A Shadowing Problem in the Detection of Overlapping Communities: Lifting the Resolution Limit through a Cascading Procedure
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{"title"=>"A shadowing problem in the detection of overlapping communities: Lifting the resolution limit through a cascading procedure", "type"=>"journal", "authors"=>[{"first_name"=>"Jean Gabriel", "last_name"=>"Young", "scopus_author_id"=>"55796127900"}, {"first_name"=>"Antoine", "last_name"=>"Allard", "scopus_author_id"=>"26532399500"}, {"first_name"=>"Laurent", "last_name"=>"Hébert-Dufresne", "scopus_author_id"=>"36865979800"}, {"first_name"=>"Louis J.", "last_name"=>"Dubé", "scopus_author_id"=>"22970907000"}], "year"=>2015, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"607101754", "pmid"=>"26461919", "scopus"=>"2-s2.0-84948799405", "issn"=>"19326203", "arxiv"=>"1211.1364", "sgr"=>"84948799405", "doi"=>"10.1371/journal.pone.0140133"}, "id"=>"7368b5b4-fdc7-3db8-975b-8feb34ed0115", "abstract"=>"Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real and artificial network datasets with three widely used community detection algorithms, we show how a simple cascading procedure allows for the detection of the missing communities. This work highlights a new detection limit of community structure, and we hope that our approach can inspire better community detection algorithms.", "link"=>"http://www.mendeley.com/research/shadowing-problem-detection-overlapping-communities-lifting-resolution-limit-through-cascading-proce", "reader_count"=>8, "reader_count_by_academic_status"=>{"Researcher"=>3, "Student > Doctoral Student"=>1, "Student > Master"=>3, "Student > Bachelor"=>1}, "reader_count_by_user_role"=>{"Researcher"=>3, "Student > Doctoral Student"=>1, "Student > Master"=>3, "Student > Bachelor"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Environmental Science"=>1, "Physics and Astronomy"=>3, "Chemistry"=>1, "Computer Science"=>2}, "reader_count_by_subdiscipline"=>{"Chemistry"=>{"Chemistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>3}, "Computer Science"=>{"Computer Science"=>2}, "Unspecified"=>{"Unspecified"=>1}, "Environmental Science"=>{"Environmental Science"=>1}}, "reader_count_by_country"=>{"Canada"=>1, "Slovenia"=>1, "Spain"=>1}, "group_count"=>0}

Scopus | Further Information

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  • {"files"=>["https://ndownloader.figshare.com/files/2356817"], "description"=>"<p><i>Left panel</i>: The yellow region is the sole detectable community with <i>k</i> = 4, 5, while its union with the black region corresponds to the community detected with <i>k</i> = 3. This pathological example illustrates the two undesirable extreme effects mentioned in the main text: either most of the network is detected as a single community, or only large and dense clusters are detected. No optimal value of <i>k</i> can be found in this case. <i>Right panel</i>: The structure of this subgraph nevertheless suggests that it could be decomposed in a dense community in the middle, surrounded by smaller communities. If the links involved in the dense community (detected with <i>k</i> = 4 or 5) were removed, a second iteration of the algorithm with <i>k</i> = 3 would lead to the detection of several smaller communities that were overshadowed by the larger one.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573061, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Shadowing_effect_for_the_CPA_/1573061", "title"=>"Shadowing effect for the CPA.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356819"], "description"=>"<p><i>Left panel</i>: The seeds (circled nodes) are expanded into two slightly overlapping communities (blue and green nodes) with <i>k</i> = 4. The orange triangle is not merged with the blue community, nor assigned, unless one select seeds of size <i>k</i> ≥ 3, which is not always possible if most of the network is dense. In such case. this value of <i>k</i> would lead to the detection of large, highly redundant and meaningless communities. <i>Right panel</i>: GCE expands the green and blue seeds (circled) to include the four nodes in the middle. The two communities are too similar, and one is discarded. This leaves the other maximal clique unassigned.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573063, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Shadowing_effect_in_GCE_/1573063", "title"=>"Shadowing effect in GCE.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356820"], "description"=>"<p>The sets <i>n</i><sub>+</sub>(<i>i</i>) and <i>n</i><sub>+</sub>(<i>j</i>) are respectively colored in green and blue. From <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.e001\" target=\"_blank\">Eq (1)</a>, we have <i>S</i>(<i>e</i><sub><i>ik</i></sub>, <i>e</i><sub><i>jk</i></sub>) = 6/13. Note that apart from nodes <i>i</i> and <i>j</i>, the neighboring nodes of the keystone <i>k</i> (colored in yellow) are not considered in the calculation of <i>S</i>(<i>e</i><sub><i>ik</i></sub>, <i>e</i><sub><i>jk</i></sub>).