Understanding Large Temporal Networks and Spatial Networks

Preface Temporal and spatial networks Modern social network analysis Network sizes Substantive concerns Citation networks Scientific citation networks Patent citation networks A US Supreme Court citation network Other types of large networks The movement of football players across the globe A large US spatial network Computational methods Data for large temporal networks The main datasets Secondary datasets The Edinburgh Associative Thesaurus (EAT)The NBER-United Nations Trade Data, 1962-2000 The Kansas Event Data (KEDS)Krebs Internet industry partnerships Data archives Induction and deduction Foundations of methods for large networks Networks Descriptions of networks Degrees Descriptions of properties Visualizations of properties Types of networks Temporal networks Some examples of temporal networks Multirelational networks An example of a multirelational temporal network Two-mode networks Large networks Small and middle sized networks Large networks Complexity of algorithms Strategies for analyzing large networks Statistical network measures Using Pajek and R together Fitting distributions Subnetworks Clusters, clusterings, partitions, hierarchies Contractions of clusters Contracted clusters - international trade Subgraphs Cuts Connectivity properties of networks Walks Equivalence relations and partitions Connectivity Condensation Bow-tie structure of the web graph The internal structure of strong components Bi-connectivity and k-connectivity Triangular and short cycle connectivities Islands Defining islands Some properties of islands Cores and generalized cores Cores Generalized cores Important vertices in networks Degrees, closeness, betweenness and other indices Clustering Computing further indices through functions Transition to methods for large networks Methods for large networks Acyclic networks Some basic properties of acyclic networks Compatible numberings: Depth and topological order Topological orderings and functions on acyclic networks Topological orderings and CPM SPC weights in acyclic networks Citation networks Analysis of citation networks Search path count method Computing SPLC and SPNP weights Implementation details Vertex weights General properties of weights SPC weights Probabilistic flow in acyclic network Nonacyclic citation networks Two-mode networks from data tables Multiplication of two-mode networks Bibliographic networks Co-authorship networks Collaboration networks Other derived networks Weights Normalizations of weights k-rings -rings and analysis of two-mode networks Two-mode cores Pathfinder Pathfinder algorithms Computing the closure over the Pathfinder semiring Spanish algorithms A sparse network algorithm Clustering, blockmodeling, and community detection The Louvain method and VOS Clustering symbolic data Symbolic objects described with distributions The leaders method An agglomerative method Approaches to temporal networks Journeys - Walks in temporal networks Measures Measures based on time slices Problems and algorithms Properties of journeys Semirings Transformation of temporal networks to static networks Evolution Levels of analysis Transition to substantive topics Scientific citation and other bibliographic networks The centrality citation network Preliminary data analyses Temporal distribution of publications Degree distributions of the centrality literature Types of works The boundary problem Transforming a citation network into an acyclic network Checking for the presence of cycles Dealing with cycles in citation networks The most important works SPC weights Obtaining SPC weights and drawing main paths The main path of the centrality citation network Line cuts Line islands The main island A geophysics and meteorology line island An optical network line island A partial summary of main path and line island results Other relevant subnetworks for a bounded network Collaboration networks Macros for collaboration networks An initial attempt of analyses of collaboration networks A brief look at the SNA literature SN5 networks Tendencies of individual authors to collaborate Participation in co-authored productions k-cores in collaboration networks The most important works SPC weights Other derived networks On the centrality and SNA collaboration networks Citation patterns in temporal United States patent data Patents Supreme Court decisions regarding patents Co-cited decisions Citations between co-cited decisions The 1976-2006 patent data Structural variables through time Temporally specific networks Identifying the starting year Defining the width of the sliding window Shrinking specific patent citation networks Structural properties Some patterns of technological development Structural properties of temporally specific networks Important subnetworks Line islands Line islands with patents tagged by keywords Vertex islands Citation patterns Patents from 1976, cited through to 2006 Utilizing supplementary variables for 1976 patents Patents from 1987, cited through to 2006 Utilizing supplementary variables for 1987 patents Comparing citation patterns for two time intervals Summary and conclusions The US Supreme Court citation network Introduction Co-cited islands of Supreme Court decisions A Native American line island Forced removal of Native American populations Regulating whites on Native American lands Curtailing the authority of Native American courts Taxing Native Americans and enforcing external laws The presence of non-Native Americans on Native American lands Some later developments A partial summary A 'Perceived Threats to Social Order' line island Perceived threats to social order The structures of the threats to social order line island Decisions involving communists and socialists The first Red Scare The second Red Scare The Warren Court on subversion Restrictions of labor groups organizing Restrictions of African Americans organizing Jehovah's Witnesses as a perceived threat Nuisance threats Direct threats to state interests Petty persecutions A partial summary Obscenity as a threat to social order The Warren Court on obscenity The Burger Court on obscenity Other perceived threats Birth control and abortion Press freedom and free speech as perceived threats Commercial speech and threats restricting it The coherence of the threats to social order line island The Dred Scott decision Citations from Dred Scott Citations to Dred Scott Methodological implications of Dred Scott Further reflections on the Supreme Court citation network Football as the world's game A brief historical overview Football clubs Football players Football in England Player migrations Institutional arrangements and the organization of football Court rulings Specific factors impacting football migration Some arguments and propositions Some preliminary results The non-English presence in the EPL Club level variations Effects of the Bosman decision Squad sizes Player fitness Starting clubs for English players EPL career lengths Overall playing careers General features of the top five European leagues Pre-modern era The modern era Flows of footballers into the top European leagues Player ages when recruited to the EPL A partial summary of results Networks of player movements to the EPL Success in the EPL The overall presence of other countries in the EPL Network flows of footballers between clubs to reach the EPL Moving directly into the EPL from local and non-local clubs Direct moves of players to the EPL from non-EPL clubs Moves from EPL clubs The 1992-1996 time slice flows with at least three moves The 1997-2001 time slice flows with at least three moves The 2002-2006 time slice flows with at least three moves Moves solely within the EPL Loans Transfers All trails of footballers to the EPL Counted features of trails to the EPL Clustering player trails Some Home Country profiles Some profiles of players from elsewhere Interpreting the clusters of player careers Summary and conclusions Mapping spatial diversity in the United States of America Mapping nations as spatial units of the United States The counties of the United States Representing networks in space Clustering with a relational constraint Conditions for hierarchical clustering methods Clustering with a relational constraint An agglomerative method for relational constraints Hierarchies Fast agglomerative clustering algorithms Nearest neighbors graphs The structure and some properties of nearest neighbor graphs The algorithm Data for constrained spatial clustering Discriminant analysis for Garreau's nations Clustering the US counties with a spatial relational constraint The eight Garreau nations in the USA The ten Woodard nations in the USA Summary On studying large networks Substance Methods, techniques, and algorithms Network data The network datasets we used The supplementary datasets we used Surprises and issues triggered by them SNA citation networks The patent citation network The Supreme Court citation network The football network The spatial network Future work The network of scientific citations The patent network The Supreme Court network The football network(s)The spatial networks Other networks Two final comments