CiteULike | Further Information

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Mendeley | Further Information

{"title"=>"Finding statistically significant communities in networks", "type"=>"journal", "authors"=>[{"first_name"=>"Andrea", "last_name"=>"Lancichinetti", "scopus_author_id"=>"25641137200"}, {"first_name"=>"Filippo", "last_name"=>"Radicchi", "scopus_author_id"=>"6508172257"}, {"first_name"=>"José J.", "last_name"=>"Ramasco", "scopus_author_id"=>"6603056876"}, {"first_name"=>"Santo", "last_name"=>"Fortunato", "scopus_author_id"=>"7005680829"}], "year"=>2011, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-79955707583", "pui"=>"361724243", "sgr"=>"79955707583", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "arxiv"=>"1012.2363", "issn"=>"19326203", "pmid"=>"21559480", "doi"=>"10.1371/journal.pone.0018961"}, "id"=>"dd0066e3-1d09-3ab0-ab4b-d16a9fc6fd1d", "abstract"=>"Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (http://www.oslom.org), and we believe it will be a valuable tool in the analysis of networks.", "link"=>"http://www.mendeley.com/research/finding-statistically-significant-communities-networks", "reader_count"=>386, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>30, "Librarian"=>1, "Researcher"=>64, "Student > Doctoral Student"=>21, "Student > Ph. D. Student"=>141, "Student > Postgraduate"=>13, "Student > Master"=>64, "Other"=>13, "Student > Bachelor"=>9, "Lecturer"=>6, "Lecturer > Senior Lecturer"=>5, "Professor"=>17}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>30, "Librarian"=>1, "Researcher"=>64, "Student > Doctoral Student"=>21, "Student > Ph. D. Student"=>141, "Student > Postgraduate"=>13, "Student > Master"=>64, "Other"=>13, "Student > Bachelor"=>9, "Lecturer"=>6, "Lecturer > Senior Lecturer"=>5, "Professor"=>17}, "reader_count_by_subject_area"=>{"Unspecified"=>15, "Agricultural and Biological Sciences"=>49, "Arts and Humanities"=>2, "Business, Management and Accounting"=>3, "Chemical Engineering"=>1, "Chemistry"=>4, "Computer Science"=>168, "Decision Sciences"=>1, "Earth and Planetary Sciences"=>1, "Economics, Econometrics and Finance"=>6, "Engineering"=>21, "Environmental Science"=>4, "Biochemistry, Genetics and Molecular Biology"=>5, "Mathematics"=>18, "Medicine and Dentistry"=>3, "Neuroscience"=>8, "Physics and Astronomy"=>38, "Psychology"=>14, "Social Sciences"=>23, "Linguistics"=>1, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Social Sciences"=>{"Social Sciences"=>23}, "Decision Sciences"=>{"Decision Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>38}, "Psychology"=>{"Psychology"=>14}, "Mathematics"=>{"Mathematics"=>18}, "Unspecified"=>{"Unspecified"=>15}, "Environmental Science"=>{"Environmental Science"=>4}, "Chemical Engineering"=>{"Chemical Engineering"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>2}, "Engineering"=>{"Engineering"=>21}, "Chemistry"=>{"Chemistry"=>4}, "Neuroscience"=>{"Neuroscience"=>8}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>6}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>49}, "Computer Science"=>{"Computer Science"=>168}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>3}, "Linguistics"=>{"Linguistics"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>5}}, "reader_count_by_country"=>{"United States"=>14, "Portugal"=>2, "Greece"=>1, "Netherlands"=>3, "Sweden"=>2, "Iran"=>1, "China"=>1, "Ireland"=>3, "Brazil"=>3, "Serbia and Montenegro"=>1, "Poland"=>1, "Slovenia"=>2, "France"=>3, "Sri Lanka"=>1, "Japan"=>1, "United Kingdom"=>6, "Switzerland"=>1, "Spain"=>7, "India"=>2, "Venezuela"=>1, "Canada"=>2, "Czech Republic"=>1, "Denmark"=>2, "Italy"=>5, "Mexico"=>1, "Germany"=>6, "Estonia"=>1}, "group_count"=>24}

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• {"month"=>"12", "year"=>"2018", "pdf_views"=>"74", "xml_views"=>"0", "html_views"=>"55"}
• {"month"=>"1", "year"=>"2019", "pdf_views"=>"45", "xml_views"=>"1", "html_views"=>"76"}
• {"month"=>"2", "year"=>"2019", "pdf_views"=>"57", "xml_views"=>"0", "html_views"=>"55"}
• {"month"=>"3", "year"=>"2019", "pdf_views"=>"52", "xml_views"=>"0", "html_views"=>"89"}
• {"month"=>"4", "year"=>"2019", "pdf_views"=>"50", "xml_views"=>"0", "html_views"=>"74"}
• {"month"=>"5", "year"=>"2019", "pdf_views"=>"64", "xml_views"=>"0", "html_views"=>"88"}
• {"month"=>"6", "year"=>"2019", "pdf_views"=>"37", "xml_views"=>"0", "html_views"=>"66"}
• {"month"=>"7", "year"=>"2019", "pdf_views"=>"44", "xml_views"=>"1", "html_views"=>"71"}
• {"month"=>"8", "year"=>"2019", "pdf_views"=>"51", "xml_views"=>"0", "html_views"=>"65"}
• {"month"=>"9", "year"=>"2019", "pdf_views"=>"45", "xml_views"=>"0", "html_views"=>"57"}
