Exploring the Morphospace of Communication Efficiency in Complex Networks
Publication Date
March 07, 2013
Journal
PLOS ONE
Authors
Joaquín Goñi, Andrea Avena Koenigsberger, Nieves Velez De Mendizabal, Martijn P. Van Den Heuvel, et al
Volume
8
Issue
3
Pages
e58070
DOI
https://dx.plos.org/10.1371/journal.pone.0058070
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0058070
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/23505455
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3591454
Europe PMC
http://europepmc.org/abstract/MED/23505455
Web of Science
000318334500047
Scopus
84874754277
Mendeley
http://www.mendeley.com/research/exploring-morphospace-communication-efficiency-complex-networks
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Mendeley | Further Information

{"title"=>"Exploring the Morphospace of Communication Efficiency in Complex Networks", "type"=>"journal", "authors"=>[{"first_name"=>"Joaquín", "last_name"=>"Goñi", "scopus_author_id"=>"24178076100"}, {"first_name"=>"Andrea", "last_name"=>"Avena-Koenigsberger", "scopus_author_id"=>"55617536100"}, {"first_name"=>"Nieves", "last_name"=>"Velez de Mendizabal", "scopus_author_id"=>"24468893900"}, {"first_name"=>"Martijn P.", "last_name"=>"van den Heuvel", "scopus_author_id"=>"24333539900"}, {"first_name"=>"Richard F.", "last_name"=>"Betzel", "scopus_author_id"=>"55367857600"}, {"first_name"=>"Olaf", "last_name"=>"Sporns", "scopus_author_id"=>"7004710859"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-84874754277", "sgr"=>"84874754277", "issn"=>"19326203", "doi"=>"10.1371/journal.pone.0058070", "pmid"=>"23505455", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pui"=>"368480594"}, "id"=>"b796592d-74a1-3c35-8198-4adff8e38511", "abstract"=>"Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system's dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (\"routing\"), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (\"diffusion\"). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology.", "link"=>"http://www.mendeley.com/research/exploring-morphospace-communication-efficiency-complex-networks", "reader_count"=>95, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>9, "Researcher"=>18, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>30, "Student > Postgraduate"=>2, "Student > Master"=>14, "Other"=>1, "Student > Bachelor"=>6, "Lecturer"=>1, "Professor"=>9}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>9, "Researcher"=>18, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>30, "Student > Postgraduate"=>2, "Student > Master"=>14, "Other"=>1, "Student > Bachelor"=>6, "Lecturer"=>1, "Professor"=>9}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Agricultural and Biological Sciences"=>18, "Arts and Humanities"=>1, "Philosophy"=>1, "Computer Science"=>10, "Engineering"=>5, "Environmental Science"=>1, "Mathematics"=>4, "Medicine and Dentistry"=>15, "Neuroscience"=>16, "Physics and Astronomy"=>6, "Psychology"=>12, "Social Sciences"=>1, "Linguistics"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>15}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>6}, "Psychology"=>{"Psychology"=>12}, "Mathematics"=>{"Mathematics"=>4}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Engineering"=>{"Engineering"=>5}, "Neuroscience"=>{"Neuroscience"=>16}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>18}, "Computer Science"=>{"Computer Science"=>10}, "Linguistics"=>{"Linguistics"=>1}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"Republic of Singapore"=>1, "Netherlands"=>2, "Hong Kong"=>1, "United States"=>1, "United Kingdom"=>1, "Germany"=>1}, "group_count"=>0}

