DOCSLIB.ORG

Ranking in Evolving Complex Networks

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Ranking in Evolving Complex Networks Physics Reports 689 (2017) 1–54 Contents lists available at ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep Ranking in evolving complex networks Hao Liao a, Manuel Sebastian Mariani b,a, *, Matú² Medo c,d,b, *, Yi-Cheng Zhang b, Ming-Yang Zhou a a National Engineering Laboratory for Big Data System Computing Technology, Guangdong Province Key Laboratory of Popular High Performance Computers, College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, PR China b Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland c Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, PR China d Department of Radiation Oncology, Inselspital, Bern University Hospital and University of Bern, 3010 Bern, Switzerland article info a b s t r a c t Article history: Complex networks have emerged as a simple yet powerful framework to represent and Accepted 15 May 2017 analyze a wide range of complex systems. The problem of ranking the nodes and the Available online 9 June 2017 edges in complex networks is critical for a broad range of real-world problems because Editor: I. Procaccia it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and Keywords: Complex networks policymakers, among others. This calls for a deep understanding of how existing ranking Ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Centrality metrics Many popular ranking algorithms (such as Google's PageRank) are static in nature and, Temporal networks as a consequence, they exhibit important shortcomings when applied to real networks Recommendation that rapidly evolve in time. At the same time, recent advances in the understanding and Network science modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of network traffic, prediction of future links, and identification of significant nodes. ' 2017 Elsevier B.V. All rights reserved. Contents 1. Introduction...............................................................................................................................................................................................3 2. Ranking with static centrality metrics ....................................................................................................................................................4 2.1. Getting started: basic language of complex networks ..............................................................................................................4 2.2. Degree and other local centrality metrics ..................................................................................................................................4 2.2.1. Degree............................................................................................................................................................................4 2.2.2. H-index..........................................................................................................................................................................5 2.2.3. Other local centrality metrics ......................................................................................................................................5 2.3. Metrics based on shortest paths..................................................................................................................................................5 2.3.1. Closeness centrality......................................................................................................................................................6 2.3.2. Betweenness centrality ................................................................................................................................................6 2.4. Coreness centrality and its relation with degree and H-index .................................................................................................6 * Corresponding authors at: Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland. E-mail addresses: [email protected] (M.S. Mariani), [email protected] (M. Medo). http://dx.doi.org/10.1016/j.physrep.2017.05.001 0370-1573/' 2017 Elsevier B.V. All rights reserved. 2 H. Liao et al. / Physics Reports 689 (2017) 1–54 2.5. Eigenvector-based centrality metrics .........................................................................................................................................7 2.5.1. Eigenvector centrality ..................................................................................................................................................7 2.5.2. Katz centrality...............................................................................................................................................................8 2.5.3. Win–loss scoring systems for ranking in sport...........................................................................................................8 2.5.4. PageRank .......................................................................................................................................................................9 2.5.5. PageRank variants......................................................................................................................................................... 10 2.5.6. HITS algorithm .............................................................................................................................................................. 11 2.6. A case study: node centrality in the Zachary's karate club network ........................................................................................ 11 2.7. Static ranking algorithms in bipartite networks........................................................................................................................ 12 2.7.1. Co-HITS algorithm ........................................................................................................................................................ 13 2.7.2. Method of reflections ................................................................................................................................................... 13 2.7.3. Fitness-complexity metric ........................................................................................................................................... 13 2.8. Rating-based ranking algorithms on bipartite networks .......................................................................................................... 14 3. The impact of network evolution on static ranking algorithms ............................................................................................................ 15 3.1. The first-mover advantage in preferential attachment and its suppression............................................................................ 15 3.2. PageRank's temporal bias and its suppression........................................................................................................................... 16 3.3. Illusion of influence in social systems ........................................................................................................................................ 18 4. Time-dependent ranking algorithms ...................................................................................................................................................... 19 4.1. Striving for time-balance: Node-based time-rescaled metrics................................................................................................. 19 4.2. Metrics with explicit penalization for older edges and/or nodes ............................................................................................. 20 4.2.1. Time-weighted degree and its use in predicting future trends................................................................................. 20 4.2.2. Penalizing old edges: Effective Contagion Matrix ...................................................................................................... 21 4.2.3. Penalizing old edges: TimedPageRank........................................................................................................................ 21 4.2.4. Focusing on a temporal window: T-Rank, SARA ........................................................................................................ 22 4.2.5. PageRank with time-dependent teleportation: CiteRank.......................................................................................... 22 4.2.6. Time-dependent reputation algorithms ..................................................................................................................... 22 4.3. Model-based ranking of nodes.................................................................................................................................................... 23 5. Ranking nodes in temporal networks.....................................................................................................................................................
