TY - JOUR AU - Chayes, Jennifer T1 - Mathematics of Web science: structure, dynamics and incentives JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences PY - 2013/ VL - 371 IS - 1987 SP - EP - UR - http://rsta.royalsocietypublishing.org/content/371/1987/20120377.abstract M3 - 10.1098/rsta.2012.0377 KW - dynamics KW - incentive KW - math KW - structure KW - webscience L1 - SN - N1 - N1 - AB - Dr Chayes’ talk described how, to a discrete mathematician, ‘all the world’s a graph, and all the people and domains merely vertices’. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online world) in the following way: first, we can model online networks as large finite graphs; second, we can sample pieces of these graphs; third, we can understand and then control processes on these graphs; and fourth, we can develop algorithms for these graphs and apply them to improve the online experience. ER - TY - BOOK AU - Dorling, Danny A2 - T1 - The Visualisation of Spatial Social Structure PB - John Wiley & Sons AD - Hoboken PY - 2012/ VL - IS - SP - EP - UR - http://public.eblib.com/EBLPublic/PublicView.do?ptiID=945112 M3 - KW - geography KW - gis KW - information KW - social KW - spatial KW - stair KW - structure KW - system L1 - SN - 9781118354001 1118354001 N1 - N1 - AB - How do you draw a map of 100,000 places, of more than a million flows of people, of changes over time and space, of different kinds of spaces, surfaces and volumes, from human travel time to landscapes of hopes, fears, migration, manufacturing and mortality? How do you turn the millions of numbers concerning some of the most important moments of our lives into images that allow us to appreciate the aggregate while still remembering the detail? The visualization of spatial social structure means, literally, making visible the geographical patterns to the way our lives have come to be s. ER - TY - CONF AU - Baur, Michael AU - Gaertler, Marco AU - Görke, Robert AU - Krug, Marcus AU - Wagner, Dorothea A2 - T1 - Generating Graphs with Predefined k-Core Structure T2 - Proceedings of the European Conference of Complex Systems PB - CY - PY - 2007/october M2 - VL - IS - SP - EP - UR - http://i11www.ira.uka.de/extra/publications/bggkw-ggpcs-07.pdf M3 - KW - analysis KW - core KW - generator KW - graph KW - structure L1 - SN - N1 - N1 - AB - The modeling of realistic networks is of great importance for modern complex systems research. Previous procedures typically model the natural growth of networks by means of iteratively adding nodes, geometric positioning information, a definition of link connectivity based on the preference for nearest neighbors or already highly connected nodes, or combine several of these approaches. Our novel model is based on the well-know concept of k-cores, originally introduced in social network analysis. Recent studies exposed the significant k-core structure of several real world systems, e.g. the AS network of the Internet. We present a simple and efficient method for generating networks which strictly adhere to the characteristics of a given k-core structure, called core fingerprint. We show-case our algorithm in a comparative evaluation with two well-known AS network generators. ER - TY - CONF AU - Brandes, Ulrik AU - Lerner, Jürgen A2 - Obiedkov, Sergei A2 - Roth, Camille T1 - Role-equivalent Actors in Networks T2 - ICFCA 2007 Satellite Workshop on Social Network Analysis and Conceptual Structures: Exploring Opportunities PB - CY - PY - 2007/ M2 - VL - IS - SP - EP - UR - http://www.inf.uni-konstanz.de/algo/publications/bl-rean-07.pdf M3 - KW - actor KW - role KW - seminar2009 KW - structure KW - sna KW - analysis KW - network KW - social L1 - SN - N1 - N1 - AB - 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. ER - TY - JOUR AU - Newman, M. E. J. T1 - Modularity and community structure in networks JO - Proceedings of the National Academy of Sciences PY - 2006/ VL - 103 IS - 23 SP - 8577 EP - 8582 UR - M3 - 10.1073/pnas.0601602103 KW - clustering KW - community KW - graph KW - modularity KW - network KW - structure L1 - SN - N1 - N1 - AB - Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as “modularity” over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets. ER - TY - RPRT AU - Golder, Scott AU - Huberman, Bernardo A. A2 - T1 - The Structure of Collaborative Tagging Systems PB - Information Dynamics Lab, HP Labs

AD - PY - 2005/08 VL - IS - SP - EP - UR - http://arxiv.org/abs/cs.DL/0508082 M3 - KW - folksonomy KW - tagging KW - structure L1 - N1 - N1 - N1 - AB - ER - TY - THES AU - Jäschke, Robert T1 - Die Struktur der Monoide binärer Relationen auf endlichen Mengen PY - 2005/ PB - Technische Universität Dresden SP - EP - UR - http://www.kde.cs.uni-kassel.de/pub/pdf/jaeschke2005struktur.pdf M3 - KW - 2005 KW - binary KW - diploma KW - monoid KW - myown KW - relation KW - semigroup KW - structure KW - thesis L1 - N1 - N1 - AB - ER - TY - CONF AU - Brandes, Ulrik AU - Lerner, Jürgen A2 - Fleischer, Rudolf A2 - Trippen, Gerhard T1 - Structural Similarity in Graphs (A Relaxation Approach for Role Assignment). T2 - ISAAC PB - Springer CY - PY - 2004/ M2 - VL - 3341 IS - SP - 184 EP - 195 UR - http://kops.ub.uni-konstanz.de/volltexte/2009/7777/ M3 - KW - actor KW - assignment KW - graph KW - relaxation KW - role KW - similarity KW - structure L1 - SN - 3-540-24131-0 N1 - N1 - AB - Standard methods for role assignment partition the vertex set of a graph in such a way that vertices in the same class can be considered to have equivalent roles in the graph. Several classes of equivalence relations such as regular equivalence and equitable partitions have been proposed for role assignment, but they all