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(PDF) Emergence of scale-free networks from local connectivity and communication trade-offs
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false; window.loswp.work = {"work":{"id":11465635,"created_at":"2015-03-16T11:18:19.307-07:00","from_world_paper_id":133344706,"updated_at":"2024-11-17T01:44:31.270-08:00","_data":{"grobid_abstract":"We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the addition of edges. A new edge is added between two nodes depending on the trade-off between a gain and a cost function of local connectivity and communication properties. We report on simulation results that indicate the appearance of powerlaw distributions of node degrees for selected parameter combinations.","publication_date":"2006,,","publication_name":"Physical Review E","grobid_abstract_attachment_id":"46692501"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Emergence of scale-free networks from local connectivity and communication trade-offs","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true,"seo_quality":null}}["work"]; window.loswp.workCoauthors = [27918447]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":46692501,"attachmentType":"pdf"}"><img alt="First page of “Emergence of scale-free networks from local connectivity and communication trade-offs”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/46692501/mini_magick20190209-10589-40ghgl.png?1549706194" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Emergence of scale-free networks from local connectivity and communication trade-offs</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="27918447" href="https://independent.academia.edu/SergioSouza20"><img alt="Profile image of Sergio Souza" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/27918447/23536324/22587958/s65_sergio.souza.jpg" />Sergio Souza</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2006, Physical Review E</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">4 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 11465635; 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The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the addition of edges. A new edge is added between two nodes depending on the trade-off between a gain and a cost function of local connectivity and communication properties. We report on simulation results that indicate the appearance of powerlaw distributions of node degrees for selected parameter combinations.</p></div></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="1911984" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/1911984/Emergence_of_scale_free_behavior_in_networks_from_limited_horizon_linking_and_cost_trade_offs">Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2447211" href="https://ufrj.academia.edu/SergioRSouza">Sergio R. Souza</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics …, 2008</p><p class="ds-related-work--abstract ds2-5-body-sm">We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are not too far apart on the sphere may be considered for being joined by an edge. Given two such nodes, the joining occurs only if the gain of doing it surpasses the cost. Our model is based on a multiplicative parameter λ that regulates, in a function of node degrees, the maximum geodesic distance that is allowed between nodes for them to be considered for joining. For n nodes distributed uniformly on the sphere, and for λ √ n within limits that depend on cost-related parameters, we have found that our growth mechanism gives rise to power-law distributions of node degree that are invariant for constant λ √ n. We also study connectivity-and distance-related properties of the networks.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs","attachmentId":31153694,"attachmentType":"pdf","work_url":"https://www.academia.edu/1911984/Emergence_of_scale_free_behavior_in_networks_from_limited_horizon_linking_and_cost_trade_offs","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/1911984/Emergence_of_scale_free_behavior_in_networks_from_limited_horizon_linking_and_cost_trade_offs"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="84688003" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/84688003/Scale_free_networks_from_self_organization">Scale-free networks from self-organization</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="84276" href="https://imperial.academia.edu/TSEvans">Tim S Evans</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of parameters. The growth mechanism is based on using local graph information only, so this is a process of self-organisation. The standard mean-field equations are an excellent approximation for network growth using these rules. We discuss the effects of finite size on the degree distribution, and compare analytical results to simulated networks. Finally, we generalise the random walk algorithm to produce weighted networks with power-law distributions of both weight and degree.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Scale-free networks from self-organization","attachmentId":89623630,"attachmentType":"pdf","work_url":"https://www.academia.edu/84688003/Scale_free_networks_from_self_organization","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/84688003/Scale_free_networks_from_self_organization"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="12665476" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/12665476/USING_SPECTRAL_RADIUS_RATIO_FOR_NODE_DEGREE_TO_ANALYZE_THE_EVOLUTION_OF_SCALE_FREE_NETWORKS_AND_SMALL_WORLD_NETWORKS">USING SPECTRAL RADIUS RATIO FOR NODE DEGREE TO ANALYZE THE EVOLUTION OF SCALE-FREE NETWORKS AND SMALL-WORLD NETWORKS</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15689241" href="https://independent.academia.edu/ComputerScienceInformationTechnologyCSIT">Computer Science & Information Technology (CS & IT) Computer Science Conference Proceedings (CSCP)</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we