Load more

Recommended publications
  • Graph Minor from Wikipedia, the Free Encyclopedia Contents
    Graph minor From Wikipedia, the free encyclopedia Contents 1 2 × 2 real matrices 1 1.1 Profile ................................................. 1 1.2 Equi-areal mapping .......................................... 2 1.3 Functions of 2 × 2 real matrices .................................... 2 1.4 2 × 2 real matrices as complex numbers ............................... 3 1.5 References ............................................... 4 2 Abelian group 5 2.1 Definition ............................................... 5 2.2 Facts ................................................. 5 2.2.1 Notation ........................................... 5 2.2.2 Multiplication table ...................................... 6 2.3 Examples ............................................... 6 2.4 Historical remarks .......................................... 6 2.5 Properties ............................................... 6 2.6 Finite abelian groups ......................................... 7 2.6.1 Classification ......................................... 7 2.6.2 Automorphisms ....................................... 7 2.7 Infinite abelian groups ........................................ 8 2.7.1 Torsion groups ........................................ 9 2.7.2 Torsion-free and mixed groups ................................ 9 2.7.3 Invariants and classification .................................. 9 2.7.4 Additive groups of rings ................................... 9 2.8 Relation to other mathematical topics ................................. 10 2.9 A note on the typography ......................................
    [Show full text]
  • Google Matrix Analysis of Wikipedia Networks
    En vue de l'obtention du DOCTORAT DE L'UNIVERSITÉ DE TOULOUSE Délivré par : Institut National Polytechnique de Toulouse (Toulouse INP) Discipline ou spécialité : Réseaux, Télécommunications, Systèmes et Architecture Présentée et soutenue par : M. SAMER EL ZANT le vendredi 6 juillet 2018 Titre : Google matrix analysis of Wikipedia networks Ecole doctorale : Mathématiques, Informatique, Télécommunications de Toulouse (MITT) Unité de recherche : Institut de Recherche en Informatique de Toulouse (I.R.I.T.) Directeur(s) de Thèse : M. DIMA SHEPELYANSKY MME KATIA JAFFRES-RUNSER Rapporteurs : M. MARIO ARIOLI, UNIVERSITA LUM JEAN MONNET M. PIERRE BORGNAT, CNRS Membre(s) du jury : M. PIERRE BORGNAT, CNRS, Président M. DIMITRI SHEPELYANSKY, CNRS TOULOUSE, Membre M. JOSE LAGES, UNIVERSITE DE FRANCHE COMTE, Membre Mme KATIA JAFFRES-RUNSER, INP TOULOUSE, Membre Mme SANDRINE MOUYSSET, UNIVERSITE TOULOUSE 3, Membre iii Acknowledgments Sincere gratitude to my supervisors Dr. Katia Jaffrès-Runser and Prof. Dima L. Shepelyansky for encouraging my research and supporting my PhD years while also providing the opportunity to enrich my knowledge through participation in international conferences. I thank him for enrolling me in a doctoral courses and schools and giving me the chance for teaching which improved my teaching and research skills. Furthermore, I would like to thank my PhD committee members, Prof. Pierre Borgnat, Prof. Mario Arioli, Dr. Sandrine Mouysset and Dr. José Lages for reading and reporting my manuscript. My thanks and appreciations also go to my colleagues in the "IRIT" for their help, support and collaboration to succeed my PhD. It was a pleasure working with all the partners in the project. Special thanks to Dr.