• {"month"=>"10", "year"=>"2019", "pdf_views"=>"67", "xml_views"=>"0", "html_views"=>"66"}
• {"month"=>"11", "year"=>"2019", "pdf_views"=>"46", "xml_views"=>"0", "html_views"=>"56"}
• {"month"=>"12", "year"=>"2019", "pdf_views"=>"43", "xml_views"=>"1", "html_views"=>"60"}
• {"month"=>"1", "year"=>"2020", "pdf_views"=>"44", "xml_views"=>"0", "html_views"=>"47"}
• {"month"=>"2", "year"=>"2020", "pdf_views"=>"80", "xml_views"=>"1", "html_views"=>"48"}
• {"month"=>"3", "year"=>"2020", "pdf_views"=>"86", "xml_views"=>"1", "html_views"=>"40"}
• {"month"=>"4", "year"=>"2020", "pdf_views"=>"99", "xml_views"=>"0", "html_views"=>"38"}
• {"month"=>"5", "year"=>"2020", "pdf_views"=>"139", "xml_views"=>"1", "html_views"=>"42"}
• {"month"=>"6", "year"=>"2020", "pdf_views"=>"36", "xml_views"=>"0", "html_views"=>"87"}
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• {"month"=>"3", "year"=>"2021", "pdf_views"=>"3", "xml_views"=>"0", "html_views"=>"3"}

Figshare

• {"files"=>["https://ndownloader.figshare.com/files/778519"], "description"=>"<p>The parameters of the graphs are: average degree\n ,\n maximum degree ,\n exponents of the power law distributions are\n for\n degree and for\n community size, S and B mean that community sizes are in the range\n \n (“small”) and \n (“big”), respectively. We considered two network sizes:\n (top)\n and \n (bottom). The two curves refer to OSLOM (diamonds) and Infomap\n (circles).</p>", "links"=>[], "tags"=>["undirected", "unweighted", "lfr", "benchmark", "graphs", "without", "overlapping"], "article_id"=>448883, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g006", "stats"=>{"downloads"=>2, "page_views"=>27, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Tests_on_undirected_and_unweighted_LFR_benchmark_graphs_without_____overlapping_communities_/448883", "title"=>"Tests on undirected and unweighted LFR benchmark graphs without\n overlapping communities.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:28:03"}
• {"files"=>["https://ndownloader.figshare.com/files/778182"], "description"=>"<p>The subgraph is\n embedded within a random graph generated by the configuration model. The\n degrees of all vertices of the network are fixed, in the figure we have\n highlighted the degrees of \n (), of the\n vertex at the\n center of the analysis () and of\n the rest of the graph \n (). These\n quantities are expressed as sums of contributions which are internal to\n their own set of vertices (as ) or\n related to subgraph (in or\n out). This notation is used in the distribution of Eq. 1.</p>", "links"=>[], "tags"=>["schematic", "subgraph", "whose"], "article_id"=>448543, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_schematic_representation_of_a_subgraph_____whose____significance_is_to_be_assessed_/448543", "title"=>"A schematic representation of a subgraph\n , whose\n significance is to be assessed.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:22:23"}
• {"files"=>["https://ndownloader.figshare.com/files/390473"], "description"=>"<div><p>Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (<a href=\"http://www.oslom.org\">http://www.oslom.org</a>), and we believe it will be a valuable tool in the analysis of networks.</p> </div>", "links"=>[], "tags"=>["communities", "in", "networks"], "article_id"=>137114, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961", "stats"=>{"downloads"=>4, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Finding_Statistically_Significant_Communities_in___Networks/137114", "title"=>"Finding Statistically Significant Communities in\n Networks", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-04-29 01:58:34"}
• {"files"=>["https://ndownloader.figshare.com/files/779288"], "description"=>"<p>Black points indicate overlapping vertices.</p>", "links"=>[], "tags"=>["oslom", "flows", "commuters", "the"], "article_id"=>449658, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g014", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Application_of_OSLOM_to_real_networks_flows_of_commuters_in_the_____UK_/449658", "title"=>"Application of OSLOM to real networks: flows of commuters in the\n UK.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:40:58"}
