Inferring General Relations between Network Characteristics from Specific Network Ensembles
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{"title"=>"Inferring general relations between network characteristics from specific network ensembles", "type"=>"journal", "authors"=>[{"first_name"=>"Stefano", "last_name"=>"Cardanobile", "scopus_author_id"=>"22984135700"}, {"first_name"=>"Volker", "last_name"=>"Pernice", "scopus_author_id"=>"23028772300"}, {"first_name"=>"Moritz", "last_name"=>"Deger", "scopus_author_id"=>"36508569700"}, {"first_name"=>"Stefan", "last_name"=>"Rotter", "scopus_author_id"=>"7004581948"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"isbn"=>"1932-6203", "pmid"=>"22701586", "doi"=>"10.1371/journal.pone.0037911", "pui"=>"364979282", "issn"=>"19326203", "sgr"=>"84862023537", "scopus"=>"2-s2.0-84862023537"}, "id"=>"6a131552-6e48-37a9-9a43-7691e82144e3", "abstract"=>"Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their ability to generate networks with large structural variability. In particular, we consider the statistical constraints which the respective construction scheme imposes on the generated networks. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This makes it possible to infer global features from local ones using regression models trained on networks with high generalization power. Our results confirm and extend previous findings regarding the synchronization properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks in good approximation. Finally, we demonstrate on three different data sets (C. elegans neuronal network, R. prowazekii metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models.", "link"=>"http://www.mendeley.com/research/inferring-general-relations-between-network-characteristics-specific-network-ensembles", "reader_count"=>52, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>4, "Student > Doctoral Student"=>6, "Researcher"=>9, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>3, "Student > Master"=>2, "Other"=>2, "Lecturer"=>1, "Professor"=>6}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>4, "Student > Doctoral Student"=>6, "Researcher"=>9, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>3, "Student > Master"=>2, "Other"=>2, "Lecturer"=>1, "Professor"=>6}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>1, "Mathematics"=>3, "Agricultural and Biological Sciences"=>18, "Medicine and Dentistry"=>4, "Neuroscience"=>5, "Physics and Astronomy"=>6, "Psychology"=>3, "Social Sciences"=>3, "Computer Science"=>6, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>4}, "Neuroscience"=>{"Neuroscience"=>5}, "Social Sciences"=>{"Social Sciences"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>6}, "Psychology"=>{"Psychology"=>3}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>18}, "Computer Science"=>{"Computer Science"=>6}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"United States"=>2, "Norway"=>1, "Ireland"=>1, "Finland"=>1, "United Kingdom"=>1, "France"=>1, "Portugal"=>1, "Switzerland"=>1, "Germany"=>3}, "group_count"=>6}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/628399"], "description"=>"<p>Statistical descriptors (thematic ordering as in figures).</p>", "links"=>[], "tags"=>["descriptors", "ordering"], "article_id"=>298893, "categories"=>["Information And Computing Sciences", "Mathematics", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Stefano Cardanobile", "Volker Pernice", "Moritz Deger", "Stefan Rotter"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0037911.t002", "stats"=>{"downloads"=>1, "page_views"=>37, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Statistical_descriptors_thematic_ordering_as_in_figures_/298893", "title"=>"Statistical descriptors (thematic ordering as in figures).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 04:17:49"}
  • {"files"=>["https://ndownloader.figshare.com/files/628431"], "description"=>"<p>Symbols and concepts.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "computer science", "physics", "mathematics"], "article_id"=>298920, "categories"=>["Information And Computing Sciences", "Mathematics", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Stefano Cardanobile", "Volker Pernice", "Moritz Deger", "Stefan Rotter"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0037911.t001", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Symbols_and_concepts_/298920", "title"=>"Symbols and concepts.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 04:17:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/628246"], "description"=>"<p>(a) Scattered data of the predicted global features for three data sets, using the regression coefficients obtained from network models with matched network size. Colors encode the model used for prediction. (b) To study whether the prediction is robust with respect to the chosen threshold, we depict the relative mean-squared error (defined as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037911#pone-0037911-g002\" target=\"_blank\">Figure 2</a>) averaged over the whole data-set of real-world networks as it depends on the threshold. The inset shows the average number of selected features for a given value of the threshold <i>σ</i>. (c) Reliability index of the correlation coefficients between pairs of features, calculated across network models. High values point toward a general statistical law for all networks. (d) Data scatters for some pairs of features with significant correlations. Different colors encode different data sets: The number of nodes and the overall connectivity is extracted to generate a set of matched networks from various models. The scattered data are extracted from surrogate networks. The large markers denote the positions of the true data set in the data cloud. The statistics of the real-world networks lie in the data cloud, suggesting that those relations correspond to relevant statistical laws of complex networks. In the upper left panel, the <i>R. prowazekii</i> metabolism network is missing because of degenerate statistics.