research-article

Generating Simple Directed Social Network Graphs for Information Spreading

Authors:

Christoph Schweimer,

Christine Gfrerer,

Florian Lugstein,

Jan A. Velimsky,

Robert Elsässer,

Bernhard C. GeigerAuthors Info & Claims

WWW '22: Proceedings of the ACM Web Conference 2022

Pages 1475 - 1485

https://doi.org/10.1145/3485447.3512194

Published: 25 April 2022 Publication History

Abstract

Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years, researchers studied several properties of social networks and designed random graph models to describe them. Many of these approaches either focus on the generation of undirected graphs or on the creation of directed graphs without modeling the dependencies between reciprocal (i.e., two directed edges of opposite direction between two nodes) and directed edges. We propose an approach to generate directed social network graphs that creates reciprocal and directed edges and considers the correlation between the respective degree sequences.

Our model relies on crawled directed graphs in Twitter, on which information w.r.t. a topic is exchanged or disseminated. While these graphs exhibit a high clustering coefficient and small average distances between random node pairs (which is typical in real-world networks), their degree sequences seem to follow a χ2-distribution rather than power law. To achieve high clustering coefficients, we apply an edge rewiring procedure that preserves the node degrees.

We compare the crawled and the created graphs, and simulate certain algorithms for information dissemination and epidemic spreading on them. The results show that the created graphs exhibit very similar topological and algorithmic properties as the real-world graphs, providing evidence that they can be used as surrogates in social network analysis. Furthermore, our model is highly scalable, which enables us to create graphs of arbitrary size with almost the same properties as the corresponding real-world networks.

References

[1]

Yong-Yeol Ahn, Seungyeop Han, Haewoon Kwak, Sue Moon, and Hawoong Jeong. 2007. Analysis of Topological Characteristics of Huge Online Social Networking Services. In Proc. Int. Conf. on World Wide Web (WWW) (Banff, Alberta, Canada). ACM, New York, NY, USA, 835–844. https://doi.org/10.1145/1242572.1242685

Digital Library

[2]

Jeff Alstott, Christine Klymko, Pamela Pyzza, and Mary Radcliffe. 2016. Local rewiring algorithms to increase clustering and grow a small world. Journal of Complex Networks 7 (Aug. 2016), 564–584. https://doi.org/10.1093/comnet/cny032

[3]

Shweta Bansal, Shashank Khandelwal, and Lauren Ancel Meyers. 2009. Exploring biological network structure with clustered random networks. BMC Bioinformatics 10, 405 (2009). https://doi.org/10.1186/1471-2105-10-405

[4]

Albert-Laszlo Barabási and Reka Albert. 1999. Emergence of Scaling in Random Networks. Science 286, 5439 (11 1999), 509–512. https://doi.org/10.1126/science.286.5439.509

[5]

Edward A Bender and E.Rodney Canfield. 1978. The asymptotic number of labeled graphs with given degree sequences. Journal of Combinatorial Theory, Series A 24, 3 (1978), 296–307. https://doi.org/10.1016/0097-3165(78)90059-6

[6]

Vincent Blondel, Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefebvre. 2008. Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 2008, 10(2008), P10008. https://doi.org/10.1088/1742-5468/2008/10/P10008

[7]

Béla Bollobás, Christian Borgs, Jennifer Chayes, and Oliver Riordan. 2003. Directed Scale-Free Graphs. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (Baltimore, Maryland) (SODA ’03). Society for Industrial and Applied Mathematics, USA, 132–139.