• {"files"=>["https://ndownloader.figshare.com/files/779491"], "description"=>"<p>From left to right, we list the number of vertices\n and\n edges , the\n average degree , the\n number of clusters , the\n average cluster size , the\n average number of memberships per vertex\n and\n the fraction of\n vertices not assigned to any cluster (homeless vertices). The values\n related to the community structure refer to the lowest hierarchical\n level.</p>", "links"=>[], "tags"=>["networks", "main"], "article_id"=>449863, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.t001", "stats"=>{"downloads"=>3, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Basic_statistics_of_the_real_networks_we_analyzed_including_the_main____features_of_their_community_structure_detected_by_OSLOM_/449863", "title"=>"Basic statistics of the real networks we analyzed, including the main\n features of their community structure, detected by OSLOM.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-04-29 02:44:23"}
• {"files"=>["https://ndownloader.figshare.com/files/778302"], "description"=>"<p>Schematic diagram of the single cluster analysis.</p>", "links"=>[], "tags"=>["diagram"], "article_id"=>448671, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g003", "stats"=>{"downloads"=>2, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_diagram_of_the_single_cluster_analysis_/448671", "title"=>"Schematic diagram of the single cluster analysis.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:24:31"}
• {"files"=>["https://ndownloader.figshare.com/files/779351"], "description"=>"<p>We show the distribution of cluster sizes obtained by OSLOM for the\n first two hierarchical levels (OSLOM 1 and OSLOM 2). For\n <i>LiveJournal</i> we can compare the distributions\n with those found with Infomap <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018961#pone.0018961-Rosvall1\" target=\"_blank\">[49]</a> and the Label\n Propagation Method (LPM) by Leung et al. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018961#pone.0018961-Leung1\" target=\"_blank\">[62]</a>.</p>", "links"=>[], "tags"=>["oslom", "friendships", "of", "users", "graph"], "article_id"=>449717, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g015", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Application_of_OSLOM_to_real_networks_friendships_of_____LiveJournal_users_left_and_sample_of_the_uk_____domain_of_the_Web_graph_right_/449717", "title"=>"Application of OSLOM to real networks: friendships of\n <i>LiveJournal</i> users (left) and sample of the .uk\n domain of the Web graph (right).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:41:57"}
• {"files"=>["https://ndownloader.figshare.com/files/778465"], "description"=>"<p>The diagram shows how the execution time of two different\n implementations of the algorithm scales with the network size\n (expressed by the number of vertices), for LFR benchmark graphs.</p>", "links"=>[], "tags"=>["computer science", "physics"], "article_id"=>448838, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g005", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Complexity_of_OSLOM_/448838", "title"=>"Complexity of OSLOM.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:27:18"}
• {"files"=>["https://ndownloader.figshare.com/files/779131"], "description"=>"<p>Stars indicate overlapping vertices.</p>", "links"=>[], "tags"=>["oslom", "association"], "article_id"=>449507, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g013", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Application_of_OSLOM_to_real_networks_the_word_association_____network_/449507", "title"=>"Application of OSLOM to real networks: the word association\n network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:38:27"}
• {"files"=>["https://ndownloader.figshare.com/files/778773"], "description"=>"<p>Stars indicate overlapping vertices.</p>", "links"=>[], "tags"=>["realization", "hierarchical", "lfr", "benchmark", "two"], "article_id"=>449140, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g009", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_realization_of_the_hierarchical_LFR_benchmark_with_two_____levels_/449140", "title"=>"A realization of the hierarchical LFR benchmark with two\n levels.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:32:20"}
• {"files"=>["https://ndownloader.figshare.com/files/778378"], "description"=>"<p>The levels of grey of the squares represent different loop levels. One\n can provide an initial partition/cover as input, from which the\n algorithm starts operating, or no input, in which case the algorithm\n will build the clusters about individual vertices, chosen at random.\n OSLOM performs first a cleaning procedure of the clusters, followed by a\n check of their internal structure and by a decision on possible cluster\n unions. This is repeated with different choices of random numbers in\n order to obtain better statistics and a more reliable information. The\n final step is to generate a super-network for the next level of the\n hierarchical analysis.</p>", "links"=>[], "tags"=>["diagram"], "article_id"=>448753, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g004", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Flux_diagram_of_OSLOM_/448753", "title"=>"Flux diagram of OSLOM.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:25:53"}
