Dimensionality of Social Networks Using Motifs and Eigenvalues
Publication Date
September 04, 2014
Journal
PLOS ONE
Authors
Anthony Bonato, David F. Gleich, Myunghwan Kim, Dieter Mitsche, et al
Volume
9
Issue
9
Pages
e106052
DOI
https://dx.plos.org/10.1371/journal.pone.0106052
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0106052
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/25188391
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4154874
Europe PMC
http://europepmc.org/abstract/MED/25188391
Web of Science
000341271500019
Scopus
84907051510
Mendeley
http://www.mendeley.com/research/dimensionality-social-networks-using-motifs-eigenvalues
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Mendeley | Further Information

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Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1662453"], "description"=>"<p>Each red dot (SVM) is the predicted dimension computed via graphlet features and a support vector machine classifier. For the Facebook data, we find that . For the LinkedIn data, we find that . And these are plotted as the red linear fit line. Our theoretical model predicts a dimension of and we plot this as the dashed line. In each figure, we show the variance in the fitted dimension as a box-plot. We estimate the variance by using only 20% of the original training data and repeating over 50 trials. There are only a few outliers for small dimensions.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161952, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.g004", "stats"=>{"downloads"=>4, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Facebook_dimension_at_left_LinkedIn_dimension_at_right_/1161952", "title"=>"Facebook dimension at left, LinkedIn dimension at right.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662454"], "description"=>"<p>Each blue point (Eigen) is the dimension of the MGEO-P sample with the minimum KL-divergence between the graph and the MGEO-P sample. We also show any other other dimensions within 5% of this divergence value. The dimensions shift modestly higher for Facebook and remain almost unchanged for LinkedIn. Both still are closely correlated with the theoretical prediction based on the model based on (dashed line). The linear fits to the predicted dimensions is plotted as the red linear fit line.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161953, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.g005", "stats"=>{"downloads"=>2, "page_views"=>24, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Facebook_data_at_left_LinkedIn_data_at_right_/1161953", "title"=>"Facebook data at left, LinkedIn data at right.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662455"], "description"=>"<p>The MGEO-P model correctly captures the peak of the distribution around 1, but fails to completely capture the tail between 1 and 2. Thus, we see meaningful difference between these profiles and hence, do not suggest that MGEO-P captures all of the properties of real-world social networks.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161954, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.g006", "stats"=>{"downloads"=>1, "page_views"=>23, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_For_three_of_the_Facebook_networks_we_show_the_eigenvalue_histogram_in_red_the_eigenvalue_histogram_from_the_best_fit_MGEO_P_network_in_blue_and_the_eigenvalue_histograms_for_samples_from_the_other_dimensions_in_grey_/1161954", "title"=>"For three of the Facebook networks, we show the eigenvalue histogram in red, the eigenvalue histogram from the best fit MGEO-P network in blue, and the eigenvalue histograms for samples from the other dimensions in grey.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662456"], "description"=>"<p>The parameters of the MGEO-P model.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161955, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.t001", "stats"=>{"downloads"=>5, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_parameters_of_the_MGEO_P_model_/1161955", "title"=>"The parameters of the MGEO-P model.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662457"], "description"=>"<p>The specific dimensional scaling lines fit to the data in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0106052#pone-0106052-g004\" target=\"_blank\">Figures 4</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0106052#pone-0106052-g005\" target=\"_blank\">5</a> illustrate the growth of the network is logarithmic in the number of nodes.</p><p>Dimension scaling for Facebook and LinkedIn.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161956, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.t002", "stats"=>{"downloads"=>7, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dimension_scaling_for_Facebook_and_LinkedIn_/1161956", "title"=>"Dimension scaling for Facebook and LinkedIn.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662458"], "description"=>"<div><p>We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an <i>m</i>-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when <i>m</i> scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.</p></div>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161957, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052", "stats"=>{"downloads"=>34, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dimensionality_of_Social_Networks_Using_Motifs_and_Eigenvalues_/1161957", "title"=>"Dimensionality of Social Networks Using Motifs and Eigenvalues", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662449"], "description"=>"<p>Each figure shows the graph “replicated” in grey on all sides in order to illustrate the torus metric. Links are drawn to the closest replicated neighbor. The blue square indicates the region . <i>Top row (left to right)</i> The MGEO-P process begins with relatively few nodes, and thus, nodes must have large influence radii (red squares) to link anywhere. As more nodes arrive, large radii result in many connections, modeling influential users, and small radii result in a few connections, modeling standard users. <i>Bottom row</i> Illustrates the final constructed graph.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161948, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.g001", "stats"=>{"downloads"=>0, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_An_example_describing_the_MGEO_P_process_on_a_graph_with_nodes_in_the_unit_square_with_torus_metric_where_and_and_/1161948", "title"=>"An example describing the MGEO-P process on a graph with nodes in the unit square with torus metric, where and and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662450"], "description"=>"<p>Throughout, red lines denote the flow of features for the MGEO-P networks whereas blue lines denote flow of features for the original networks. At the bottom, we show an enlarged representation of the 8 graphlets we use.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161949, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.g002", "stats"=>{"downloads"=>3, "page_views"=>27, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_At_left_and_center_we_have_the_steps_involved_in_fitting_via_graphlets_at_right_and_center_we_have_the_steps_involved_in_fitting_via_spectral_histogram_/1161949", "title"=>"At left and center, we have the steps involved in fitting via graphlets; at right and center, we have the steps involved in fitting via spectral histogram.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-04 04:06:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1662451"], "description"=>"<p>We see similar scaling for both types of networks, but with slightly different offsets. For Facebook, with ; for LinkedIn with . The regularity in the LinkedIn sizes is due to our construction of those networks.</p>", "links"=>[], "tags"=>["influence regions", "network model", "eigenvalue distribution", "social networks", "nod", "m scales logarithmically", "motif counts", "logarithmic dimension hypothesis"], "article_id"=>1161950, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Anthony Bonato", "David F. Gleich", "Myunghwan Kim", "Dieter Mitsche", "Paweł Prałat", "Yanhua Tian", "Stephen J. Young"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0106052.g003", "stats"=>{"downloads"=>2, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_scale_of_the_network_data_involved_in_our_study_varies_over_three_orders_of_magnitude_/1161950", "title"=>"The scale of the network data involved in our study varies over three orders of magnitude.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-04 04:06:35"}

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