show the evaluation of the spectral radius for node degree as the basis to analyze the variation in the node degrees during the evolution of scale-free networks and smallworld networks. Spectral radius is the principal eigenvalue of the adjacency matrix of a network graph and spectral radius ratio for node degree is the ratio of the spectral radius and the average node degree. We observe a very high positive correlation between the spectral radius ratio for node degree and the coefficient of variation of node degree (ratio of the standard deviation of node degree and average node degree). We show how the spectral radius ratio for node degree can be used as the basis to tune the operating parameters of the evolution models for scale-free networks and small-world networks as well as evaluate the impact of the number of links added per node introduced during the evolution of a scale-free network and evaluate the impact of the probability of rewiring during the evolution of a small-world network from a regular network.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"USING SPECTRAL RADIUS RATIO FOR NODE DEGREE TO ANALYZE THE EVOLUTION OF SCALE-FREE NETWORKS AND SMALL-WORLD NETWORKS","attachmentId":37769633,"attachmentType":"pdf","work_url":"https://www.academia.edu/12665476/USING_SPECTRAL_RADIUS_RATIO_FOR_NODE_DEGREE_TO_ANALYZE_THE_EVOLUTION_OF_SCALE_FREE_NETWORKS_AND_SMALL_WORLD_NETWORKS","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/12665476/USING_SPECTRAL_RADIUS_RATIO_FOR_NODE_DEGREE_TO_ANALYZE_THE_EVOLUTION_OF_SCALE_FREE_NETWORKS_AND_SMALL_WORLD_NETWORKS"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="23201223" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/23201223/Effects_of_Evolution_on_the_Emergence_of_Scale_Free_Networks">Effects of Evolution on the Emergence of Scale Free Networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="34116417" href="https://unimaas.academia.edu/GerhardWeiss">Gerhard Weiss</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Artificial Life 14: Proceedings of the Fourteenth International Conference on the Synthesis and Simulation of Living Systems, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">The evolution of cooperation in social networks, and the emergence of these networks using simple rules of attachment, have both been studied extensively although mostly in separation. In real-world scenarios, however, these two fields are typically intertwined, where individuals' behavior affect the structural emergence of the network and vice versa. Although much progress has been made in understanding each of the aforementioned fields, many joint characteristics are still unrevealed. In this paper we propose the Simultaneous Emergence and Evolution (SEE) model, aiming at unifying the study of these two fields. The SEE model combines the continuous action prisoner's dilemma (modeling the evolution of cooperation) with preferential attachment (used to model network emergence), enabling the simultaneous study of both structural emergence and behavioral evolution of social networks. A set of empirical experiments show that the SEE model is capable of generating realistic complex networks, while at the same time allowing for the study of the impact of initial conditions on the evolution of cooperation.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Effects of Evolution on the Emergence of Scale Free Networks","attachmentId":43690144,"attachmentType":"pdf","work_url":"https://www.academia.edu/23201223/Effects_of_Evolution_on_the_Emergence_of_Scale_Free_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/23201223/Effects_of_Evolution_on_the_Emergence_of_Scale_Free_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="83718340" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/83718340/Size_dependent_degree_distribution_of_a_scale_free_growing_network">Size-dependent degree distribution of a scale-free growing network</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="158798226" href="https://independent.academia.edu/joserobertomendes">jose roberto mendes</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Size-dependent degree distribution of a scale-free growing network","attachmentId":88972166,"attachmentType":"pdf","work_url":"https://www.academia.edu/83718340/Size_dependent_degree_distribution_of_a_scale_free_growing_network","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/83718340/Size_dependent_degree_distribution_of_a_scale_free_growing_network"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="43186775" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/43186775/Analysis_of_a_Model_for_Generating_Weakly_Scale_free_Networks">Analysis of a Model for Generating Weakly Scale-free Networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="13834696" href="https://kfunigraz.academia.edu/RaheelAnwar">Raheel Anwar</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Discrete Mathematics and Theoretical Computer Science, 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">It is commonly believed that real networks are scale-free and the fraction of nodes P (k) with degree k satisfies the power-law P (k) ∝ k −γ for k > kmin > 0. Preferential attachment is the mechanism that has been considered responsible for such organization of these networks. In many real networks, degree distribution before the kmin varies very slowly to the extent of being uniform as compared to the degree distribution for k > kmin. In this paper, we propose a model that describes this particular degree distribution for the whole range of k > 0. We adopt a two step approach. In the first step, at every time stamp we add a new node to the network and attach it to an existing node using preferential attachment method. In the second step, we add edges between existing pairs of nodes with the node selection based on the uniform probability distribution. Our approach generates weakly scale-free networks that closely follow the degree distribution of real-world networks. We perform a comprehensive mathematical analysis of the model in the discrete domain and compare the degree distribution generated by this model with that of real-world networks.