• {"files"=>["https://ndownloader.figshare.com/files/779412"], "description"=>"<p>The maps show the position of the airports, which are represented by\n symbols, indicating the communities found by applying OSLOM directly\n to the corresponding network, without exploiting the information of\n previous snapshots. The diagram shows the “seasonality”\n of air traffic. The normalized mutual information (diamonds) was\n computed comparing the cover of the system at time\n \n adjusted by OSLOM on the network at time\n , and\n the cover obtained by applying OSLOM directly to the system at time\n . The\n circles are estimates of the similarity of the network matrices of\n snapshots separated by (one\n year). For each year we took four snapshots, by cumulating the\n traffic of each trimester. The most stable networks are typically in\n winter (vertical lines).</p>", "links"=>[], "tags"=>["oslom", "airport"], "article_id"=>449785, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g016", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Application_of_OSLOM_to_real_networks_US_airport_____network_/449785", "title"=>"Application of OSLOM to real networks: US airport\n network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:43:05"}
• {"files"=>["https://ndownloader.figshare.com/files/778995"], "description"=>"<p>The communities are those of an LFR benchmark graph (undirected,\n unweighted and without overlapping clusters), with\n ,\n ,\n ,\n . The\n cluster size ranges from to\n \n vertices. The noise comes by adding vertices which are randomly\n linked to the existing vertices, via preferential attachment. The\n test consists in checking whether the community finding algorithm at\n study (here OSLOM, Infomap and COPRA) is able to find the\n communities of the planted partition of the LFR benchmark and to\n recognize as homeless the other vertices.</p>", "links"=>[], "tags"=>["graphs", "communities"], "article_id"=>449368, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g012", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Test_on_graphs_including_communities_and_noise_/449368", "title"=>"Test on graphs including communities and noise.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:36:08"}
• {"files"=>["https://ndownloader.figshare.com/files/778650"], "description"=>"<p>The parameters are: ,\n ,\n ,\n ,\n . S and\n B indicate the usual ranges of community sizes we use:\n and\n ,\n respectively. We tested OSLOM against two recent methods to find\n covers in graphs: COPRA <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018961#pone.0018961-Gregory2\" target=\"_blank\">[52]</a> and MOSES\n <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018961#pone.0018961-McDaid1\" target=\"_blank\">[54]</a>. The left panel displays the normalized\n mutual information (NMI) between the planted cover and the one\n recovered by the algorithm, as a function of the fraction of\n overlapping vertices. Each overlapping vertex is shared between two\n clusters. The four curves correspond to different values of the\n mixing parameter \n ( and\n ) and\n to the community size ranges S and B. The right panel shows a test\n on graphs whose vertices are all shared between clusters. Each\n vertex is member of the same number of clusters. The plot shows the\n NMI as a function of the number of memberships of the vertices. Each\n curve corresponds to a given value of the average degree\n . The\n graph parameters are ,\n ,\n ,\n ,\n .\n Community sizes are in the range .</p>", "links"=>[], "tags"=>["undirected", "unweighted", "lfr", "benchmark", "overlapping"], "article_id"=>449014, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g008", "stats"=>{"downloads"=>7, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Test_on_undirected_and_unweighted_LFR_benchmark_with_overlapping_____communities_/449014", "title"=>"Test on undirected and unweighted LFR benchmark with overlapping\n communities.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:30:14"}
