On the Robustness of In- and Out-Components in a Temporal Network
Publication Date
February 06, 2013
Journal
PLoS ONE
Authors
Mario Konschake, Hartmut H. K. Lentz, Franz J. Conraths, Philipp Hövel, et al
Volume
8
Issue
2
Pages
e55223
DOI
https://dx.plos.org/10.1371/journal.pone.0055223
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0055223
Web of Science
000315153400069
Scopus
84873563287
Mendeley
http://www.mendeley.com/research/robustness-outcomponents-temporal-network
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Mendeley | Further Information

{"title"=>"On the Robustness of In- and Out-Components in a Temporal Network", "type"=>"journal", "authors"=>[{"first_name"=>"Mario", "last_name"=>"Konschake", "scopus_author_id"=>"37031302400"}, {"first_name"=>"Hartmut H K", "last_name"=>"Lentz", "scopus_author_id"=>"36711837100"}, {"first_name"=>"Franz J.", "last_name"=>"Conraths", "scopus_author_id"=>"56948253100"}, {"first_name"=>"Philipp", "last_name"=>"Hövel", "scopus_author_id"=>"14056159100"}, {"first_name"=>"Thomas", "last_name"=>"Selhorst", "scopus_author_id"=>"6701652156"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"doi"=>"10.1371/journal.pone.0055223", "sgr"=>"84873563287", "issn"=>"19326203", "pui"=>"368304242", "isbn"=>"1932-6203", "pmid"=>"23405124", "scopus"=>"2-s2.0-84873563287"}, "id"=>"ac88dbd3-4dd7-3f8d-ba1d-978f7517a92f", "abstract"=>"<sec><title>Background</title><p>Many networks exhibit time-dependent topologies, where an edge only exists during a certain period of time. The first measurements of such networks are very recent so that a profound theoretical understanding is still lacking. In this work, we focus on the propagation properties of infectious diseases in time-dependent networks. In particular, we analyze a dataset containing livestock trade movements. The corresponding networks are known to be a major route for the spread of animal diseases. In this context chronology is crucial. A disease can only spread if the temporal sequence of trade contacts forms a chain of causality. Therefore, the identification of relevant nodes under time-varying network topologies is of great interest for the implementation of counteractions.</p></sec><sec><title>Methodology/Findings</title><p>We find that a time-aggregated approach might fail to identify epidemiologically relevant nodes. Hence, we explore the adaptability of the concept of centrality of nodes to temporal networks using a data-driven approach on the example of animal trade. We utilize the size of the in- and out-component of nodes as centrality measures. Both measures are refined to gain full awareness of the time-dependent topology and finite infectious periods. We show that the size of the components exhibit strong temporal heterogeneities. In particular, we find that the size of the components is overestimated in time-aggregated networks. For disease control, however, a risk assessment independent of time and specific disease properties is usually favored. We therefore explore the disease parameter range, in which a time-independent identification of central nodes remains possible.</p></sec><sec><title>Conclusions</title><p>We find a ranking of nodes according to their component sizes reasonably stable for a wide range of infectious periods. Samples based on this ranking are robust enough against varying disease parameters and hence are promising tools for disease control.</p></sec>", "link"=>"http://www.mendeley.com/research/robustness-outcomponents-temporal-network", "reader_count"=>51, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>2, "Researcher"=>14, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>2, "Student > Master"=>2, "Other"=>1, "Student > Bachelor"=>1, "Lecturer > Senior Lecturer"=>2, "Professor"=>5}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>2, "Researcher"=>14, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>2, "Student > Master"=>2, "Other"=>1, "Student > Bachelor"=>1, "Lecturer > Senior Lecturer"=>2, "Professor"=>5}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>6, "Environmental Science"=>2, "Mathematics"=>6, "Agricultural and Biological Sciences"=>13, "Medicine and Dentistry"=>1, "Arts and Humanities"=>1, "Veterinary Science and Veterinary Medicine"=>8, "Physics and Astronomy"=>8, "Computer Science"=>4}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>8}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>13}, "Computer Science"=>{"Computer Science"=>4}, "Mathematics"=>{"Mathematics"=>6}, "Unspecified"=>{"Unspecified"=>6}, "Environmental Science"=>{"Environmental Science"=>2}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Veterinary Science and Veterinary Medicine"=>{"Veterinary Science and Veterinary Medicine"=>8}}, "reader_count_by_country"=>{"United States"=>2, "United Kingdom"=>2, "Switzerland"=>1, "Germany"=>2}, "group_count"=>5}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/493256"], "description"=>"<p>Panel A: Outbreak probability as given by the fraction of primary infections causing at least one secondary infection. The dashed line shows the outbreak probability of the time-aggregated network, i.e. the fraction of nodes with non-vanishing out-degree. Panel B: Average out-components of primary infections, i.e. the <i>number</i> of follow-up infections. The 50% confidence interval is indicated by the shaded area. Only for a significant fraction of the network can be infected. For increasing , both values approach a saturation. For days, approximately every second primary infection will cause follow-up infections which will reach on average of the network. Both numbers are significantly lower than their counterparts in the static network, as indicated by the dashed line. Here approximately of all primary infections cause follow-up infections with a mean size of epidemic of almost of the network.