</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573064, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g003", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Calculation_of_the_similarity_between_two_links_/1573064", "title"=>"Calculation of the similarity between two links.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356821"], "description"=>"<p>The pairwise unions of the three sets <i>n</i><sub>+</sub>(<i>a</i>), <i>n</i><sub>+</sub>(<i>b</i>) and <i>n</i><sub>+</sub>(<i>c</i>) contain considerably more elements that their corresponding intersections since nodes <i>a</i>, <i>b</i> and <i>c</i> all have high degrees. According to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.e001\" target=\"_blank\">Eq (1)</a>, this implies that <i>e</i><sub><i>ab</i></sub>, <i>e</i><sub><i>bc</i></sub> and <i>e</i><sub><i>ac</i></sub> share lower similarities—namely <i>S</i>(<i>e</i><sub><i>ac</i></sub>, <i>e</i><sub><i>bc</i></sub>) = <i>S</i>(<i>e</i><sub><i>ab</i></sub>, <i>e</i><sub><i>bc</i></sub>) = 3/22 and <i>S</i>(<i>e</i><sub><i>ab</i></sub>, <i>e</i><sub><i>ac</i></sub>) = 3/17—than if the triangle had been completely isolated (<i>S</i>(<i>e</i><sub><i>ac</i></sub>, <i>e</i><sub><i>bc</i></sub>) = <i>S</i>(<i>e</i><sub><i>ab</i></sub>, <i>e</i><sub><i>bc</i></sub>) = <i>S</i>(<i>e</i><sub><i>ab</i></sub>, <i>e</i><sub><i>ac</i></sub>) = 1). It is therefore likely that these three links will be left unassigned.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573065, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g004", "stats"=>{"downloads"=>2, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Shadowing_effect_for_the_LCA_/1573065", "title"=>"Shadowing effect for the LCA.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356822"], "description"=>"<p>(<i>Left</i>) The number of unassigned links after one iteration of the CPA (corresponding to a typical use) is shown in yellow, and the final state is shown in dark brown. Whenever more than 2 iterations were performed, the intermediate results are shown in orange. For the <i>Gnutella</i> network, the optimal value was <i>k</i> = 3 at the first iteration, leading to an immediate complete detection of the community structure. For the purpose of selecting <i>k</i>, we consider that a cover contains an extensive community if the largest community is twice as large as the second largest community. In the case of the <i>Internet</i> and <i>Protein</i> networks, which contains large unbreakable clique, we used a looser criterion (<i>c</i> ⋅ <i>n</i><sub>largest</sub> < <i>n</i><sub>2nd largest</sub>, with <i>c</i> = 0.25 and <i>c</i> = 0.30, respectively). (<i>Center</i>) Results of a canonical use of GCE are shown in beige and shades of red correspond to subsequent iterations. The final state is shown in dark red. (<i>Right</i>) Results of a canonical use of the LCA are shown in white and shades of blue correspond to subsequent iterations. The final state is shown in dark blue. Note that all results are normalized to the number of assignable links in the original network. For the CPA, this corresponds to the number of links that belong to at least one 3-clique. For GCE, this corresponds to the number of links that belong to a component that contains at least one <i>k</i>-clique (<i>k</i> ≥ 3). For the LCA, a link is considered assignable if at least one of the two nodes it joins have a degree greater than one. Numerical results are summarized in the Supporting Information (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.s002\" target=\"_blank\">S2 Table</a>).</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573066, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g005", "stats"=>{"downloads"=>4, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Fraction_of_remaining_assignable_links_for_real_networks_using_the_cascading_approach_/1573066", "title"=>"Fraction of remaining assignable links for real networks using the cascading approach.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356824"], "description"=>"<p>(<i>Left</i>) Increase in running time for the CPA algorithm. (<i>Center</i>) Increase in running time for the GCE algorithm. (<i>Right</i>) Increase in running time for the LCA algorithm. Numerical results are summarized in the Supporting Information (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.s002\" target=\"_blank\">S2 Table</a>).