Digital Library

[8]

Béla Bollobás. 1980. A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs. European Journal of Combinatorics 1, 4 (1980), 311–316. https://doi.org/10.1016/S0195-6698(80)80030-8

[9]

Angela Bonifati, Irena Holubová, Arnau Prat-Pérez, and Sherif Sakr. 2020. Graph Generators: State of the Art and Open Challenges. ACM Comput. Surv. 53, 2, Article 36 (April 2020), 30 pages. https://doi.org/10.1145/3379445

Digital Library

[10]

Tom Britton, Maria Deijfen, and Anders Martin-Löf. 2006. Generating Simple Random Graphs with Prescribed Degree Distribution. Journal of Statistical Physics 124 (Oct. 2006), 1377–1397. https://doi.org/10.1007/s10955-006-9168-x

[11]

Marne C. Cario and Barry L. Nelson. 1997. Modeling and Generating Random Vectors with Arbitrary Marginal Distributions and Correlation Matrix. Department of Industrial Engineering and Management Sciences. Northwesern University, Evanston, IL, USA.

[12]

Ningyuan Chen and Mariana Olvera-Cravioto. 2013. Directed random graphs with given degree distributions. Stochastic Systems 3, 1 (2013), 147 – 186. https://doi.org/10.1214/12-SSY076

[13]

Fan Chung and Linyuan Lu. 2002. Connected Components in Random Graphs with Given Expected Degree Sequences. Annals of Combinatorics 6 (11 2002), 125–145. https://doi.org/10.1007/PL00012580

[14]

Matteo Cinelli, Gianmarco De Francisci Morales, Alessandro Galeazzi, Walter Quattrociocchi, and Michele Starnini. 2021. The echo chamber effect on social media. Proceedings of the National Academy of Sciences 118, 9 (2021). https://doi.org/10.1073/pnas.2023301118

[15]

Thomas Cormen, Charles Leiserson, Ronald Rivest, and Clifford Stein. 2001. Introduction to Algorithms. MIT Press and McGraw-Hill.

[16]

Alan Demers, Dan Greene, Carl Hauser, Wes Irish, John Larson, Scott Shenker, Howard Sturgis, Dan Swinehart, and Doug Terry. 1987. Epidemic algorithms for replicated database maintenance. In Proc. ACM Symposium on Principles of Distributed Computing (PODC). ACM, USA, 1–12. https://doi.org/10.1145/41840.41841

Digital Library

[17]

Luc Devroye. 1986. Non-Uniform Random Variate Generation. Springer-Verlag, New York, NY, USA.

[18]

Ralf Diekmann, Andreas Frommer, and Burkhard Monien. 1999. Efficient schemes for nearest neighbor load balancing. Parallel Comput. 25, 7 (1999), 789–812. https://doi.org/10.1016/S0167-8191(99)00018-6

Digital Library

[19]

Nurcan Durak, Tamara G. Kolda, Ali Pinar, and C. Seshadhri. 2013. A scalable null model for directed graphs matching all degree distributions: In, out, and reciprocal. In Proc. IEEE Network Science Workshop (NSW). 23–30. https://doi.org/10.1109/NSW.2013.6609190

[20]

Paul Erdös and Alfred Rényi. 1959. On Random Graphs I. Publicationes Mathematicae Debrecen 6 (1959), 290–297.

[21]

Uriel Feige, David Peleg, Prabhakar Raghavan, and Eli Upfal. 1990. Randomized Broadcast in Networks. Random Structures and Algorithms 1 (1990), 447–460. https://doi.org/10.1007/3-540-52921-7_62

[22]

Bailey K. Fosdick, Daniel B. Larremore, Joel Nishimura, and Johan Ugander. 2018. Configuring Random Graph Models with Fixed Degree Sequences. SIAM Rev. 60, 2 (2018), 315–355. https://doi.org/10.1137/16M1087175

[23]

Michael Garey and David Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company.

