this paper, we describe GMap: a practical tool for visualizing relational data with geographic-like maps. We illustrate the effectiveness of this approach with examples from several domains All the maps referenced in this paper can be found in http://www.research.att.com/~yifanhu/GMap

The ease and lack of cost associated with taking digital photographs have allowed people to amass large personal photograph collections. These collections contain valuable information about their owners' social relationships. This paper is a preliminary investigation into how digital photo collections can provide useful data for the study of social networks. Results from an analysis of 23 subjects' photo collections demonstrate the feasibility of this approach. The relationship between perceived closeness and network position, as well as future questions, are also discussed.

Social bookmarking systems constitute an established part of the Web 2.0. In such systems users describe bookmarks by keywords called tags. The structure behind these social systems, called folksonomies, can be viewed as a tripartite hypergraph of user, tag and resource nodes. This underlying network shows specific structural properties that explain its growth and the possibility of serendipitous exploration. Today’s search engines represent the gateway to retrieve information from the World Wide Web. Short queries typically consisting of two to three words describe a user’s information need. In response to the displayed results of the search engine, users click on the links of the result page as they expect the answer to be of relevance. This clickdata can be represented as a folksonomy in which queries are descriptions of clicked URLs. The resulting network structure, which we will term logsonomy is very similar to the one of folksonomies. In order to find out about its properties, we analyze the topological characteristics of the tripartite hypergraph of queries, users and bookmarks on a large snapshot of del.icio.us and on query logs of two large search engines. All of the three datasets show small world properties. The tagging behavior of users, which is explained by preferential attachment of the tags in social bookmark systems, is reflected in the distribution of single query words in search engines. We can conclude that the clicking behaviour of search engine users based on the displayed search results and the tagging behaviour of social bookmarking users is driven by similar dynamics.

Social networking services are a fast-growing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in real-life social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, each with more than 10 million users, respectively. We have access to complete data of Cyworld's ilchon (friend) relationships and analyze its degree distribution, clustering property, degree correlation, and evolution over time. We also use Cyworld data to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace and orkut. Cyworld, the oldest of the three, demonstrates a changing scaling behavior over time in degree distribution. The latest Cyworld data's degree distribution exhibits a multi-scaling behavior, while those of MySpace and orkut have simple scaling behaviors with different exponents. Very interestingly, each of the two e ponents corresponds to the different segments in Cyworld's degree distribution. Certain online social networking services encourage online activities that cannot be easily copied in real life; we show that they deviate from close-knit online social networks which show a similar degree correlation pattern to real-life social networks.

Abstract. Communities in social networks are often defined as groups of densely connected actors. However, members of the same dense group are not equal but may differ largely in their social position or in the role they play. Furthermore, the same positions can be found across the borders of dense communities so that networks contain a significant group structure which does not coincide with the structure of dense groups. This papers gives a survey over formalizations of network-positions with a special emphasis on the use of algebraic notions.

Novel aspects of human dynamics and social interactions are investigated by means of mobile phone data. Using extensive phone records resolved in both time and space, we study the mean collective behavior at large scales and focus on the occurrence of anomalous events. We discuss how these spatiotemporal anomalies can be described using standard percolation theory tools. We also investigate patterns of calling activity at the individual level and show that the interevent time of consecutive calls is heavy-tailed. This finding, which has implications for dynamics of spreading phenomena in social networks, agrees with results previously reported on other human activities.

Social resource sharing systems like YouTube and del.icio.us have acquired a large number of users within the last few years. They provide rich resources for data analysis, information retrieval, and knowledge discovery applications. A first step towards this end is to gain better insights into content and structure of these systems. In this paper, we will analyse the main network characteristics of two of these systems. We consider their underlying data structures - so-called folksonomies - as tri-partite hypergraphs, and adapt classical network measures like characteristic path length and clustering coefficient to them. Subsequently, we introduce a network of tag co-occurrence and investigate some of its statistical properties, focusing on correlations in node connectivity and pointing out features that reflect emergent semantics within the folksonomy. We show that simple statistical indicators unambiguously spot non-social behavior such as spam.

A key argument for modeling knowledge in ontologies is the easy reuse and re-engineering of the knowledge. However, current ontology engineering tools provide only basic functionalities for analyzing ontologies. Since ontologies can be considered as graphs, graph analysis techniques are a suitable answer for this need. Graph analysis has been performed by sociologists for over 60 years, and resulted in the vivid research area of Social Network Analysis (SNA).While social network structures currently receive high attention in the Semantic Web community, there are only very few SNA applications, and virtually none for analyzing the structure of ontologies. We illustrate the benefits of applying SNA to ontologies and the Semantic Web, and discuss which research topics arise on the edge between the two areas. In particular, we discuss how different notions of centrality describe the core content and structure of an ontology. From the rather simple notion of degree centrality over betweenness centrality to the more complex eigenvector centrality, we illustrate the insights these measures provide on two ontologies, which are different in purpose, scope, and size.

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution P(τw)∼τw−α with α=3∕2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by α=1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display α=1, the surface mail based communication belongs to the α=3∕2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity. Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensity of the connections. These features, however, have mainly not been considered in past studies where links are usually represented as binary states, i.e., either present or absent. Here, we study the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network. We define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices. This information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network. These results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks.

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. Here we measure mixing patterns in a variety of networks and find that social networks are mostly assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortatively mixed network, which we study both analytically and numerically. Within this model we find that networks percolate more easily if they are assortative and that they are also more robust to vertex removal.

Galois lattices are introduced as a device to provide a general representation for two mode social network data. It is shown that Galois lattices yield a single visual image of such data in cases where most alternative models produce dual images. The inzage provided by the Galois lattice produces, moreover, an inzage that can suggest useful insights about the structural properties of the data. An example, based on data from Davis, Gardner, and Gardner (1941), is used to spell out in detail the kinds of structural insights that can be gained from this approach. In addition, other potential applications are suggested.