Community Structure and Multi-Modal Oscillations in Complex Networks
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{"title"=>"Community Structure and Multi-Modal Oscillations in Complex Networks", "type"=>"journal", "authors"=>[{"first_name"=>"Henry", "last_name"=>"Dorrian", "scopus_author_id"=>"55879864900"}, {"first_name"=>"Jon", "last_name"=>"Borresen", "scopus_author_id"=>"9244053000"}, {"first_name"=>"Martyn", "last_name"=>"Amos", "scopus_author_id"=>"36726116700"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"isbn"=>"1932-6203", "pmid"=>"24130720", "doi"=>"10.1371/journal.pone.0075569", "pui"=>"370004453", "issn"=>"19326203", "sgr"=>"84885396361", "scopus"=>"2-s2.0-84885396361"}, "id"=>"40af4155-f4ab-3e34-aa30-f08e6b7d93a5", "abstract"=>"In many types of network, the relationship between structure and function is of great significance. We are particularly interested in community structures, which arise in a wide variety of domains. We apply a simple oscillator model to networks with community structures and show that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we show that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of topological hierarchy and that such modes may be directly related to network structure. We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.", "link"=>"http://www.mendeley.com/research/community-structure-multimodal-oscillations-complex-networks", "reader_count"=>21, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>4, "Researcher"=>6, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>3, "Other"=>1, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>4, "Researcher"=>6, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>3, "Other"=>1, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Engineering"=>5, "Environmental Science"=>2, "Biochemistry, Genetics and Molecular Biology"=>1, "Agricultural and Biological Sciences"=>2, "Arts and Humanities"=>1, "Neuroscience"=>2, "Physics and Astronomy"=>4, "Psychology"=>1, "Computer Science"=>3}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>5}, "Neuroscience"=>{"Neuroscience"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Psychology"=>{"Psychology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Computer Science"=>{"Computer Science"=>3}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Environmental Science"=>{"Environmental Science"=>2}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"Slovenia"=>1}, "group_count"=>1}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1232960"], "description"=>"<p>For such a network there exist parameter regimes where the smaller, globally connected sub-graphs may synchronise but the network as a whole does not (partial synchronisation or clustering).</p>", "links"=>[], "tags"=>["graph"], "article_id"=>820023, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Example_graph_with_community_structure_one_level_of_hierarchy_/820023", "title"=>"Example graph with community structure (one level of hierarchy).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232962"], "description"=>"<p>Time series for order parameter, , showing oscillatory dynamics for a network of Kuramoto oscillators coupled as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g001\" target=\"_blank\">Figure 1</a>. The coupling strength and the frequencies are normally distributed with standard deviation . Note, for such parameter values it is possible to observe full synchronisation or oscillating dynamics as shown above depending on the individual frequencies of the oscillators. The example demonstrated here, although fairly typical, is not the only observable dynamics for such a network.</p>", "links"=>[], "tags"=>["simulation"], "article_id"=>820025, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulation_for_the_network_in_Figure_1_/820025", "title"=>"Kuramoto simulation for the network in Figure 1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232964"], "description"=>"<p>Time series of global order parameter, , for increasingly perturbed hierarchical network of Kuramoto oscillators. New links are highlighted by arrows, demonstrating the robustness of dynamics to symmetry breaking, with . Each simulation uses the same initial conditions and oscillator frequencies as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g002\" target=\"_blank\">Figure 2</a>. Similar observations occur whether the simulations are conducted as individual runs (as shown here) or with the network structure being perturbed as the simulation is performed. Note: Although the time series for <b>C</b> and <b>D</b> appear very similar they are simulations from their respective graphs.</p>", "links"=>[], "tags"=>["simulation", "pertubed", "hierarchical"], "article_id"=>820027, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulation_for_increasingly_pertubed_hierarchical_network_/820027", "title"=>"Kuramoto simulation for increasingly pertubed hierarchical network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232965"], "description"=>"<p>Time series for global order parameter, , for various networks of coupled Kuramoto oscillators. Each network has been rewired using the Xswap rewiring algorithm which maintains the degree of each node. Two pairs of edges have been rewired from one graph to the next from <b>A</b> through to <b>E</b> and that the oscillating behaviour begins to break down as the hierarchical structure is decreased. . Again the same initial conditions and internal oscillator frequencies are used as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g002\" target=\"_blank\">Figure 2</a>.