Digital Library

[24]

George Giakkoupis. 2011. Tight bounds for rumor spreading in graphs of a given conductance. In Proc. Int. Symposium on Theoretical Aspects of Computer Science (STACS). 57–68. https://doi.org/10.4230/LIPIcs.STACS.2011.57

[25]

E. N. Gilbert. 1959. Random Graphs. Annals of Mathematical Statistics 30, 4 (1959), 1141–1144. https://doi.org/10.1214/aoms/1177706098

[26]

Catherine S. Greenhill. 2015. The switch Markov chain for sampling irregular graphs (Extended Abstract). In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015, Piotr Indyk (Ed.). SIAM, 1564–1572. https://doi.org/10.1137/1.9781611973730.103

[27]

Weisen Guo and Steven B. Kraines. 2009. A Random Network Generator with Finely Tunable Clustering Coefficient for Small-World Social Networks. In Proc. Int. Conf. on Computational Aspects of Social Networks (CASON). IEEE Computer Society, USA, 10–17. https://doi.org/10.1109/CASoN.2009.13

Digital Library

[28]

Herbert W. Hethcote. 2000. The Mathematics of Infectious Diseases. SIAM Rev. 42, 4 (2000), 599–653. https://doi.org/10.1137/S0036144500371907

Digital Library

[29]

Richard Karp, Scott Shenker, Christian Schindelhauer, and Berthold Vöcking. 2000. Randomized Rumor Spreading. In Proc. IEEE Symposium on Foundations in Computer Science (FOCS). IEEE Computer Society, USA, 565–574. https://doi.org/10.1109/SFCS.2000.892324

[30]

Tamara Kolda, Ali Pinar, Todd Plantenga, and C. Seshadhri. 2014. A scalable generative graph model with community structure. SIAM Journal on Scientific Computing 36 (2014), C424––C452. https://doi.org/10.1137/130914218

Digital Library

[31]

Haewoon Kwak, Changhyun Lee, Hosung Park, and Sue Moon. 2010. What is Twitter, a Social Network or a News Media?. In Proceedings of the 19th International Conference on World Wide Web (Raleigh, North Carolina, USA) (WWW ’10). Association for Computing Machinery, New York, NY, USA, 591–600. https://doi.org/10.1145/1772690.1772751

Digital Library

[32]

John W. McDonald, Peter W.F. Smith, and Jonathan J. Forster. 2007. Markov chain Monte Carlo exact inference for social networks. Social Networks 29, 1 (2007), 127–136. https://doi.org/10.1016/j.socnet.2006.04.003

[33]

Alan Mislove, Massimiliano Marcon, Krishna P. Gummadi, Peter Druschel, and Bobby Bhattacharjee. 2007. Measurement and Analysis of Online Social Networks. In Proc. ACM SIGCOMM Conference on Internet Measurement (IMC) (San Diego, California, USA). ACM, New York, NY, USA, 29–42. https://doi.org/10.1145/1298306.1298311

Digital Library

[34]

Seth Myers, Aneesh Sharma, Pankaj Gupta, and Jimmy Lin. 2014. Information network or social network?: The structure of the twitter follow graph. In Proc. Int. Conf. on World Wide Web (WWW) (Seoul, Korea). ACM, New York, NY, USA, 493–498. https://doi.org/10.1145/2567948.2576939

Digital Library

[35]

Roger B. Nelsen. 2006. An introduction to copulas.Springer, New York. http://www.worldcat.org/search?qt=worldcat_org_all&q=0387286594

[36]

Mark Newman. 2003. The Structure and Function of Complex Networks. SIAM Rev. 45(2)(2003), 167–256. https://doi.org/10.1137/S003614450342480

Digital Library

[37]

Mark Newman. 2009. Random Graphs with Clustering. Physical review letters 103 (07 2009), 058701. https://doi.org/10.1103/PhysRevLett.103.058701

[38]

Karl Pearson. 1907. On Further Methods of Determining Correlation. Journal of the Royal Statistical Society 70 (1907), 655–656. https://doi.org/10.2307/2339568

[39]

Thomas Sauerwald. 2010. On Mixing and Edge Expansion Properties in Randomized Broadcasting. Algorithmica 56(1)(2010), 51–88. https://doi.org/10.1007/s00453-008-9245-4

[40]

