Abstract
Many online collaboration networks struggle to gain user activity and become self-sustaining due to the ramp-up problem or dwindling activity within the system. Prominent examples include online encyclopedias such as (Semantic) MediaWikis, Question and Answering portals such as StackOverflow, and many others. Only a small fraction of these systems manage to reach self-sustaining activity, a level of activity that prevents the system from reverting to a nonactive state. In this article, we model and analyze activity dynamics in synthetic and empirical collaboration networks. Our approach is based on two opposing and well-studied principles: (i) without incentives, users tend to lose interest to contribute and thus, systems become inactive, and (ii) people are susceptible to actions taken by their peers (social or peer influence). With the activity dynamics model that we introduce in this article we can represent typical situations of such collaboration networks. For example, activity in a collaborative network, without external impulses or investments, will vanish over time, eventually rendering the system inactive. However, by appropriately manipulating the activity dynamics and/or the underlying collaboration networks, we can jump-start a previously inactive system and advance it toward an active state. To be able to do so, we first describe our model and its underlying mechanisms. We then provide illustrative examples of empirical datasets and characterize the barrier that has to be breached by a system before it can become self-sustaining in terms of critical mass and activity dynamics. Additionally, we expand on this empirical illustration and introduce a new metric p—the Activity Momentum—to assess the activity robustness of collaboration networks.
- Daniel M. Abrams and Steven H. Strogatz. 2003. Linguistics: Modelling the dynamics of language death. Nature 424, 6951 (2003), 900--900.Google Scholar
- Alberto Acerbi, Stefano Ghirlanda, and Magnus Enquist. 2012. The logic of fashion cycles. PloS One 7, 3 (2012), e32541.Google Scholar
Cross Ref
- Ashton Anderson, Daniel Huttenlocher, Jon Kleinberg, and Jure Leskovec. 2012. Discovering value from community activity on focused question answering sites: A case study of stack overflow. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 850--858. Google Scholar
Digital Library
- R. M. Anderson and R. M. May. 1991. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, USA.Google Scholar
- Sinan Aral, Lev Muchnik, and Arun Sundararajan. 2009. Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks. Proceedings of the National Academy of Sciences 106, 51 (2009), 21544--21549.Google Scholar
Cross Ref
- Sinan Aral and Dylan Walker. 2012. Identifying influential and susceptible members of social networks. Science 337, 6092 (2012), 337--341.Google Scholar
Cross Ref
- Joan L. Aron, Michael O’leary, Ronald A. Gove, Shiva Azadegan, and M. Cristina Schneider. 2002. The benefits of a notification process in addressing the worsening computer virus problem: Results of a survey and a simulation model. Computers and Security 21, 2 (March 2002), 142--163. DOI:http://dx.doi.org/10.1016/S0167-4048(02)00210-9 Google Scholar
Digital Library
- Robert Axelrod. 1997. Advancing the art of simulation in the social sciences. In Simulating Social Phenomena. Springer, 21--40.Google Scholar
- Norman T. J. Bailey and others. 1975. The Mathematical Theory of Infectious Diseases and its Applications. Charles Griffin & Company Ltd., High Wycombe, Bucks HP13 6LE, UK.Google Scholar
- Albert-Laszlo Barabâsi, Hawoong Jeong, Zoltan Néda, Erzsebet Ravasz, Andras Schubert, and Tamas Vicsek. 2002. Evolution of the social network of scientific collaborations. Physica A: Statistical Mechanics and its Applications 311, 3 (2002), 590--614.Google Scholar
- Andrea Baronchelli, Maddalena Felici, Vittorio Loreto, Emanuele Caglioti, and Luc Steels. 2006. Sharp transition towards shared vocabularies in multi-agent systems. Journal of Statistical Mechanics: Theory and Experiment 2006, 06 (2006), P06014.Google Scholar
Cross Ref
- Alain Barrat, Marc Barthelemy, and Alessandro Vespignani. 2008. Dynamical Processes on Complex Networks. Vol. 1. Google Scholar