</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573068, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g006", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_relative_increase_in_running_time_due_to_iterated_application_of_detection_algorithms_on_real_networks_/1573068", "title"=>"Average relative increase in running time due to iterated application of detection algorithms on real networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356826"], "description"=>"<p>(<i>Left panel</i>) CPA, (<i>Center panel</i>) GCE, and (<i>Right panel</i>) LCA applied to the <i>Words</i> network. The distributions obtained after the first iteration are shown using light gray square markers, and subsequent iterations (whenever required) are respectively marked by circles, triangles, rhombuses, pentagons and inverted triangles. Filled black markers indicate the last iteration. In the center panel, we omit for clarity the iterations that uncover very few communities (3rd, 4th, 7th and 8th). Interestingly, the size of the detected communities roughly follows the same distribution at each iteration. Therefore, the final size distribution (blue line) has also roughly the same shape as the one obtained with standard algorithms. Although this is not a direct proof, it suggests that the communities unveiled through cascading are similar to the ones detected by a “traditional” use of the detection algorithm. In other words, these communities are significant and are not simple artifacts of the cascading approach.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573070, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g007", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distribution_of_the_size_of_the_detected_communities_in_terms_of_nodes_at_each_iteration_of_the_cascading_approach_/1573070", "title"=>"Distribution of the size of the detected communities (in terms of nodes) at each iteration of the cascading approach.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356828"], "description"=>"<p>(<i>Top left panel</i>) Triangle detected with LCA at the third iteration. (<i>Top right panel</i>) Star detected with LCA at the third iteration. (<i>Bottom panel</i>) Dense community detected with the CPA at the second iteration. The detected communities are shown (red) as well as their neighboring nodes (grey). Red and grey labels identify respectively semantic fields and individual words.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573072, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g008", "stats"=>{"downloads"=>3, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Sample_of_the_communities_detected_with_the_cascading_approach_on_the_Words_network_/1573072", "title"=>"Sample of the communities detected with the cascading approach on the Words network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356829"], "description"=>"<p>Complete detection is achieved with 6 iterations for <i>Amazon</i> (black squares), 8 iterations for <i>DBLP</i> (orange circles), and 10 iterations for the <i>YouTube</i> (blue triangles). (<i>Top left panel</i>) Normalized mutual information as a function of the number of iterations. (<i>Top center panel</i>) Selected similarity threshold at each iteration (cf. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.e001\" target=\"_blank\">Eq (1)</a>). (<i>Top right panel</i>) Density of the optimal link partition, in the sparser network. (<i>Bottom left panel</i>) Elapsed fraction of the total running time, averaged over 10 independent realizations. (<i>Bottom center panel</i>) Cumulative fraction of <i>assigned</i> edges. (<i>Bottom right panel</i>) Number of detected communities at each iteration. Numerical results are summarized in the Supporting Information (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.s004\" target=\"_blank\">S4 Table</a>).</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573073, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g009", "stats"=>{"downloads"=>2, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Case_study_of_real_networks_with_meta_information_using_the_cascading_LCA_meta_algorithm_/1573073", "title"=>"Case study of real networks with meta-information, using the cascading LCA meta-algorithm.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356831"], "description"=>"<p>Relative change in normalized mutual information obtained by comparing the structure detected by the pure LCA and the cascading LCA, when applied to LF networks. All results are discrete points, but solid curves are added to guide the eye. (<i>Left panel</i>) Lightly mixed LF networks with a mixing parameter <i>μ</i> = 0.1. (<i>Right panel</i>) Heavily mixed LF networks <i>μ</i> = 0.6. We use networks of <i>N</i> = 5 000 nodes of average degree 〈<i>k</i>〉 = 20, that belongs to Ω = 2 communities (<i>if</i> they overlap). The fraction of overlapping nodes goes from 0 to 1 (y-axis). The value of the exponent of the community size distribution <i>τ</i><sub>2</sub> ranges from 1.25 to 3.75 (x-axis). Averaged data is shown on the color map (10 different networks for each point), while the distribution of raw data is shown in the plots to the right and bellow (black dots). Within raw data plots, the solid curve shows the average and the gray area indicates the standard deviation.