</p>", "links"=>[], "tags"=>["simulations", "rewired", "hierarchical"], "article_id"=>820028, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulations_for_rewired_hierarchical_networks_/820028", "title"=>"Kuramoto simulations for rewired hierarchical networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232966"], "description"=>"<p>Each network contains clusters of 45 randomly connected nodes with approximately connections in each cluster. Here the frequencies are normally distributed with . (<b>A</b>) 50 additional random connections over the whole network; (<b>B</b>) 100 additional connections; (<b>C</b>) 150 additional connections. Note: The oscillatory regions indicate the parameter regimes where oscillatory behaviour will be observed.</p>", "links"=>[], "tags"=>["bifurcations", "parameter", "networks", "clustered"], "article_id"=>820029, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Coupling_strength_bifurcations_for_order_parameter_for_networks_of_clustered_random_networks_/820029", "title"=>"Coupling strength bifurcations for order parameter for networks of clustered random networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232967"], "description"=>"<p>Time series for global order parameter, with (<b>A</b>), (<b>B</b>), and (<b>C</b>) showing multi-modal dynamics. The simulations are for networks described in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g005\" target=\"_blank\">Figure 5</a> and the parameter values taken from the oscillating regions.</p>", "links"=>[], "tags"=>["simulations", "networks", "clustered"], "article_id"=>820030, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulations_for_networks_of_clustered_random_networks_/820030", "title"=>"Kuramoto simulations for networks of clustered random networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232968"], "description"=>"<p>For such a network there exist parameter regimes where the smaller, globally connected sub-graphs may synchronise but the network as a whole does not (partial synchronisation or clustering).</p>", "links"=>[], "tags"=>["graph"], "article_id"=>820031, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Example_graph_with_community_structure_two_levels_of_hierarchy_/820031", "title"=>"Example graph with community structure (two levels of hierarchy).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232969"], "description"=>"<p>(<b>A</b>) Time series of global order parameter for a network with two levels of hierarchy with  = 0.0012 and . (<b>B</b>) Fourier spectrum for the signal in <b>A</b> demonstrating the modes of oscillation in the signal. Two strong peaks can be seen ( and ) followed by their respective echoes ( and ).</p>", "links"=>[], "tags"=>["simulation", "corresponding", "fourier"], "article_id"=>820032, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulation_and_corresponding_Fourier_spectrum_for_the_network_shown_in_Figure_7_/820032", "title"=>"Kuramoto simulation and corresponding Fourier spectrum for the network shown in Figure 7.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232972"], "description"=>"<p>(<b>A</b>) Non-partitioned representation of human metabolic network. (<b>B</b>) Partitioned representation of human metabolic network in which the network is partitioned into sub-cellular networks. The Mathematica spring algorithm is used to display the network structures, it is apparent that the two versions have a very different structure.</p>", "links"=>[], "tags"=>["representations", "versions", "metabolic"], "article_id"=>820035, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g009"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Graphical_representations_of_two_versions_of_the_same_human_metabolic_network_/820035", "title"=>"Graphical representations of two versions of the same human metabolic network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232974"], "description"=>"<p>(<b>A</b>) Time series of global order parameter for the network shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g009\" target=\"_blank\">Figure 9 </a><b>A</b> with . As no region of oscillation was found in the bifurcations for this network, parameter values were set to the same as those for the partitioned network, for the purposes of comparison. (<b>B</b>) Corresponding Fourier spectrum showing no strong peaks due to the signal not showing oscillatory behaviour.