Digital Library
- Marc Barthélemy. 2011. Spatial networks. Physics Reports 499, 1 (2011), 1--101.Google Scholar
- Frank M. Bass. 1976. A new product growth model for consumer durables. In Mathematical Models in Marketing. Springer, 351--353.Google Scholar
- James J. Binney, N. J. Dowrick, A. J. Fisher, and M. Newman. 1992. The Theory of Critical Phenomena: An Introduction to the Renormalization Group. Oxford University Press, Inc. Google Scholar
Digital Library
- B. M. Bolker and B. T. Grenfell. 1993. Chaos and biological complexity in measles dynamics. Proceedings of the Royal Society of London. Series B: Biological Sciences 251, 1330 (1993), 75--81.Google Scholar
- Benjamin Bolker and Bryan Grenfell. 1995. Space, persistence and dynamics of measles epidemics. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 348, 1325 (1995), 309--320.Google Scholar
- Tom Britton. 2010. Stochastic epidemic models: A survey. Mathematical Biosciences 225, 1 (2010), 24--35.Google Scholar
Cross Ref
- Claudio Castellano, Santo Fortunato, and Vittorio Loreto. 2009. Statistical physics of social dynamics. Reviews of Modern Physics 81, 2 (2009), 591.Google Scholar
Cross Ref
- Claudio Castellano, Matteo Marsili, and Alessandro Vespignani. 2000. Nonequilibrium phase transition in a model for social influence. Physical Review Letters 85, 16 (2000), 3536.Google Scholar
Cross Ref
- Xavier Castelló, Víctor M. Eguíluz, and Maxi San Miguel. 2006. Ordering dynamics with two non-excluding options: Bilingualism in language competition. New Journal of Physics 8, 12 (2006), 308.Google Scholar
Cross Ref
- Justin Cheng and Michael S. Bernstein. 2014. Catalyst: Triggering collective action with thresholds. (2014).Google Scholar
- Nicholas A. Christakis and James H. Fowler. 2008. The collective dynamics of smoking in a large social network. New England Journal of Medicine 358, 21 (2008), 2249--2258.Google Scholar
Cross Ref
- Fan Chung, Linyuan Lu, and Van Vu. 2003a. Eigenvalues of random power law graphs. Annals of Combinatorics 7, 1 (2003), 21--33.Google Scholar
Cross Ref
- Fan Chung, Linyuan Lu, and Van Vu. 2003b. Spectra of random graphs with given expected degrees. Proceedings of the National Academy of Sciences 100, 11 (2003), 6313--6318.Google Scholar
Cross Ref
- Peter Clifford and Aidan Sudbury. 1973. A model for spatial conflict. Biometrika 60, 3 (1973), 581--588.Google Scholar
Cross Ref
- Vittoria Colizza, Alain Barrat, Marc Barthélemy, and Alessandro Vespignani. 2006. The role of the airline transportation network in the prediction and predictability of global epidemics. Proceedings of the National Academy of Sciences of the United States of America 103, 7 (2006), 2015--2020.Google Scholar
Cross Ref
- Cristian Danescu-Niculescu-Mizil, Robert West, Dan Jurafsky, Jure Leskovec, and Christopher Potts. 2013. No country for old members: User lifecycle and linguistic change in online communities. In Proceedings of the 22nd International Conference on World Wide Web (WWW’13). International World Wide Web Conferences Steering Committee, Republic and Canton of Geneva, Switzerland, 307--318. Google Scholar
Digital Library
- Klaus Dietz. 1967. Epidemics and rumours: A survey. Journal of the Royal Statistical Society. Series A (General) (1967), 505--528.Google Scholar
- Sergey N. Dorogovtsev, Alexander V. Goltsev, and José F. F. Mendes. 2008. Critical phenomena in complex networks. Reviews of Modern Physics 80, 4 (2008), 1275.Google Scholar
Cross Ref
- Neil M. Ferguson, Derek A. T. Cummings, Simon Cauchemez, Christophe Fraser, Steven Riley, Aronrag Meeyai, Sopon Iamsirithaworn, and Donald S. Burke. 2005. Strategies for containing an emerging influenza pandemic in southeast Asia. Nature 437, 7056 (2005), 209--214.Google Scholar
Cross Ref
- Neil M. Ferguson, Matt J. Keeling, W. John Edmunds, Raymond Gani, Bryan T. Grenfell, Roy M. Anderson, and Steve Leach. 2003. Planning for smallpox outbreaks. Nature 425, 6959 (2003), 681--685.Google Scholar
- Leon Festinger. 1950. Social Pressures in Informal Groups: A Study of Human Factors in Housing. Stanford University Press.Google Scholar