• {"files"=>["https://ndownloader.figshare.com/files/778575"], "description"=>"<p>The network sizes are (left)\n and \n (right), the maximum degree and\n the community size ranges from to\n . The\n other parameters are the same as those used for the graphs of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018961#pone-0018961-g006\" target=\"_blank\">Fig. 6</a>. The two\n curves refer to OSLOM (diamonds) and Infomap (circles).</p>", "links"=>[], "tags"=>["undirected", "unweighted", "lfr", "benchmark", "graphs", "overlapping"], "article_id"=>448947, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g007", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Tests_on_large_undirected_and_unweighted_LFR_benchmark_graphs_____without_overlapping_communities_/448947", "title"=>"Tests on large undirected and unweighted LFR benchmark graphs\n without overlapping communities.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:29:07"}
• {"files"=>["https://ndownloader.figshare.com/files/778246"], "description"=>"<p>The score is the\n -th\n smallest score of the external vertices. In this particular case there\n are external vertices. In the figure, we plot\n ,\n ,\n ,\n ,\n (from left\n to right). As an example, the shaded areas show the cumulative\n probability for a few\n values of that would\n correspond to the values estimated in a practical situation. In this\n case, the black area, , is the\n least extensive and so . If\n , the\n vertices with scores ,\n ,\n and\n will be\n added to .</p>", "links"=>[], "tags"=>["distributions", "scores", "of", "vertices", "subgraph", "the"], "article_id"=>448609, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Probability_distributions_of_the_scores_____of____vertices_external_to_a_given_subgraph_of_the____graph_/448609", "title"=>"Probability distributions of the scores\n of\n vertices external to a given subgraph of the\n graph.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:23:29"}
• {"files"=>["https://ndownloader.figshare.com/files/778865"], "description"=>"<p>We compare three pairs of partitions: the lowest hierarchical\n partition found by the algorithm (indicated by\n ) with\n the set of micro-communities of the benchmark (Fine); the lowest\n hierarchical partition found by the algorithm with the set of\n macro-communities of the benchmark (Coarse); the second lowest\n hierarchical partition found by the algorithm (indicated by\n ) with\n the set of macro-communities of the benchmark. The corresponding\n similarities are plotted as a function of\n , for\n fixed . There\n are \n vertices, the average degree , the\n maximum degree , the\n size of the macro-communities lies between\n and\n \n vertices, the size of the micro-communities lies between\n and\n \n vertices. The exponents of the degree and community size\n distributions are and\n .</p>", "links"=>[], "tags"=>["hierarchical", "lfr", "benchmark", "graphs", "undirected", "overlapping"], "article_id"=>449234, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g010", "stats"=>{"downloads"=>1, "page_views"=>18, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Test_on_hierarchical_LFR_benchmark_graphs_unweighted_undirected_____and_without_overlapping_clusters_/449234", "title"=>"Test on hierarchical LFR benchmark graphs (unweighted, undirected\n and without overlapping clusters).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:33:54"}
• {"files"=>["https://ndownloader.figshare.com/files/778948"], "description"=>"<p>We plot the fraction of vertices belonging to non-trivial clusters\n (i.e. to clusters with more than one and less than\n \n vertices, where is as\n usual the size of the graph), as a function of the average degree of\n the graph. The curves correspond to Erdös-Rényi graphs\n (diamonds) and scale-free networks (circles). All graphs have\n \n vertices. The only parameter needed to build Erdös-Rényi\n graphs is the probability that a pair of vertices is connected,\n which is determined by the average degree\n . The\n scale-free networks were built with the configuration model <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018961#pone.0018961-Molloy1\" target=\"_blank\">[39]</a>, starting from a fixed degree sequence for\n the vertices obeying the predefinite power law distribution. The\n parameters of the distribution are: degree exponent\n ,\n maximum degree .</p>", "links"=>[], "tags"=>["computer science", "physics"], "article_id"=>449321, "categories"=>["Information And Computing Sciences", "Physics"], "users"=>["Andrea Lancichinetti", "Filippo Radicchi", "José J. Ramasco", "Santo Fortunato"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018961.g011", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Test_on_random_graphs_/449321", "title"=>"Test on random graphs.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-04-29 02:35:21"}

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Relative Metric

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F1000Prime