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Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/979920"], "description"=>"<p>Scatter plot of and for four canonical network models at different densities: the Erdös-Rényi model (gray), the preferential attachment model (green), the Watts-Strogatz small-world model (red) and the one-dimensional lattice model (blue). The average degree is indicated at the plot line for the lattice model and dotted lines indicate equivalent average degrees for the rest of the models. Network size is fixed at 50 nodes. Each point represents mean values and shaded areas correspond to the 90% confidence interval. To obtain each data point (for each model and each average degree), 100 sample graphs were generated, except for the regular lattice given its deterministic nature. The clique coordinates are given as a reference point with maximum density and thus maximum but very low . As the density increases, monotonically increases whereas tends to monotonically decrease.</p>", "links"=>[], "tags"=>["routing", "shortest-path-probability", "canonical"], "article_id"=>646477, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Joaquin Goni", "Andrea Avena-Koenigsberger", "Nieves Velez de Mendizabal", "Martijn P. van den Heuvel", "Richard F. Betzel", "Olaf Sporns"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0058070.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relation_of_routing_efficiency_and_shortest_path_probability_for_canonical_network_models_/646477", "title"=>"Relation of routing efficiency and shortest-path-probability for canonical network models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:51:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/979923"], "description"=>"<p>Descriptors shown are: number of nodes , average degree , characteristic path length , routing efficiency , shortest-path probability , diffusion efficiency and resources efficiency .</p>", "links"=>[], "tags"=>["measures", "idealized"], "article_id"=>646480, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Joaquin Goni", "Andrea Avena-Koenigsberger", "Nieves Velez de Mendizabal", "Martijn P. van den Heuvel", "Richard F. Betzel", "Olaf Sporns"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0058070.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Graph_and_efficiency_measures_for_seven_idealized_network_topologies_/646480", "title"=>"Graph and efficiency measures for seven idealized network topologies.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:51:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/979925"], "description"=>"<p>Results shown are for evolutionary processes driven by network efficiency measures for networks with and . Blue and red squares indicate the reference points of regular lattices and randomized networks respectively. Green points indicate the initial seed population. Gray circles indicate evolving networks over epochs, with darker shades of gray indicating networks encountered in later epochs. Orange points show Pareto-front (non-dominated) solutions. (a) Snapshots illustrating the expansion of the Pareto fronts at epochs 2, 25, 50, 100, and 200. (b) Final solutions were reached after 517, 704, 977, and 433 epochs for fronts 1, 2, 3, and 4 respectively. Black asterisks denote positions of the example graphs shown in insets. Yellow points show dominated solutions of the final populations. Grey points show coordinates visited during the evolutionary process at different epochs (denoted by the gray-level).</p>", "links"=>[], "tags"=>["optimization"], "article_id"=>646482, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Joaquin Goni", "Andrea Avena-Koenigsberger", "Nieves Velez de Mendizabal", "Martijn P. van den Heuvel", "Richard F. Betzel", "Olaf Sporns"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0058070.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Multi_objective_optimization_in_the_efficiency_morphospace_/646482", "title"=>"Multi-objective optimization in the efficiency morphospace.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:51:39"}
  • {"files"=>["https://ndownloader.figshare.com/files/979928"], "description"=>"<p>Results shown are for networks with and . Heat maps are based on a square grid with cells measuring 0.05 units in each dimension. For each cell, graph measures coming from graphs falling on those coordinates at any epoch of the evolutionary processes (one for each front) were averaged. (a) Degree entropy. (b) Assortativity. (c) Modularity. (d) Scaled resource efficiency .</p>", "links"=>[], "tags"=>["measures", "evolved"], "article_id"=>646485, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Joaquin Goni", "Andrea Avena-Koenigsberger", "Nieves Velez de Mendizabal", "Martijn P. van den Heuvel", "Richard F. Betzel", "Olaf Sporns"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0058070.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Graph_measures_for_evolved_networks_/646485", "title"=>"Graph measures for evolved networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:52:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/979930"], "description"=>"<p>The figure shows a scatter plot of and for 23 real-world networks (for description of data sets see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058070#pone.0058070.s001\" target=\"_blank\">Text S1</a>). Blue and red squares indicate lattice and random reference points, respectively, linked by the green reference line. The gray line represents the linear regression across all 23 real-world networks ().</p>", "links"=>[], "tags"=>["real-world", "networks"], "article_id"=>646487, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Joaquin Goni", "Andrea Avena-Koenigsberger", "Nieves Velez de Mendizabal", "Martijn P. van den Heuvel", "Richard F. Betzel", "Olaf Sporns"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0058070.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Placing_real_world_networks_in_the_efficiency_morphospace_/646487", "title"=>"Placing real-world networks in the efficiency morphospace.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:52:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/979935", "https://ndownloader.figshare.com/files/979945", "https://ndownloader.figshare.com/files/979947", "https://ndownloader.figshare.com/files/979948", "https://ndownloader.figshare.com/files/979950", "https://ndownloader.figshare.com/files/979952", "https://ndownloader.figshare.com/files/979956", "https://ndownloader.figshare.com/files/979966"], "description"=>"<div><p>Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system's dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (“routing”), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (“diffusion”). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology.</p> </div>", "links"=>[], "tags"=>["exploring", "morphospace", "networks"], "article_id"=>646492, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Joaquin Goni", "Andrea Avena-Koenigsberger", "Nieves Velez de Mendizabal", "Martijn P. van den Heuvel", "Richard F. Betzel", "Olaf Sporns"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0058070.s001", "https://dx.doi.org/10.1371/journal.pone.0058070.s002", "https://dx.doi.org/10.1371/journal.pone.0058070.s003", "https://dx.doi.org/10.1371/journal.pone.0058070.s004", "https://dx.doi.org/10.1371/journal.pone.0058070.s005", "https://dx.doi.org/10.1371/journal.pone.0058070.s006", "https://dx.doi.org/10.1371/journal.pone.0058070.s007", "https://dx.doi.org/10.1371/journal.pone.0058070.s008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Exploring_the_Morphospace_of_Communication_Efficiency_in_Complex_Networks__/646492", "title"=>"Exploring the Morphospace of Communication Efficiency in Complex Networks", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-03-08 08:53:39"}

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Relative Metric

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