- Andreas Flache and Michael W. Macy. 2007. Local convergence and global diversity: The robustness of cultural homophily. arXiv Preprint physics/0701333 (2007).Google Scholar
- Serge Galam, Yuval Gefen, and Yonathan Shapir. 1982. Sociophysics: A new approach of sociological collective behaviour. I. Mean-behaviour description of a strike. Journal of Mathematical Sociology 9, 1 (1982), 1--13.Google Scholar
Cross Ref
- Serge Galam and Serge Moscovici. 1991. Towards a theory of collective phenomena: Consensus and attitude changes in groups. European Journal of Social Psychology 21, 1 (1991), 49--74.Google Scholar
Cross Ref
- Ayalvadi Ganesh, Laurent Massoulié, and Don Towsley. 2005. The effect of network topology on the spread of epidemics. In Proceedings of the IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2005), Vol. 2. IEEE, 1455--1466.Google Scholar
Cross Ref
- Herbert W. Hethcote. 1978. An immunization model for a heterogeneous population. Theoretical Population Biology 14, 3 (1978), 338--349.Google Scholar
Cross Ref
- Herbert W. Hethcote. 2000. The mathematics of infectious diseases. SIAM Review 42, 4 (2000), 599--653. Google Scholar
Digital Library
- Richard A. Holley and Thomas M. Liggett. 1975. Ergodic theorems for weakly interacting infinite systems and the voter model. The Annals of Probability (1975), 643--663.Google Scholar
- Lars Hufnagel, Dirk Brockmann, and Theo Geisel. 2004. Forecast and control of epidemics in a globalized world. Proceedings of the National Academy of Sciences of the United States of America 101, 42 (2004), 15124--15129.Google Scholar
Cross Ref
- José Luis Iribarren and Esteban Moro. 2009. Impact of human activity patterns on the dynamics of information diffusion. Physical Review Letters 103, 3 (2009), 038702.Google Scholar
Cross Ref
- Matt J. Keeling and Pejman Rohani. 2002. Estimating spatial coupling in epidemiological systems: A mechanistic approach. Ecology Letters 5, 1 (2002), 20--29.Google Scholar
Cross Ref
- Jeffrey O. Kephart, Gregory B. Sorkin, David M. Chess, and Steve R. White. 1997. Fighting computer viruses: Biological metaphors offer insights into many aspects of computer viruses and can inspire defenses against them. Scientific American (1997).Google Scholar
- Jeffrey O. Kephart and Steve R. White. 1991. Directed-graph epidemiological models of computer viruses. In Proceedings of the 1991 IEEE Computer Society Symposium on Research in Security and Privacy. IEEE, 343--359.Google Scholar
- Jeffrey O. Kephart and Steve R. White. 1993. Measuring and modeling computer virus prevalence. In Proceedings of the 1993 IEEE Computer Society Symposium on Research in Security and Privacy. IEEE, 2--15. Google Scholar
Digital Library
- Jeffrey O. Kephart, Steve R. White, and David M. Chess. 1993. Computers and epidemiology. IEEE Spectrum 30, 5 (1993), 20--26. Google Scholar
Digital Library
- Aniket Kittur and Robert E. Kraut. 2008. Harnessing the wisdom of crowds in wikipedia: Quality through coordination. In Proceedings of the 2008 ACM Conference on Computer Supported Cooperative Work. ACM, 37--46. Google Scholar
Digital Library
- Konstantin Klemm, Víctor M. Eguíluz, Raúl Toral, and Maxi San Miguel. 2003a. Global culture: A noise-induced transition in finite systems. Physical Review E 67, 4 (2003), 045101.Google Scholar
Cross Ref
- Konstantin Klemm, Víctor M. Eguíluz, Raúl Toral, and Maxi San Miguel. 2003b. Nonequilibrium transitions in complex networks: A model of social interaction. Physical Review E 67, 2 (2003), 026120.Google Scholar
Cross Ref
- Jure Leskovec, Lada A. Adamic, and Bernardo A. Huberman. 2007. The dynamics of viral marketing. ACM Transactions on the Web 1, 1 (2007), 5. Google Scholar
Digital Library
- Jure Leskovec, Lars Backstrom, and Jon Kleinberg. 2009. Meme-tracking and the dynamics of the news cycle. In Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 497--506. Google Scholar
Digital Library
- C. C. Lin and L. A. Segel. 1988. Mathematics Applied to Deterministic Problems in the Natural Sciences. Vol. 1. SIAM.Google Scholar
- Alun L. Lloyd and Robert M. May. 1996. Spatial heterogeneity in epidemic models. Journal of Theoretical Biology 179, 1 (1996), 1--11.Google Scholar
Cross Ref
