Mapping Change in Large Networks
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{"title"=>"Mapping change in large networks", "type"=>"journal", "authors"=>[{"first_name"=>"Martin", "last_name"=>"Rosvall", "scopus_author_id"=>"9241534000"}, {"first_name"=>"Carl T.", "last_name"=>"Bergstrom", "scopus_author_id"=>"7004918484"}], "year"=>2010, "source"=>"PLoS ONE", "identifiers"=>{"pmid"=>"20111700", "doi"=>"10.1371/journal.pone.0008694", "sgr"=>"77749239782", "arxiv"=>"0812.1242", "isbn"=>"1932-6203", "scopus"=>"2-s2.0-77749239782", "issn"=>"19326203", "pui"=>"358424336"}, "id"=>"abb9bf3f-ee93-3371-b9d1-1f6425dc09df", "abstract"=>"Change is a fundamental ingredient of interaction patterns in biology, technology, the economy, and science itself: Interactions within and between organisms change; transportation patterns by air, land, and sea all change; the global financial flow changes; and the frontiers of scientific research change. Networks and clustering methods have become important tools to comprehend instances of these large-scale structures, but without methods to distinguish between real trends and noisy data, these approaches are not useful for studying how networks change. Only if we can assign significance to the partitioning of single networks can we distinguish meaningful structural changes from random fluctuations. Here we show that bootstrap resampling accompanied by significance clustering provides a solution to this problem. To connect changing structures with the changing function of networks, we highlight and summarize the significant structural changes with alluvial diagrams and realize de Solla Price's vision of mapping change in science: studying the citation pattern between about 7000 scientific journals over the past decade, we find that neuroscience has transformed from an interdisciplinary specialty to a mature and stand-alone discipline.", "link"=>"http://www.mendeley.com/research/mapping-change-large-networks-2", "reader_count"=>483, "reader_count_by_academic_status"=>{"Unspecified"=>9, "Professor > Associate Professor"=>29, "Librarian"=>7, "Researcher"=>110, "Student > Doctoral Student"=>22, "Student > Ph. D. Student"=>154, "Student > Postgraduate"=>23, "Student > Master"=>55, "Other"=>21, "Student > Bachelor"=>19, "Lecturer"=>4, "Lecturer > Senior Lecturer"=>4, "Professor"=>26}, "reader_count_by_user_role"=>{"Unspecified"=>9, "Professor > Associate Professor"=>29, "Librarian"=>7, "Researcher"=>110, "Student > Doctoral Student"=>22, "Student > Ph. D. Student"=>154, "Student > Postgraduate"=>23, "Student > Master"=>55, "Other"=>21, "Student > Bachelor"=>19, "Lecturer"=>4, "Lecturer > Senior Lecturer"=>4, "Professor"=>26}, "reader_count_by_subject_area"=>{"Unspecified"=>23, "Agricultural and Biological Sciences"=>94, "Arts and Humanities"=>7, "Philosophy"=>2, "Business, Management and Accounting"=>24, "Chemistry"=>5, "Computer Science"=>132, "Decision Sciences"=>3, "Earth and Planetary Sciences"=>7, "Economics, Econometrics and Finance"=>9, "Engineering"=>17, "Environmental Science"=>12, "Biochemistry, Genetics and Molecular Biology"=>4, "Materials Science"=>3, "Mathematics"=>26, "Medicine and Dentistry"=>10, "Neuroscience"=>6, "Design"=>5, "Physics and Astronomy"=>35, "Psychology"=>14, "Social Sciences"=>41, "Linguistics"=>4}, "reader_count_by_subdiscipline"=>{"Materials Science"=>{"Materials Science"=>3}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>10}, "Social Sciences"=>{"Social Sciences"=>41}, "Decision Sciences"=>{"Decision Sciences"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>35}, "Psychology"=>{"Psychology"=>14}, "Mathematics"=>{"Mathematics"=>26}, "Unspecified"=>{"Unspecified"=>23}, "Environmental Science"=>{"Environmental Science"=>12}, "Arts and Humanities"=>{"Arts and Humanities"=>7}, "Design"=>{"Design"=>5}, "Engineering"=>{"Engineering"=>17}, "Chemistry"=>{"Chemistry"=>5}, "Neuroscience"=>{"Neuroscience"=>6}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>7}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>9}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>94}, "Computer Science"=>{"Computer Science"=>132}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>24}, "Linguistics"=>{"Linguistics"=>4}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>4}, "Philosophy"=>{"Philosophy"=>2}}, "reader_count_by_country"=>{"Republic of Singapore"=>1, "United States"=>39, "Malaysia"=>1, "Portugal"=>1, "Netherlands"=>8, "Sweden"=>1, "Austria"=>1, "Korea (South)"=>1, "Ireland"=>2, "China"=>2, "Poland"=>1, "Brazil"=>3, "Slovenia"=>1, "France"=>6, "Chile"=>1, "Sri Lanka"=>1, "Japan"=>3, "United Kingdom"=>17, "Belarus"=>1, "Switzerland"=>4, "Spain"=>2, "India"=>1, "Canada"=>2, "Belgium"=>2, "Finland"=>1, "South Africa"=>2, "Italy"=>3, "Mexico"=>1, "Australia"=>1, "Germany"=>9}, "group_count"=>23}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/865662"], "description"=>"<p>By repeatedly resampling of the weighted links from the original networks, we create “bootstrap worlds” of 1000 resampled networks. By clustering these bootstrap networks, and comparing to the clustering of the original networks, we can estimate the degree of support that the data provide in assigning each node to a cluster. In the bottom networks, the darker colors represent nodes that are clustered together in at least 95% of the 1000 bootstrap networks. The alluvial diagram highlights and summarizes the structural changes between the time 1 and time 2 significance clusters. The height of each block represents the volume of flow through the cluster. The clusters are ordered from bottom to top by their size, with mutually nonsignificant clusters placed together and separated by a third of the standard spacing. The orange module merges with the red module, but the nodes are not clustered together in 95% of the bootstrap networks. The blue module splits, but the significant nodes in the blue and purple modules are clustered together in more than 5% of the bootstrap networks. Neither change is significant.