suffer from the strictness of classifying vertices into being either equivalent or not. It is an open problem how to allow for varying degrees of similarity. Proposals include ad-hoc algorithmic approaches and optimization approaches which are computationally hard. In this paper we introduce the concept of structural similarity by relaxation of equitable partitions, thus providing a theoretical foundation for similarity measures which enjoys desirable properties with respect to existence, structure, and tractability. ER - TY - JOUR AU - Clauset, Aaron AU - Newman, M.E.J. AU - Moore, Cristopher T1 - Finding community structure in very large networks JO - Physical Review E PY - 2004/ VL - 70 IS - SP - EP - UR - http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:cond-mat/0408187 M3 - KW - community KW - detection KW - gn KW - large KW - network KW - newman KW - structure L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Kumar, Ravi AU - Novak, Jasmine AU - Raghavan, Prabhakar AU - Tomkins, Andrew T1 - Structure and evolution of blogspace JO - Commun. ACM PY - 2004/ VL - 47 IS - 12 SP - 35 EP - 39 UR - http://doi.acm.org/10.1145/1035134.1035162 M3 - KW - blogging KW - seminar2006 KW - structure KW - community L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Newman, M.E.J. AU - Girvan, M. T1 - Finding and evaluating community structure in networks JO - Physical Review E PY - 2004/ VL - 69 IS - SP - EP - UR - http://arxiv.org/abs/cond-mat/0308217 M3 - 10.1103/PhysRevE.69.026113 KW - community KW - detection KW - girvan KW - gn KW - modularity KW - network KW - newman KW - structure L1 - SN - N1 - N1 - AB - We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems. ER - TY - GEN AU - Tyler, Joshua R. AU - Wilkinson, Dennis M. AU - Huberman, Bernardo A. A2 - T1 - Email as Spectroscopy: Automated Discovery of Community Structure within Organizations JO - PB - Kluwer, B.V. AD - Deventer, The Netherlands, The Netherlands PY - 2003/ VL - IS - SP - 81 EP - 96 UR - http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:cond-mat/0303264 M3 - KW - gn KW - detection KW - email KW - structure KW - community L1 - N1 - N1 - AB - We describe a method for the automatic identification of communities of practice from email logs within an organization. We use a betweenness centrality algorithm that can rapidly find communities within a graph representing information flows. We apply this algorithm to an email corpus of nearly one million messages collected over a two-month span, and show that the method is effective at identifying true communities, both formal and informal, within these scale-free graphs. This approach also enables the identification of leadership roles within the communities. These studies are complemented by a qualitative evaluation of the results in the field. ER - TY - JOUR AU - Girvan, Michelle AU - Newman, M.E.J. T1 - Community structure in social and biological networks JO - Proceedings of the National Academy of Science PY - 2002/ VL - 99 IS - 12 SP - 7821 EP - 7826 UR - M3 - KW - social KW - gn KW - detection KW - structure KW - community KW - network L1 - SN - N1 - N1 - AB - A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known---a collaboration network and a food web---and find that it detects significant and informative community divisions in both cases. ER - TY - JOUR AU - Wille, Rudolf AU - Wille, Uta T1 - Coordinatization of ordinal structures JO - Order PY - 1996/10 VL - 13 IS - 3 SP - 281 EP - 294 UR - http://dx.doi.org/10.1007/BF00338747 M3 - KW - algebra KW - order KW - ordinal KW - structure L1 - SN - N1 - N1 - AB - Dependencies between attributes in ordinal data contexts are algebraically described. Suitable conditions are analysed which allow coordinatizations of ordinal contexts (ordinal structures) by ordered n-quasigroups, ordered abelian groups, and ordered fields. The presented development offers a new approach to conjoint measurement.

ER - ER - TY - JOUR AU - White, Howard D. AU - Griffith, Belver C. T1 - Author cocitation: A literature measure of intellectual structure JO - Journal of the American Society for Information Science PY - 1981/ VL - 32 IS - 3 SP - 163 EP - 171 UR - http://dx.doi.org/10.1002/asi.4630320302 M3 - 10.1002/asi.4630320302 KW - analysis KW - citation KW - literature KW - structure L1 - SN - N1 - N1 - AB - It is shown that the mapping of a particular area of science, in this case information science, can be done using authors as units of analysis and the cocitations of pairs of authors as the variable that indicates their “distances” from each other. The analysis assumes that the more two authors are cited together, the closer the relationship between them. The raw data are cocitation counts drawn online from Social Scisearch (Social Sciences Citation Index) over the period 1972–1979. The resulting map shows (1) identifiable author groups (akin to “schools”) of information science, (2) locations of these groups with respect to each other, (3) the degree of centrality and peripherality of authors within groups, (4) proximities of authors within group and across group boundaries (“border authors” who seem to connect various areas of research), and (5) positions of authors with respect to the map's axes, which were arbitrarily set spanning the most divergent groups in order to aid interpretation. Cocitation analysis of authors offers a new technique that might contribute to the understanding of intellectual structure in the sciences and possibly in other areas to the extent that those areas rely on serial publications. The technique establishes authors, as well as documents, as an effective unit in analyzing subject specialties. ER -