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Understanding Large Temporal Networks and Spatial Networks - Vladimir Batagelj

Year 2014


Preface1. Temporal and spatial networks1.1 Modern social network analysis1.2 Network sizes1.3 Substantive concerns1.3.1 Citation networks1.3.1.1 Scientific citation networks1.3.1.2 Patent citation networks1.3.1.3 A US Supreme Court citation network1.3.2 Other types of large networks1.3.2.1 The movement of football players across the globe1.3.2.2 A large US spatial network1.4 Computational methods1.5 Data for large temporal networks1.5.1 The main datasets1.5.2 Secondary datasets1.5.2.1 The Edinburgh Associative Thesaurus (EAT) The NBER-United Nations Trade Data, 1962-20001.5.2.3 The Kansas Event Data (KEDS) Krebs Internet industry partnerships1.5.2.5 Data archives1.6 Induction and deduction2. Foundations of methods for large networks2.1 Networks2.1.1 Descriptions of networks2.1.2 Degrees2.1.3 Descriptions of properties2.1.4 Visualizations of properties2.2 Types of networks2.2.1 Temporal networks2.2.1.1 Some examples of temporal networks2.2.2 Multirelational networks2.2.2.1 An example of a multirelational temporal network 2.2.3 Two-mode networks2.3 Large networks2.3.1 Small and middle sized networks2.3.2 Large networks2.3.3 Complexity of algorithms2.4 Strategies for analyzing large networks2.5 Statistical network measures2.5.1 Using Pajek and R together2.5.2 Fitting distributions2.6 Subnetworks2.6.1 Clusters, clusterings, partitions, hierarchies2.6.2 Contractions of clusters2.6.2.1 Contracted clusters - international trade2.6.3 Subgraphs2.6.4 Cuts2.7 Connectivity properties of networks2.7.1 Walks2.7.2 Equivalence relations and partitions2.7.3 Connectivity2.7.4 Condensation2.7.5 Bow-tie structure of the web graph2.7.6 The internal structure of strong components2.7.7 Bi-connectivity and k-connectivity2.8 Triangular and short cycle connectivities2.9 Islands2.9.1 Defining islands2.9.2 Some properties of islands2.10 Cores and generalized cores2.10.1 Cores2.10.2 Generalized cores2.11 Important vertices in networks2.11.1 Degrees, closeness, betweenness and other indices2.11.2 Clustering2.11.3 Computing further indices through functions2.12 Transition to methods for large networks3. Methods for large networks3.1 Acyclic networks3.1.1 Some basic properties of acyclic networks3.1.2 Compatible numberings: Depth and topological order3.1.3 Topological orderings and functions on acyclic networks3.1.3.1 Topological orderings and CPM3.2 SPC weights in acyclic networks3.2.1 Citation networks3.2.2 Analysis of citation networks3.2.3 Search path count method3.2.4 Computing SPLC and SPNP weights3.2.5 Implementation details3.2.6 Vertex weights3.2.7 General properties of weights3.2.8 SPC weights3.3 Probabilistic flow in acyclic network3.4 Nonacyclic citation networks3.5 Two-mode networks from data tables3.5.1 Multiplication of two-mode networks3.6 Bibliographic networks3.6.1 Co-authorship networks3.6.2 Collaboration networks3.6.3 Other derived networks3.7 Weights3.7.1 Normalizations of weights3.7.2 k-rings3.7.3 4-rings and analysis of two-mode networks3.7.4 Two-mode cores3.8 Pathfinder3.8.1 Pathfinder algorithms3.8.2 Computing the closure over the Pathfinder semiring3.8.3 Spanish algorithms3.8.4 A sparse network algorithm3.9 Clustering, blockmodeling, and community detection3.9.1 The Louvain method and VOS3.10 Clustering symbolic data3.10.1 Symbolic objects described with distributions3.10.2 The leaders method3.10.3 An agglomerative method3.11 Approaches to temporal networks3.11.1 Journeys - Walks in temporal networks3.11.2 Measures3.11.2.1 Measures based on time slices3.11.3 Problems and algorithms3.11.3.1 Properties of journeys3.11.3.2 Semirings3.11.3.3 Transformation of temporal networks to static networks3.11.4 Evolution3.12 Levels of analysis3.13 Transition to substantive topics4. Scientific citation and other bibliographic networks4.1 The centrality citation network4.2 Preliminary data analyses4.2.1 Temporal distribution of publications4.2.2 Degree distributions of the centrality literature4.2.3 Types of works4.2.4 The boundary problem4.3 Transforming a citation network into an acyclic network4.3.1 Checking for the presence of cycles4.3.2 Dealing with cycles in citation networks4.4 The most important works4.5 SPC weights4.5.1 Obtaining SPC weights and drawing main paths4.5.2 The main path of the centrality citation network4.6 Line cuts4.7 Line islands4.7.1 The main island4.7.2 A geophysics and meteorology line island4.7.3 An optical network line island4.7.4 A partial summary of main path and line island results4.8 Other relevant subnetworks for a bounded network4.9 Collaboration networks4.9.1 Macros for collaboration networks4.9.2 An initial attempt of analyses of collaboration networks4.10 A brief look at the SNA literature SN5 networks4.10.1.1 Tendencies of individual authors to collaborate4.10.1.2 Participation in co-authored productions4.10.1.3 k-cores in collaboration networks4.10.1.4 The most important works4.10.1.5 SPC weights4.10.1.6 Other derived networks4.11 On the centrality and SNA collaboration networks5. Citation patterns in temporal United States patent data5.1 Patents5.2 Supreme Court decisions regarding patents5.2.1 Co-cited decisions5.2.2 Citations between co-cited decisions5.3 The 1976-2006 patent data5.4 Structural variables through time5.4.1 Temporally specific