C. Seshadhri, T. G. Kolda, and A. Pinar. 2012. Community structure and scale-free collections of Erdős-Rényi graphs. Physical Review E 85(2012). https://doi.org/10.1103/PhysRevE.85.056109

[41]

Christian Staudt and Henning Meyerhenke. 2016. Engineering parallel algorithms for community detection in massive networks. IEEE Transactions on Parallel and Distributed Systems 27(1) (2016), 171–184. https://doi.org/10.1109/TPDS.2015.2390633

Digital Library

[42]

Lionel Tabourier, Camille Roth, and Jean-Philippe Cointet. 2011. Generating Constrained Random Graphs Using Multiple Edge Switches. ACM J. Exp. Algorithmics 16, Article 1.7 (dec 2011), 15 pages. https://doi.org/10.1145/1963190.2063515

Digital Library

[43]

Trevor Tao. 2016. An improved MCMC algorithm for generating random graphs from constrained distributions. Network Science 4, 1 (2016), 117–139. https://doi.org/10.1017/nws.2015.35

[44]

Duncan J. Watts and Steven H. Strogatz. 1998. Collective dynamics of ‘small-world’ networks. Nature 393, 6684 (1998), 440–442. https://doi.org/10.1038/30918

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Generating Simple Directed Social Network Graphs for Information Spreading

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cover image ACM Conferences

WWW '22: Proceedings of the ACM Web Conference 2022

April 2022

3764 pages

ISBN:9781450390965

DOI:10.1145/3485447

Editors:
Frédérique Laforest
INSA Lyon, France
,
Raphaël Troncy
EURECOM, France
,
Elena Simperl
King’s College London, UK
,
Deepak Agarwal
Pinterest, USA
,
Aristides Gionis
KTH Royal Institute of Technology, Sweden
,
Ivan Herman
W3C / retired
,
Lionel Médini
Université Lyon 1, France

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Published: 25 April 2022

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WWW '22

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WWW '22: The ACM Web Conference 2022

April 25 - 29, 2022

Virtual Event, Lyon, France

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Cited By

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https://dl.acm.org/doi/10.14778/3654621.3654623
Wei SWang LWu HZhou MLi QXiao Y(2024)Link prediction method for social networks based on a hierarchical and progressive user interaction matrixKnowledge-Based Systems10.1016/j.knosys.2024.111929297(111929)Online publication date: Aug-2024
https://doi.org/10.1016/j.knosys.2024.111929
Vakhitov GUstin PGafarov FPopov L(2024)Development of an Indicator of Social Success of Social Network Users to Improve Intelligent Management Systems12th World Conference “Intelligent System for Industrial Automation” (WCIS-2022)10.1007/978-3-031-53488-1_9(76-83)Online publication date: 18-Feb-2024
https://doi.org/10.1007/978-3-031-53488-1_9
Olvera Astivia OKroc EZumbo B(2023)Simultaneous estimation of the intermediate correlation matrix for arbitrary marginal densitiesBehavior Research Methods10.3758/s13428-023-02123-356:3(1852-1862)Online publication date: 31-May-2023
https://doi.org/10.3758/s13428-023-02123-3
Yang KZhou ZSun WWang PWang XWang YSingh ASun YAkoglu LGunopulos DYan XKumar ROzcan FYe J(2023)EXTRACT and REFINE: Finding a Support Subgraph Set for Graph RepresentationProceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3580305.3599339(2953-2964)Online publication date: 6-Aug-2023
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Szustak LLawenda MArming SBankhamer GSchweimer CElsässer R(2023)Profiling and optimization of Python-based social sciences applications on HPC systems by means of task and data parallelismFuture Generation Computer Systems10.1016/j.future.2023.07.005148:C(623-635)Online publication date: 1-Nov-2023
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Schweimer C(2022)Fast generation of simple directed social network graphs with reciprocal edges and high clusteringSocial Network Analysis and Mining10.1007/s13278-022-00963-z12:1Online publication date: 3-Sep-2022
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