</p>", "links"=>[], "tags"=>["clustering", "alluvial", "diagram"], "article_id"=>536120, "categories"=>["Mathematics", "Physics", "Information And Computing Sciences"], "users"=>["Martin Rosvall", "Carl T. Bergstrom"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008694.g004", "stats"=>{"downloads"=>4, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Significance_clustering_and_alluvial_diagram_for_mapping_change_in_large_networks_/536120", "title"=>"Significance clustering and alluvial diagram for mapping change in large networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-27 01:42:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/865323"], "description"=>"<p>The standard approach to cluster networks is to minimize an objective function over possible partitions of the network, as in the left side of the diagram. By repeated resampling of the weighted links from the original network, we create a “bootstrap world” of resampled networks. By clustering these as well, and comparing to the clustering of the original network, we can estimate the degree of support that the data provide in assigning each node to a cluster. In the bottom network, the darker nodes are clustered together in at least 95% of the 1000 bootstrap networks.</p>", "links"=>[], "tags"=>["clustering"], "article_id"=>535785, "categories"=>["Mathematics", "Physics", "Information And Computing Sciences"], "users"=>["Martin Rosvall", "Carl T. Bergstrom"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008694.g001", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Significance_clustering_of_networks_/535785", "title"=>"Significance clustering of networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-27 01:36:25"}
  • {"files"=>["https://ndownloader.figshare.com/files/429611", "https://ndownloader.figshare.com/files/429687", "https://ndownloader.figshare.com/files/429743"], "description"=>"<div><p>Change is a fundamental ingredient of interaction patterns in biology, technology, the economy, and science itself: Interactions within and between organisms change; transportation patterns by air, land, and sea all change; the global financial flow changes; and the frontiers of scientific research change. Networks and clustering methods have become important tools to comprehend instances of these large-scale structures, but without methods to distinguish between real trends and noisy data, these approaches are not useful for studying how networks change. Only if we can assign significance to the partitioning of single networks can we distinguish meaningful structural changes from random fluctuations. Here we show that bootstrap resampling accompanied by significance clustering provides a solution to this problem. To connect changing structures with the changing function of networks, we highlight and summarize the significant structural changes with alluvial diagrams and realize de Solla Price's vision of mapping change in science: studying the citation pattern between about 7000 scientific journals over the past decade, we find that neuroscience has transformed from an interdisciplinary specialty to a mature and stand-alone discipline.</p></div>", "links"=>[], "tags"=>["networks"], "article_id"=>144812, "categories"=>["Mathematics", "Physics", "Information And Computing Sciences"], "users"=>["Martin Rosvall", "Carl T. Bergstrom"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0008694.s001", "https://dx.doi.org/10.1371/journal.pone.0008694.s002", "https://dx.doi.org/10.1371/journal.pone.0008694.s003"], "stats"=>{"downloads"=>28, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Mapping_Change_in_Large_Networks/144812", "title"=>"Mapping Change in Large Networks", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2010-01-27 01:20:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/865556"], "description"=>"<p>This set of scientific fields show the major shifts in the last decade of science. Each significance clustering for the citation networks in years 2001, 2003, 2005, and 2007 occupies a column in the diagram and is horizontally connected to preceding and succeeding significance clusterings by stream fields. Each block in a column represents a field and the height of the block reflects citation flow through the field. The fields are ordered from bottom to top by their size with mutually nonsignificant fields placed together and separated by half the standard spacing. We use a darker color to indicate the significant subset of each cluster. All journals that are clustered in the field of neuroscience in year 2007 are colored to highlight the fusion and formation of neuroscience.</p>", "links"=>[], "tags"=>["computer science/information technology", "mathematics/mathematical computing", "physics/interdisciplinary physics"], "article_id"=>536021, "categories"=>["Mathematics", "Physics", "Information And Computing Sciences"], "users"=>["Martin Rosvall", "Carl T. Bergstrom"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008694.g003", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mapping_change_in_science_/536021", "title"=>"Mapping change in science.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-27 01:40:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/865456"], "description"=>"<p>An alluvial diagram (bottom), with clusters ordered by size, reveals changes in network structures over time. Here the height of each block represents the volume of flow through the cluster, with significant subsets in darker color. The orange module merges with the red module, but the nodes are not clustered together in 95% of the bootstrap networks. The blue module splits, but the significant nodes in the blue and purple modules are clustered together in more than 5% of the bootstrap networks. With a 5% significance threshold, neither change is significant.</p>", "links"=>[], "tags"=>["computer science/information technology", "mathematics/mathematical computing", "physics/interdisciplinary physics"], "article_id"=>535918, "categories"=>["Mathematics", "Physics", "Information And Computing Sciences"], "users"=>["Martin Rosvall", "Carl T. Bergstrom"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008694.g002", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mapping_change_in_networks_/535918", "title"=>"Mapping change in networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-27 01:38:38"}

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Relative Metric

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