</p>", "links"=>[], "tags"=>["simulation", "corresponding", "fourier", "unpartitioned", "metabolic"], "article_id"=>820037, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g010"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulation_and_corresponding_Fourier_spectrum_for_the_unpartitioned_human_metabolic_network_/820037", "title"=>"Kuramoto simulation and corresponding Fourier spectrum for the unpartitioned human metabolic network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232976"], "description"=>"<p>(<b>A</b>) Time series of global order parameter for the network shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g009\" target=\"_blank\">Figure 9</a> (<b>B</b> with . These variables were optimised to obtain a strong oscillatory dynamic. <b>B</b>) Corresponding Fourier spectrum showing a strong peak in the Fourier transform at mode = 7, followed by an echo at mode = 15, demonstrating the oscillatory behaviour of the signal.</p>", "links"=>[], "tags"=>["simulation", "corresponding", "fourier", "partitioned", "metabolic"], "article_id"=>820039, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g011"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulation_and_corresponding_Fourier_spectrum_for_the_partitioned_human_metabolic_network_/820039", "title"=>"Kuramoto simulation and corresponding Fourier spectrum for the partitioned human metabolic network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232977"], "description"=>"<p>The London Underground (<b>A</b>) and New York Metro (<b>B</b>) networks, represented as non spatially-arranged graphs (i.e. they represent station <i>connectivity</i>, rather than the actual geographical locations of stations). Note the presence of two central clusters in the New York graph, which represent the concentration of stations in South Manhattan and Brooklyn. Both of these networks representations were generated using the Mathematica spring algorithm.</p>", "links"=>[], "tags"=>["representations", "underground", "railway"], "article_id"=>820040, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g012"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Graphical_representations_of_two_underground_railway_networks_/820040", "title"=>"Graphical representations of two underground railway networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232979"], "description"=>"<p>(<b>A</b>) Time series of global order parameter for the network shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g012\" target=\"_blank\">Figure 12 </a><b>A</b> with . These values were chosen to maximise the oscillatory behaviour. (<b>B</b>) Corresponding Fourier spectrum for signal in <b>A</b>.</p>", "links"=>[], "tags"=>["simulation", "corresponding", "fourier", "london"], "article_id"=>820042, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g013"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulation_and_corresponding_Fourier_spectrum_for_the_London_Underground_/820042", "title"=>"Kuramoto simulation and corresponding Fourier spectrum for the London Underground.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/1232980"], "description"=>"<p>(<b>A</b>) Time series of global order parameter for the network shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075569#pone-0075569-g012\" target=\"_blank\">Figure 12 </a><b>B</b> with . These values were chosen to maximise the oscillatory behaviour. (<b>B</b>) Corresponding Fourier spectrum for signal in <b>A</b>.</p>", "links"=>[], "tags"=>["simulation", "corresponding", "fourier", "york"], "article_id"=>820044, "categories"=>["Science Policy", "Information And Computing Sciences", "Biological Sciences", "Ecology"], "users"=>["Henry Dorrian", "Jon Borresen", "Martyn Amos"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0075569.g014"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kuramoto_simulation_and_corresponding_Fourier_spectrum_for_the_New_York_Metro_/820044", "title"=>"Kuramoto simulation and corresponding Fourier spectrum for the New York Metro.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-10-10 07:59:15"}

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  • {"unique-ip"=>"1", "full-text"=>"0", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"unique-ip"=>"9", "full-text"=>"10", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"6", "full-text"=>"4", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"6", "full-text"=>"6", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}

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/Ecology", "average_usage"=>[290, 478, 601, 716, 816, 914, 1016, 1112, 1203, 1285, 1373, 1451, 1516]}, {"subject_area"=>"/Biology and life sciences/Neuroscience", "average_usage"=>[261, 444, 554, 655, 748, 834, 923, 1004, 1089, 1170, 1244, 1315, 1380]}, {"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/Neural networks", "average_usage"=>[284, 481, 590, 705, 782, 880, 969, 1051, 1141, 1227, 1337, 1399, 1463]}, {"subject_area"=>"/People and places/Geographical locations", "average_usage"=>[263, 456, 571, 673, 776, 866, 955, 1040, 1132, 1217, 1310, 1391, 1454]}, {"subject_area"=>"/Physical sciences", "average_usage"=>[254, 431, 547, 651, 748, 842, 932, 1017, 1098, 1178, 1259, 1336, 1404]}, {"subject_area"=>"/Physical sciences/Mathematics", "average_usage"=>[259, 431, 541, 639, 727, 816, 898, 980, 1061, 1136, 1214, 1294, 1356]}]}
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