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Analysis of a Model for Generating Weakly Scale-free Networks","attachmentId":63453087,"attachmentType":"pdf","work_url":"https://www.academia.edu/43186775/Analysis_of_a_Model_for_Generating_Weakly_Scale_free_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/43186775/Analysis_of_a_Model_for_Generating_Weakly_Scale_free_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="26052106" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/26052106/Emergence_of_Scaling_in_Random_Networks">Emergence of Scaling in Random Networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="49914793" href="https://independent.academia.edu/%E6%8B%B4%E5%AE%9D%E5%88%98">拴宝 刘</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems. * alb@nd.edu</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Emergence of Scaling in Random Networks","attachmentId":46391818,"attachmentType":"pdf","work_url":"https://www.academia.edu/26052106/Emergence_of_Scaling_in_Random_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/26052106/Emergence_of_Scaling_in_Random_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="32428509" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32428509/Growing_Scale_free_Networks_by_a_Mediation_Driven_Attachment_Rule">Growing Scale-free Networks by a Mediation-Driven Attachment Rule</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62710135" href="https://independent.academia.edu/kamrulHossain8">Kamrul Hassan</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We propose a model that generates a class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links (m) with which incoming nodes join the existing network. Here, each new node first picks an existing node at random, and connects not with this but with m of its neighbors also picked at random. Counter-intuitively enough, such a mediation-driven attachment rule gives rise to superhubs for small m due to the winners take all effect, and hubs for large m due to the winners take some effect. To solve it analytically, we use mean-field approximation where we find that the inverse harmonic mean of degrees of the neighborhood of each existing node and their mean play a crucial role in determining the quality of the degree distribution.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Growing Scale-free Networks by a Mediation-Driven Attachment Rule","attachmentId":52622844,"attachmentType":"pdf","work_url":"https://www.academia.edu/32428509/Growing_Scale_free_Networks_by_a_Mediation_Driven_Attachment_Rule","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/32428509/Growing_Scale_free_Networks_by_a_Mediation_Driven_Attachment_Rule"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="18707817" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18707817/Deterministic_scale_free_networks">Deterministic scale-free networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38775154" href="https://elte-hu.academia.edu/Tam%C3%A1sVicsek">Tamás Vicsek</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 2001</p><p class="ds-related-work--abstract ds2-5-body-sm">Scale-free networks are abundant in nature, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes appear to be randomly connected to each other. Here we propose a simple model that generates scale-free networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Deterministic scale-free networks","attachmentId":40211668,"attachmentType":"pdf","work_url":"https://www.academia.edu/18707817/Deterministic_scale_free_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18707817/Deterministic_scale_free_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="6179113" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/6179113/Temporal_Dynamics_of_Scale_Free_Networks">Temporal Dynamics of Scale-Free Networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="5377302" href="https://telaviv.academia.edu/ErezShmueli">Erez Shmueli</a></div><p class="ds-related-work--metadata ds2-5-body-xs">SBP, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">Many social, biological, and technological networks display substantial non-trivial topological features. One well-known and much studied feature of such networks is the scale-free power-law distribution of nodes' degrees. Several works further suggest models for generating complex networks which comply with one or more of these topological features. For example, the known Barabasi-Albert "preferential attachment" model tells us how to create scale-free networks.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Temporal Dynamics of Scale-Free Networks","attachmentId":33062409,"attachmentType":"pdf","work_url":"https://www.academia.edu/6179113/Temporal_Dynamics_of_Scale_Free_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/6179113/Temporal_Dynamics_of_Scale_Free_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":46692501,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":46692501,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_46692501" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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data-collection-position="5" data-entity-id="22486134" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/22486134/On_the_formation_of_structure_in_growing_networks">On the formation of structure in growing networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="316649" href="https://javeriana.academia.edu/Finke">Jorge Finke</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Mechanics: Theory and Experiment, 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the formation of structure in growing 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