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573075, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g010", "stats"=>{"downloads"=>2, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_the_communities_detected_with_the_pure_LCA_and_a_cascading_version_of_the_LCA_for_LF_networks_/1573075", "title"=>"Comparison of the communities detected with the pure LCA and a cascading version of the LCA, for LF networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356833"], "description"=>"<p>Coefficient of variation <i>c</i><sub><i>v</i></sub> of the community size distribution for (<i>left panel</i>) lightly mixed LF networks with a mixing parameter <i>μ</i> = 0.1 and (<i>right panel</i>) heavily mixed LF networks <i>μ</i> = 0.6. The coefficient of variation is the ratio of the standard deviation over the mean. See the caption of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.g010\" target=\"_blank\">Fig 10</a> for explanations of the layout of this figure.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573077, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g011", "stats"=>{"downloads"=>1, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Heterogeneous_community_sizes_at_the_initial_iteration_of_the_LCA_to_LF_networks_/1573077", "title"=>"Heterogeneous community sizes at the initial iteration of the LCA to LF networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356834"], "description"=>"<p>Raw running times are computed to the millisecond precision and averaged over 10 independent and complete iterations. The network generating process is not included in the total running time. (<i>Left panel</i>) Lightly mixed LF networks with a mixing parameter <i>μ</i> = 0.1. (<i>Right panel</i>) Heavily mixed LF networks <i>μ</i> = 0.6. See the caption of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.g010\" target=\"_blank\">Fig 10</a> for explanations of the layout of this figure.</p>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573078, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0140133.g012", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relative_increase_in_running_time_caused_by_the_cascading_approach_/1573078", "title"=>"Relative increase in running time caused by the cascading approach.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-10-13 02:45:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/2356836", "https://ndownloader.figshare.com/files/2356837", "https://ndownloader.figshare.com/files/2356838", "https://ndownloader.figshare.com/files/2356839", "https://ndownloader.figshare.com/files/2356840", "https://ndownloader.figshare.com/files/2356841", "https://ndownloader.figshare.com/files/2356842", "https://ndownloader.figshare.com/files/2356843", "https://ndownloader.figshare.com/files/2356844"], "description"=>"<div><p>Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real and artificial network datasets with three widely used community detection algorithms, we show how a simple cascading procedure allows for the detection of the missing communities. This work highlights a new detection limit of community structure, and we hope that our approach can inspire better community detection algorithms.</p></div>", "links"=>[], "tags"=>["community detection", "effect accounts", "community structure", "network datasets", "denser communities", "detection limit", "function modules", "sparser ones", "community detection algorithms", "overlapping communities", "detection algorithms", "Shadowing Problem", "Procedure Community detection", "unassigned links"], "article_id"=>1573080, "categories"=>["Uncategorised"], "users"=>["Jean-Gabriel Young", "Antoine Allard", "Laurent Hébert-Dufresne", "Louis J. Dubé"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0140133.s001", "https://dx.doi.org/10.1371/journal.pone.0140133.s002", "https://dx.doi.org/10.1371/journal.pone.0140133.s003", "https://dx.doi.org/10.1371/journal.pone.0140133.s004", "https://dx.doi.org/10.1371/journal.pone.0140133.s005", "https://dx.doi.org/10.1371/journal.pone.0140133.s006", "https://dx.doi.org/10.1371/journal.pone.0140133.s007", "https://dx.doi.org/10.1371/journal.pone.0140133.s008", "https://dx.doi.org/10.1371/journal.pone.0140133.s009"], "stats"=>{"downloads"=>7, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_Shadowing_Problem_in_the_Detection_of_Overlapping_Communities_Lifting_the_Resolution_Limit_through_a_Cascading_Procedure_/1573080", "title"=>"A Shadowing Problem in the Detection of Overlapping Communities: Lifting the Resolution Limit through a Cascading Procedure", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-10-13 02:45:52"}

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  • {"unique-ip"=>"4", "full-text"=>"3", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"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"=>"3"}
  • {"unique-ip"=>"5", "full-text"=>"4", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"7", "full-text"=>"8", "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"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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