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{"title"=>"Network centrality of metro systems", "type"=>"journal", "authors"=>[{"first_name"=>"Sybil", "last_name"=>"Derrible", "scopus_author_id"=>"26422952800"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "isbn"=>"1932-6203", "pui"=>"365221029", "sgr"=>"84863705798", "doi"=>"10.1371/journal.pone.0040575", "scopus"=>"2-s2.0-84863705798", "pmid"=>"22792373"}, "id"=>"fa039fee-7fb4-3fa4-a5c1-a70e3591176a", "abstract"=>"Whilst being hailed as the remedy to the world's ills, cities will need to adapt in the 21(st) century. In particular, the role of public transport is likely to increase significantly, and new methods and technics to better plan transit systems are in dire need. This paper examines one fundamental aspect of transit: network centrality. By applying the notion of betweenness centrality to 28 worldwide metro systems, the main goal of this paper is to study the emergence of global trends in the evolution of centrality with network size and examine several individual systems in more detail. Betweenness was notably found to consistently become more evenly distributed with size (i.e. no \"winner takes all\") unlike other complex network properties. Two distinct regimes were also observed that are representative of their structure. Moreover, the share of betweenness was found to decrease in a power law with size (with exponent 1 for the average node), but the share of most central nodes decreases much slower than least central nodes (0.87 vs. 2.48). Finally the betweenness of individual stations in several systems were examined, which can be useful to locate stations where passengers can be redistributed to relieve pressure from overcrowded stations. Overall, this study offers significant insights that can help planners in their task to design the systems of tomorrow, and similar undertakings can easily be imagined to other urban infrastructure systems (e.g., electricity grid, water/wastewater system, etc.) to develop more sustainable cities.", "link"=>"http://www.mendeley.com/research/network-centrality-metro-systems", "reader_count"=>85, "reader_count_by_academic_status"=>{"Unspecified"=>4, "Professor > Associate Professor"=>4, "Researcher"=>13, "Student > Doctoral Student"=>7, "Student > Ph. D. Student"=>25, "Student > Postgraduate"=>2, "Student > Master"=>16, "Other"=>5, "Student > Bachelor"=>5, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>4, "Professor > Associate Professor"=>4, "Researcher"=>13, "Student > Doctoral Student"=>7, "Student > Ph. D. Student"=>25, "Student > Postgraduate"=>2, "Student > Master"=>16, "Other"=>5, "Student > Bachelor"=>5, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>5, "Agricultural and Biological Sciences"=>7, "Chemistry"=>1, "Computer Science"=>12, "Earth and Planetary Sciences"=>4, "Economics, Econometrics and Finance"=>4, "Engineering"=>21, "Environmental Science"=>4, "Biochemistry, Genetics and Molecular Biology"=>2, "Mathematics"=>4, "Medicine and Dentistry"=>1, "Design"=>2, "Physics and Astronomy"=>2, "Social Sciences"=>15}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Social Sciences"=>{"Social Sciences"=>15}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Mathematics"=>{"Mathematics"=>4}, "Unspecified"=>{"Unspecified"=>5}, "Environmental Science"=>{"Environmental Science"=>4}, "Design"=>{"Design"=>2}, "Engineering"=>{"Engineering"=>21}, "Chemistry"=>{"Chemistry"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>4}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>4}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>7}, "Computer Science"=>{"Computer Science"=>12}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>2}}, "reader_count_by_country"=>{"United States"=>3, "Brazil"=>1, "Italy"=>1, "United Kingdom"=>1, "South Africa"=>1, "Spain"=>1}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/613372"], "description"=>"<p>Node betweenness and power law exponents.</p>", "links"=>[], "tags"=>["betweenness"], "article_id"=>283872, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.t002", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Node_betweenness_and_power_law_exponents_/283872", "title"=>"Node betweenness and power law exponents.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 02:53:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/612902"], "description"=>"<p>The left side is the sketch of the system where the shapes of the lines are kept even though the graph is isomorphic. Termini are illustrated by black circles and transfers stations by white circles. The right side of the graph shows the adjacency matrix (i.e. ‘1′ when a connection exist and ‘0′ otherwise). Note that link EK does not exist in real life, hence the greyed node E and the dotted line in the matrix.</p>", "links"=>[], "tags"=>["graph", "lyon", "metro", "adjacency"], "article_id"=>283398, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.g002", "stats"=>{"downloads"=>2, "page_views"=>30, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_graph_of_Lyon_metro_system_and_its_adjacency_matrix_/283398", "title"=>"Schematic graph of Lyon metro system and its adjacency matrix.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 02:51:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/613397"], "description"=>"*<p>minimum non-zero values since termini have no betweenness.</p>", "links"=>[], "tags"=>["28", "metro"], "article_id"=>283899, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.t001", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Results_for_28_metro_networks_/283899", "title"=>"Results for 28 metro networks.