</p>", "links"=>[], "tags"=>["real-world"], "article_id"=>298740, "categories"=>["Information And Computing Sciences", "Mathematics", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Stefano Cardanobile", "Volker Pernice", "Moritz Deger", "Stefan Rotter"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0037911.g003", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Prediction_of_global_features_in_real_world_networks_/298740", "title"=>"Prediction of global features in real-world networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:17:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/628369"], "description"=>"<p>Correlated feature pairs with highest reliability index.</p>", "links"=>[], "tags"=>["pairs", "highest"], "article_id"=>298863, "categories"=>["Information And Computing Sciences", "Mathematics", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Stefano Cardanobile", "Volker Pernice", "Moritz Deger", "Stefan Rotter"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0037911.t003", "stats"=>{"downloads"=>1, "page_views"=>35, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Correlated_feature_pairs_with_highest_reliability_index_/298863", "title"=>"Correlated feature pairs with highest reliability index.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 04:17:39"}
  • {"files"=>["https://ndownloader.figshare.com/files/628133"], "description"=>"<p>(a) Residual prediction errors. For the global features, we train a linear regression model with the data generated by one particular network model with random parameters and we test data from the remaining models. The residual prediction error is given by the mean-squared error normalized by the overall standard deviation of the corresponding feature. A value of 1 indicates the result obtained if the true mean of the population was known and used as a predictor. Note that using the empirical population mean as a predictor leads to a relative error larger than 1. MF network models perform consistently around 1, whereas other models have occasionally very large errors. (b) The coefficients of the linear regressor from the MF(3,3) set, normalized by the standard deviation of the local features used for the prediction. We excluded WS due to their very poor performance here. For some of the global features, the magnitude of the coefficients is consistent over the network models. For example, the positive contribution of the variance of the in-degree to the synchronization index and negative contribution to the synchronization time is consistent with the dynamic interpretation of these measures.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "computer science", "physics", "mathematics"], "article_id"=>298621, "categories"=>["Information And Computing Sciences", "Mathematics", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Stefano Cardanobile", "Volker Pernice", "Moritz Deger", "Stefan Rotter"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0037911.g002", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Prediction_of_global_features_from_local_ones_/298621", "title"=>"Prediction of global features from local ones.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:16:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/627988"], "description"=>"<p>(a) Scattered data of two global features for realizations of different types of networks (size <i>N</i> = 1000), displayed in loglog scale. On the horizontal axis the synchronization index SI, on the vertical axis the mean out -shell OSM of the corresponding graph are shown. (b) Correlations between pairs of features, arranged in a matrix (size <i>N</i> = 1000). For BA and WS networks, a clear structure is visible, due to the thematic ordering of the features. Strong correlations are, in fact, the major cause for the low feature entropy generated by non-MF networks, quantified in Panel (c). Entropy of the multivariate distribution of features. The feature entropy generated by MF networks is considerably higher, and it scales linearly with the number of nodes in the networks.</p>", "links"=>[], "tags"=>["generated"], "article_id"=>298482, "categories"=>["Information And Computing Sciences", "Mathematics", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Stefano Cardanobile", "Volker Pernice", "Moritz Deger", "Stefan Rotter"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0037911.g001", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Variability_generated_by_various_network_models_/298482", "title"=>"Variability generated by various network models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 04:15:37"}

PMC Usage Stats | Further Information

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Relative Metric

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