    [Show full text]
  • Ranking in Evolving Complex Networks
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by RERO DOC Digital Library Published in "Physics Reports doi: 10.1016/j.physrep.2017.05.001, 2017" which should be cited to refer to this work. Ranking in evolving complex networks Hao Liao a, Manuel Sebastian Mariani b,a,*, Matúš Medo c,d,b,*, Yi-Cheng Zhang b, Ming-Yang Zhou a a National Engineering Laboratory for Big Data System Computing Technology, Guangdong Province Key Laboratory of Popular High Performance Computers, College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, PR China b Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland c Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, PR China d Department of Radiation Oncology, Inselspital, Bern University Hospital and University of Bern, 3010 Bern, Switzerland Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and Keywords: policymakers, among others. This calls for a deep understanding of how existing ranking Complex networks algorithms perform, and which are their possible biases that may impair their effectiveness. Ranking Many popular ranking algorithms (such as Google’s PageRank) are static in nature and, Centrality metrics as a consequence, they exhibit important shortcomings when applied to real networks Temporal networks that rapidly evolve in time.
    [Show full text]
  • Google Matrix Analysis of Directed Networks
    Google matrix analysis of directed networks Leonardo Ermann Departamento de F´ısicaTe´orica,GIyA, Comisi´onNacional de Energ´ıaAt´omica,Buenos Aires, Argentina Klaus M. Frahm and Dima L. Shepelyansky Laboratoire de Physique Th´eorique du CNRS, IRSAMC, Universit´ede Toulouse, UPS, 31062 Toulouse, France (Dated: July 25, 2014; Revised: January 27, 2015) In the past decade modern societies have developed enormous communication and social networks. Their classification and information retrieval processing has become a formidable task for the society. Due to the rapid growth of the World Wide Web, and social and communication networks, new mathematical methods have been invented to characterize the properties of these networks in a more detailed and precise way. Various search engines use extensively such methods. It is highly important to develop new tools to classify and rank massive amount of network information in a way that is adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency using various examples including World Wide Web, Wikipedia, software architectures, world trade, social and citation networks, brain neural networks, DNA sequences and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos and Random Matrix theory. Keywords: Markov chains, World Wide Web, search engines, complex networks, PageRank, 2DRank, CheiRank \The Library exists ab aeterno." B. Universal emergence of PageRank 18 Jorge Luis Borges The Library of Babel C. Two-dimensional ranking for University networks 20 IX. Wikipedia networks 20 A. Two-dimensional ranking of Wikipedia articles 20 Contents B.
    [Show full text]
  • Crisis Contagion in the World Trade Network Célestin Coquidé1, José Lages1* and Dima L
    Coquidé et al. Applied Network Science (2020) 5:67 Applied Network Science https://doi.org/10.1007/s41109-020-00304-z RESEARCH Open Access Crisis contagion in the world trade network Célestin Coquidé1, José Lages1* and Dima L. Shepelyansky2 *Correspondence: [email protected] Abstract 1Institut UTINAM, UMR 6213, CNRS, We present a model of worldwide crisis contagion based on the Google matrix analysis Université Bourgogne of the world trade network obtained from the UN Comtrade database. The fraction of Franche-Comté, Besançon, France Full list of author information is bankrupted countries exhibits an on-off phase transition governed by a bankruptcy available at the end of the article threshold κ related to the trade balance of the countries. For κ>κc, the contagion is circumscribed to less than 10% of the countries, whereas, for κ<κc, the crisis is global with about 90% of the countries going to bankruptcy. We measure the total cost of the crisis during the contagion process. In addition to providing contagion scenarios, our model allows to probe the structural trading dependencies between countries. For different networks extracted from the world trade exchanges of the last two decades, the global crisis comes from the Western world. In particular, the source of the global crisis is systematically the Old Continent and The Americas (mainly US and Mexico). Besides the economy of Australia, those of Asian countries, such as China, India, Indonesia, Malaysia and Thailand, are the last to fall during the contagion. Also, the four BRIC are among the most robust countries to the world trade crisis.
    [Show full text]