</p>", "links"=>[], "tags"=>["probabilities", "out-component", "sizes", "infectious", "periods"], "article_id"=>163770, "categories"=>["Physics", "Information And Computing Sciences", "Infectious Diseases", "Biotechnology"], "users"=>["Mario Konschake", "Hartmut H. K. Lentz", "Franz J. Conraths", "Philipp Hövel", "Thomas Selhorst"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055223.g001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Outbreak_probabilities_A_and_out_component_sizes_B_for_different_infectious_periods_/163770", "title"=>"Outbreak probabilities (A) and out-component sizes (B) for different infectious periods .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-06 01:02:50"}
  • {"files"=>["https://ndownloader.figshare.com/files/493581"], "description"=>"<p>Each curve corresponds to one node. The top hundred nodes with the largest out-components are shown. Curves representing nodes with higher ranking are darker than those with lower rankings. For illustration purposes an arbitrarily chosen node is displayed in red.</p>", "links"=>[], "tags"=>["nodes", "out-component"], "article_id"=>164102, "categories"=>["Physics", "Information And Computing Sciences", "Infectious Diseases", "Biotechnology"], "users"=>["Mario Konschake", "Hartmut H. K. Lentz", "Franz J. Conraths", "Philipp Hövel", "Thomas Selhorst"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055223.g003", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Ranking_of_nodes_according_to_their_mean_out_component_size_/164102", "title"=>"Ranking of nodes according to their mean out-component size .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-06 01:08:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/493397"], "description"=>"<p>Panel A shows the size of the out-component for an exemplary node as a function of . For many times , the size of the out-component has similar values close to , but for some we also find to vanish. Panel B shows the distribution for all nodes, i.e. the top view of panel A for all nodes of the network. Each horizontal line represents one node, the example node chosen for panel A is indicated by the dotted orange line. For the sake of clarity, only every 100th node is plotted. Nodes are arranged according to their averaged value of over all from top to bottom, i.e. the node with the largest averaged out-component is displayed as the top line of the panel.</p>", "links"=>[], "tags"=>["exemplary", "infectious"], "article_id"=>163919, "categories"=>["Physics", "Information And Computing Sciences", "Infectious Diseases", "Biotechnology"], "users"=>["Mario Konschake", "Hartmut H. K. Lentz", "Franz J. Conraths", "Philipp Hövel", "Thomas Selhorst"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055223.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distribution_of_for_an_exemplary_infectious_period_of_days_/163919", "title"=>"Distribution of for an exemplary infectious period of days.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-06 01:05:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/493682"], "description"=>"<p>Shown are the mean intersections and for three different sample sizes (red), (blue), and (green) of the network representing approximately , , or nodes, respectively. The sampling is calculated based on the mean largest out-component over all and (see text for details). is based on averaging over all pairs with or respectively. Confidence intervals are given by the shaded areas.</p>", "links"=>[], "tags"=>["samples", "out-component"], "article_id"=>164206, "categories"=>["Physics", "Information And Computing Sciences", "Infectious Diseases", "Biotechnology"], "users"=>["Mario Konschake", "Hartmut H. K. Lentz", "Franz J. Conraths", "Philipp Hövel", "Thomas Selhorst"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055223.g004", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Robustness_of_samples_based_on_the_out_component_size_of_nodes_/164206", "title"=>"Robustness of samples based on the out-component size of nodes.