- Ira M. Longini, Azhar Nizam, Shufu Xu, Kumnuan Ungchusak, Wanna Hanshaoworakul, Derek A. T. Cummings, and M. Elizabeth Halloran. 2005. Containing pandemic influenza at the source. Science 309, 5737 (2005), 1083--1087.Google Scholar
- Gerald Marwell, Pamela E. Oliver, and Ralph Prahl. 1988. Social networks and collective action: A theory of the critical mass, III. American Journal of Sociology 94, 3 (1988), 502--534.Google Scholar
Cross Ref
- Robert M. May and Roy M. Anderson. 1984. Spatial heterogeneity and the design of immunization programs. Mathematical Biosciences 72, 1 (1984), 83--111.Google Scholar
Cross Ref
- James W. Minett and William S. Y. Wang. 2008. Modelling endangered languages: The effects of bilingualism and social structure. Lingua 118, 1 (2008), 19--45.Google Scholar
Cross Ref
- Mauro Mobilia. 2003. Does a single zealot affect an infinite group of voters? Physical Review Letters 91, 2 (2003), 028701.Google Scholar
Cross Ref
- Mauro Mobilia and Ivan T. Georgiev. 2005. Voting and catalytic processes with inhomogeneities. Physical Review E 71, 4 (2005), 046102.Google Scholar
Cross Ref
- Mauro Mobilia, A. Petersen, and Sidney Redner. 2007. On the role of zealotry in the voter model. Journal of Statistical Mechanics: Theory and Experiment 2007, 08 (2007), P08029.Google Scholar
Cross Ref
- Yamir Moreno, Romualdo Pastor-Satorras, and Alessandro Vespignani. 2002. Epidemic outbreaks in complex heterogeneous networks. The European Physical Journal B-Condensed Matter and Complex Systems 26, 4 (2002), 521--529.Google Scholar
Cross Ref
- J. D. Murray. 2002. Mathematical Biology. Springer, New York. http://www.worldcat.org/search?qt=worldcat_org_all&q==9780387952239.Google Scholar
- Seth A. Myers, Chenguang Zhu, and Jure Leskovec. 2012. Information diffusion and external influence in networks. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 33--41. Google Scholar
Digital Library
- Mark Newman. 2010. Networks: An Introduction. Oxford University Press. Google Scholar
Digital Library
- Mark E. J. Newman. 2001. Scientific collaboration networks. I. Network construction and fundamental results. Physical Review E 64, 1 (2001), 016131.Google Scholar
Cross Ref
- Mark E. J. Newman, Stephanie Forrest, and Justin Balthrop. 2002. Email networks and the spread of computer viruses. Physical Review E 66, 3 (2002), 035101.Google Scholar
Cross Ref
- Pamela Oliver, Gerald Marwell, and Ruy Teixeira. 1985. A theory of the critical mass. I. Interdependence, group heterogeneity, and the production of collective action. American Journal of Sociology (1985), 522--556.Google Scholar
- Pamela E. Oliver and Gerald Marwell. 1988. The paradox of group size in collective action: A theory of the critical mass. II. American Sociological Review (1988), 1--8.Google Scholar
- Romualdo Pastor-Satorras, Claudio Castellano, Piet Van Mieghem, and Alessandro Vespignani. 2014. Epidemic processes in complex networks. arXiv Preprint arXiv:1408.2701 (2014).Google Scholar
- Romualdo Pastor-Satorras and Alessandro Vespignani. 2001a. Epidemic dynamics and endemic states in complex networks. Physical Review E 63, 6 (2001), 066117.Google Scholar
Cross Ref
- Romualdo Pastor-Satorras and Alessandro Vespignani. 2001b. Epidemic spreading in scale-free networks. Physical Review Letters 86, 14 (2001), 3200.Google Scholar
Cross Ref
- Romualdo Pastor-Satorras and Alessandro Vespignani. 2002. Epidemic dynamics in finite size scale-free networks. Physical Review E 65, 3 (2002), 035108.Google Scholar
Cross Ref
- Romualdo Pastor-Satorras and Alessandro Vespignani. 2007. Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge University Press. Google Scholar
Digital Library
- Daphne R. Raban, Mihai Moldovan, and Quentin Jones. 2010. An empirical study of critical mass and online community survival. In Proceedings of the 2010 ACM Conference on Computer Supported Cooperative Work (CSCW’10). ACM, New York, NY, 71--80. DOI:http://dx.doi.org/10.1145/1718918.1718932 Google Scholar
Digital Library
- Bruno Ribeiro. 2014. Modeling and predicting the growth and death of membership-based websites. In Proceedings of the 23rd International Conference on World Wide Web (WWW’14), 653--664. DOI:http://dx.doi.org/10.1145/2566486.2567984 Google Scholar
Digital Library