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 02:53:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/613001"], "description"=>"<p>The regression fits a second degree polynomial and the statistical significance is surprisingly high; only Chicago does not fit the regression as well (perhaps due to its five-lined directed elevated section in the so called “loop” area).</p>", "links"=>[], "tags"=>["betweenness", "centrality"], "article_id"=>283500, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.g003", "stats"=>{"downloads"=>2, "page_views"=>30, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_average_betweenness_centrality_C_B_with_network_size_/283500", "title"=>"Evolution of average betweenness centrality <i>C<sub>B</sub></i> with network size.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 02:51:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/613349"], "description"=>"<p>Five most central stations and their betweenness centralities for metros with <i>N</i> ≥20.</p>", "links"=>[], "tags"=>["stations", "betweenness", "centralities", "metros"], "article_id"=>283846, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.t003", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Five_most_central_stations_and_their_betweenness_centralities_for_metros_with_N_20_/283846", "title"=>"Five most central stations and their betweenness centralities for metros with <i>N</i> ≥20.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 02:53:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/612787"], "description"=>"<p>Circle representation of 32 metro networks in the world (using NodeXL <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040575#pone.0040575-Smith1\" target=\"_blank\">[<b>52</b>]</a>).</p>", "links"=>[], "tags"=>["32", "metro", "networks", "nodexl"], "article_id"=>283280, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.g001", "stats"=>{"downloads"=>2, "page_views"=>52, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Circle_representation_of_32_metro_networks_in_the_world_using_NodeXL_52_/283280", "title"=>"Circle representation of 32 metro networks in the world (using NodeXL [<b>52</b>]).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 02:50:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/613180"], "description"=>"<p>Two clear and distinct regimes can be observed here. The high coefficient of Chicago and Stockholm, whilst being comparatively small, suggests the dominance of a radial feature. On the other hand, the lower coefficient of Paris, considering its size, suggests a dominant grid pattern. New York and London can be seen as hybrids, having fairly high coefficients whilst being large, which is quite intuitive (grid pattern in the center, joined with a radial pattern in the peripheries).</p>", "links"=>[], "tags"=>["quadratic", "coefficients", "cumulative", "distributions"], "article_id"=>283677, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.g006", "stats"=>{"downloads"=>5, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_quadratic_coefficients_a_o_of_cumulative_distributions_with_network_size_/283677", "title"=>"Evolution of quadratic coefficients |<i>a<sub>o</sub></i>| of cumulative distributions with network size.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 02:52:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/613289"], "description"=>"<p>While both centralities fit power law functions, the exponent of highest betweenness is much lower than the lowest betweenness, suggesting that the loss of share in betweenness from most central nodes does not decay as fast as for least central nodes.</p>", "links"=>[], "tags"=>["highest", "lowest", "non-zero", "betweenness", "centralities"], "article_id"=>283787, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.g007", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_highest_C_Bhi_and_lowest_non_zero_C_Blo_betweenness_centralities_with_size_/283787", "title"=>"Evolution of highest <i>C<sub>Bhi</sub></i> and lowest non-zero <i>C<sub>Blo</sub></i> betweenness centralities with size.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 02:53:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/613124"], "description"=>"<p>Evolution of quadratic coefficients |<i>a<sub>n</sub></i>| of normalized cumulative distributions with network size.</p>", "links"=>[], "tags"=>["quadratic", "coefficients", "normalized", "cumulative", "distributions"], "article_id"=>283621, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.g005", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_quadratic_coefficients_a_n_of_normalized_cumulative_distributions_with_network_size_/283621", "title"=>"Evolution of quadratic coefficients |<i>a<sub>n</sub></i>| of normalized cumulative distributions with network size.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 02:52:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/613055"], "description"=>"<p>Although it can be difficult to pinpoint one specific system, the main message here is that betweenness consistently becomes more distributed with network growth. The absence of a “winner takes all” paradigm is surprising considering it is often the case with other complex network properties (e.g., in scale-free networks).</p>", "links"=>[], "tags"=>["distributions", "normalized", "betweenness", "centrality", "28"], "article_id"=>283553, "categories"=>["Physics", "Mathematics", "Ecology"], "users"=>["Sybil Derrible"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0040575.g004", "stats"=>{"downloads"=>1, "page_views"=>22, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cumulative_distributions_CD_of_normalized_betweenness_centrality_for_28_metros_/283553", "title"=>"Cumulative distributions (<i>CD</i>) of normalized betweenness centrality for 28 metros.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 02:51:56"}

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Relative Metric

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