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-06 01:10:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/482781", "https://ndownloader.figshare.com/files/482784", "https://ndownloader.figshare.com/files/482789"], "description"=>"<div><h3>Background</h3><p>Many networks exhibit time-dependent topologies, where an edge only exists during a certain period of time. The first measurements of such networks are very recent so that a profound theoretical understanding is still lacking. In this work, we focus on the propagation properties of infectious diseases in time-dependent networks. In particular, we analyze a dataset containing livestock trade movements. The corresponding networks are known to be a major route for the spread of animal diseases. In this context chronology is crucial. A disease can only spread if the temporal sequence of trade contacts forms a chain of causality. Therefore, the identification of relevant nodes under time-varying network topologies is of great interest for the implementation of counteractions.</p> <h3>Methodology/Findings</h3><p>We find that a time-aggregated approach might fail to identify epidemiologically relevant nodes. Hence, we explore the adaptability of the concept of centrality of nodes to temporal networks using a data-driven approach on the example of animal trade. We utilize the size of the in- and out-component of nodes as centrality measures. Both measures are refined to gain full awareness of the time-dependent topology and finite infectious periods. We show that the size of the components exhibit strong temporal heterogeneities. In particular, we find that the size of the components is overestimated in time-aggregated networks. For disease control, however, a risk assessment independent of time and specific disease properties is usually favored. We therefore explore the disease parameter range, in which a time-independent identification of central nodes remains possible.</p> <h3>Conclusions</h3><p>We find a ranking of nodes according to their component sizes reasonably stable for a wide range of infectious periods. Samples based on this ranking are robust enough against varying disease parameters and hence are promising tools for disease control.</p> </div>", "links"=>[], "tags"=>["robustness", "in-", "out-components", "temporal", "network"], "article_id"=>155923, "categories"=>["Physics", "Information And Computing Sciences", "Infectious Diseases", "Biotechnology"], "users"=>["Mario Konschake", "Hartmut H. K. Lentz", "Franz J. Conraths", "Philipp Hövel", "Thomas Selhorst"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0055223.s001", "https://dx.doi.org/10.1371/journal.pone.0055223.s002", "https://dx.doi.org/10.1371/journal.pone.0055223.s003"], "stats"=>{"downloads"=>13, "page_views"=>58, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/On_the_Robustness_of_In_and_Out_Components_in_a_Temporal_Network__/155923", "title"=>"On the Robustness of In- and Out-Components in a Temporal Network", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-02-06 01:38:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/493782"], "description"=>"<p>The relative size of the intersection of the top nodes is based on their value of the dynamic out-component and on static measures of centrality. In the upper panel the comparison for a fixed infectious period of days is shown and in the lower one for a fixed infectious period of days.</p>", "links"=>[], "tags"=>["out-component", "static"], "article_id"=>164306, "categories"=>["Physics", "Information And Computing Sciences", "Infectious Diseases", "Biotechnology"], "users"=>["Mario Konschake", "Hartmut H. K. Lentz", "Franz J. Conraths", "Philipp Hövel", "Thomas Selhorst"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0055223.g005", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_between_the_dynamic_out_component_and_static_measures_/164306", "title"=>"Comparison between the dynamic out-component and static measures.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-06 01:11:46"}

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  • {"unique-ip"=>"1", "full-text"=>"2", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"6", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"4", "full-text"=>"5", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
  • {"unique-ip"=>"4", "full-text"=>"6", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
  • {"unique-ip"=>"5", "full-text"=>"2", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"9"}

Relative Metric

{"start_date"=>"2013-01-01T00:00:00Z", "end_date"=>"2013-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences", "average_usage"=>[269, 466, 588, 697, 800, 896, 988, 1076, 1165, 1254, 1340, 1417]}, {"subject_area"=>"/Biology and life sciences/Veterinary science", "average_usage"=>[313, 571, 709, 825, 944, 1048, 1145, 1261, 1354, 1434, 1524, 1599, 1684]}, {"subject_area"=>"/Computer and information sciences", "average_usage"=>[297, 488, 616, 724, 828, 939, 1038, 1127, 1223, 1311, 1393, 1479, 1556]}, {"subject_area"=>"/Computer and information sciences/Network analysis", "average_usage"=>[340, 548, 701, 844, 945, 1073, 1189, 1282, 1391, 1488, 1562, 1660, 1731]}, {"subject_area"=>"/Medicine and health sciences/Epidemiology", "average_usage"=>[263, 452, 568, 671, 758, 847, 921, 1023, 1101, 1187, 1264, 1340, 1394]}, {"subject_area"=>"/Medicine and health sciences/Infectious diseases", "average_usage"=>[297, 523, 655, 765, 866, 971, 1070, 1159, 1256, 1337, 1424, 1496, 1568]}, {"subject_area"=>"/Physical sciences/Mathematics", "average_usage"=>[259, 431, 541, 639, 727, 816, 898, 980, 1061, 1136, 1214, 1294, 1356]}]}
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