- Leonid A. Rvachev and Ira M. Longini. 1985. A mathematical model for the global spread of influenza. Mathematical Biosciences 75, 1 (1985), 3--22.Google Scholar
Cross Ref
- Jacob Solomon and Rick Wash. 2014. Critical mass of what? Exploring community growth in WikiProjects. (2014).Google Scholar
- Luc Steels. 1995. A self-organizing spatial vocabulary. Artificial Life 2, 3 (1995), 319--332. Google Scholar
Digital Library
- Steven H. Strogatz. 1994. Nonlinear Dynamics And Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity). Perseus Books Group.Google Scholar
- Bongwon Suh, Gregorio Convertino, Ed H. Chi, and Peter Pirolli. 2009. The singularity is not near: Slowing growth of wikipedia. In Proceedings of the 5th International Symposium on Wikis and Open Collaboration. ACM, 8. Google Scholar
Digital Library
- Claudio J. Tessone and Raul Toral. 2009. Diversity-induced resonance in a model for opinion formation. The European Physical Journal B-Condensed Matter and Complex Systems 71, 4 (2009), 549--555.Google Scholar
Cross Ref
- Federico Vazquez, Paul L. Krapivsky, and Sidney Redner. 2003. Constrained opinion dynamics: Freezing and slow evolution. Journal of Physics A: Mathematical and General 36, 3 (2003), L61.Google Scholar
Cross Ref
- F. Vazquez and S. Redner. 2004. Ultimate fate of constrained voters. Journal of Physics A: Mathematical and General 37, 35 (2004), 8479.Google Scholar
Cross Ref
- Alessandro Vespignani. 2012. Modelling dynamical processes in complex socio-technical systems. Nature Physics 8, 1 (2012), 32--39.Google Scholar
Cross Ref
- Claudia Wagner, Silvia Mitter, Christian Körner, and Markus Strohmaier. 2012. When social bots attack: Modeling susceptibility of users in online social networks. Making Sense of Microposts (#MSM2012 Workshop) (2012), 2.Google Scholar
- Simon Walk and Markus Strohmaier. 2014. Characterizing and predicting activity in semantic MediaWiki communities. In 3rd International Workshop on Semantic Web Collaborative Spaces (SWCS’14). 21. Google Scholar
Digital Library
- William S. Y. Wang and James W. Minett. 2005. The invasion of language: Emergence, change and death. Trends in Ecology and Evolution 20, 5 (2005), 263--269.Google Scholar
Cross Ref
- Yang Wang, Deepayan Chakrabarti, Chenxi Wang, and Christos Faloutsos. 2003. Epidemic spreading in real networks: An eigenvalue viewpoint. In Proceedings of the 22nd International Symposium on Reliable Distributed Systems, 2003. IEEE, 25--34.Google Scholar
Cross Ref
- Wolfgang Weidlich. 1971. The statistical description of polarization phenomena in society. British Journal of Mathematical and Statistical Psychology 24, 2 (1971), 251--266.Google Scholar
Cross Ref
- Fa-Yueh Wu. 1982. The Potts model. Reviews of Modern Physics 54, 1 (1982), 235.Google Scholar
Cross Ref
- Jie Yang, Ke Tao, Alessandro Bozzon, and Geert-Jan Houben. 2014. Sparrows and owls: Characterisation of expert behaviour in stackoverflow. In User Modeling, Adaptation, and Personalization. Springer, 266--277.Google Scholar
Index Terms
Activity Dynamics in Collaboration Networks
Recommendations
Exploring the Impact of Trolls on Activity Dynamics in Real-World Collaboration Networks
WWW '17 Companion: Proceedings of the 26th International Conference on World Wide Web CompanionWhen new users join social networking websites, they often form collaboration ties with existing users, which in turn may result in some level of activity on the site. However, for various reasons, new users often fail to create such ties and their ...
Effect of developer collaboration activity on software quality in two large scale projects
We modelled the collaboration activity for two large-scale software.We extracted the defect induction and fixing data for two large software.We identified the effect of collaboration activity on software quality. Developers work together during software ...
Dynamics in spectral solutions of Burgers equation
For low values of the viscosity coefficient, Burgers equation can develop sharp discontinuities, which are difficult to simulate in a computer. Oscillations can occur by discretization through spectral collocation methods, due to Gibbs phenomena. Under ...






Comments