networksIdentifying the starting yearDefining the width of the sliding window5.4.2 Shrinking specific patent citation networks5.4.3 Structural properties5.5 Some patterns of technological development5.5.1 Structural properties of temporally specific networks5.6 Important subnetworks5.6.1 Line islands5.6.2 Line islands with patents tagged by keywords5.6.3 Vertex islands5.7 Citation patterns5.7.1 Patents from 1976, cited through to 20065.7.1.1 Utilizing supplementary variables for 1976 patents5.7.2 Patents from 1987, cited through to 20065.7.2.1 Utilizing supplementary variables for 1987 patents5.8 Comparing citation patterns for two time intervals5.9 Summary and conclusions6. The US Supreme Court citation network6.1 Introduction6.2 Co-cited islands of Supreme Court decisions6.3 A Native American line island6.3.1 Forced removal of Native American populations6.3.2 Regulating whites on Native American lands6.3.3 Curtailing the authority of Native American courts6.3.4 Taxing Native Americans and enforcing external laws6.3.5 The presence of non-Native Americans on Native American lands6.3.6 Some later developments6.3.7 A partial summary6.4 A 'Perceived Threats to Social Order' line island6.4.1 Perceived threats to social order6.4.2 The structures of the threats to social order line island6.4.3 Decisions involving communists and socialists6.4.3.1 The first Red Scare6.4.3.2 The second Red Scare6.4.3.3 The Warren Court on subversion6.4.4 Restrictions of labor groups organizing6.4.5 Restrictions of African Americans organizing6.4.6 Jehovah's Witnesses as a perceived threat6.4.6.1 Nuisance threats6.4.6.2 Direct threats to state interests6.4.6.3 Petty persecutions6.4.6.4 A partial summary6.4.7 Obscenity as a threat to social order6.4.7.1 The Warren Court on obscenity6.4.7.2 The Burger Court on obscenity6.5 Other perceived threats6.5.1.1 Birth control and abortion6.5.1.2 Press freedom and free speech as perceived threats6.5.1.3 Commercial speech and threats restricting it6.5.1.4 The coherence of the threats to social order line island6.6 The Dred Scott decision6.6.1 Citations from Dred Scott6.6.2 Citations to Dred Scott6.6.3 Methodological implications of Dred Scott6.7 Further reflections on the Supreme Court citation network7. Football as the world's game7.1 A brief historical overview7.2 Football clubs7.3 Football players7.4 Football in England7.5 Player migrations7.6 Institutional arrangements and the organization of football7.7 Court rulings7.8 Specific factors impacting football migration7.9 Some arguments and propositions7.10 Some preliminary results7.10.1 The non-English presence in the EPL7.10.1.1 Club level variations7.10.1.2 Effects of the Bosman decision7.10.1.3 Squad sizes7.10.2 Player fitness7.10.3 Starting clubs for English players7.10.3.1 EPL career lengths7.10.3.2 Overall playing careers7.10.4 General features of the top five European leagues7.10.4.1 Pre-modern era7.10.4.2 The modern era7.10.5 Flows of footballers into the top European leagues7.11 Player ages when recruited to the EPL7.12 A partial summary of results8. Networks of player movements to the EPL8.1 Success in the EPL8.2 The overall presence of other countries in the EPL8.3 Network flows of footballers between clubs to reach the EPL8.3.1 Moving directly into the EPL from local and non-local clubs8.3.2 Direct moves of players to the EPL from non-EPL clubs8.4 Moves from EPL clubs8.4.1 The 1992-1996 time slice flows with at least three moves8.4.2 The 1997-2001 time slice flows with at least three moves8.4.3 The 2002-2006 time slice flows with at least three moves8.5 Moves solely within the EPL8.5.1 Loans8.5.2 Transfers8.6 All trails of footballers to the EPL8.6.1 Counted features of trails to the EPL8.6.2 Clustering player trails8.6.2.1 Some Home Country profiles8.6.2.2 Some profiles of players from elsewhere8.6.3 Interpreting the clusters of player careers8.7 Summary and conclusions9. Mapping spatial diversity in the United States of America9.1 Mapping nations as spatial units of the United States9.1.1 The counties of the United States9.2 Representing networks in space9.3 Clustering with a relational constraint9.3.1 Conditions for hierarchical clustering methods9.3.2 Clustering with a relational constraint9.3.3 An agglomerative method for relational constraints9.3.4 Hierarchies9.3.5 Fast agglomerative clustering algorithms9.3.5.1 Nearest neighbors graphs9.3.5.2 The structure and some properties of nearest neighbor graphs9.3.5.3 The algorithm9.4 Data for constrained spatial clustering9.4.1 Discriminant analysis for Garreau's nations9.5 Clustering the US counties with a spatial relational constraint9.5.1 The eight Garreau nations in the USA9.5.2 The ten Woodard nations in the USA9.6 Summary10. On studying large networks10.1 Substance10.2 Methods, techniques, and algorithms10.3 Network data10.3.1.1 The network datasets we used10.3.1.2 The supplementary datasets we used10.4 Surprises and issues triggered by them10.4.1.1 SNA citation networks10.4.1.2 The patent citation network10.4.1.3 The Supreme Court citation network10.4.1.4 The football network10.4.1.5 The spatial network10.5 Future work10.5.1.1 The network of scientific citations10.5.1.2 The patent network10.5.1.3 The Supreme Court network10.5.1.4 The football network(s) The spatial networks10.5.1.6 Other networks10.6 Two final commentsReferences
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