Hostname: page-component-76d6cb85b7-6jg5l Total loading time: 0 Render date: 2026-07-12T21:30:19.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Multigroup connectivity structures and their implications

Published online by Cambridge University Press:  18 November 2019

Shadi Mohagheghi Open the ORCID record for Shadi Mohagheghi [Opens in a new window] ,
Pushkarini Agharkar ,
Francesco Bullo  and
Noah E. Friedkin Open the ORCID record for Noah E. Friedkin [Opens in a new window]
Shadi Mohagheghi*
Affiliation:
Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA
Pushkarini Agharkar
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA (emails: pushkarini.a@gmail.com; bullo@engineering.ucsb.edu)
Francesco Bullo
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA (emails: pushkarini.a@gmail.com; bullo@engineering.ucsb.edu)
Noah E. Friedkin
Affiliation:
Department of Sociology, University of California at Santa Barbara, Santa Barbara, CA, USA (email: friedkin@soc.ucsb.edu)
*
*Corresponding author. Email: shadi.mohagheghi@gmail.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We investigate the implications of different forms of multigroup connectivity. Four multigroup connectivity modalities are considered: co-memberships, edge bundles, bridges, and liaison hierarchies. We propose generative models to generate these four modalities. Our models are variants of planted partition or stochastic block models conditioned under certain topological constraints. We report findings of a comparative analysis in which we evaluate these structures, controlling for their edge densities and sizes, on mean rates of information propagation, convergence times to consensus, and steady-state deviations from the consensus value in the presence of noise as network size increases.

Keywords

multigroup networksconnectivity modalitiesrandom graphscomparative analysis

Information

Type
Original Article
Information
Network Science , Volume 7 , Issue 4 , December 2019 , pp. 459 - 475
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2019

References

Abbe, E. (2017). Community detection and stochastic block models: Recent developments. Journal of Machine Learning Research, 18(1), 6446–6531.Google Scholar
Aicher, C., Jacobs, A. Z., & Clauset, A. (2014). Learning latent block structure in weighted networks. Journal of Complex Networks, 3, 221–248.CrossRefGoogle Scholar
Airoldi, E. M., Blei, D. M., Fienberg, S. E., & Xing, E. P. (2008). Mixed membership stochastic blockmodels. Journal of Machine Learning Research, 9, 1981–2014.Google ScholarPubMed
Allen, L. J. S. (1994). Some discrete-time SI, SIR, and SIS epidemic models. Mathematical Biosciences, 124(1), 83–105.CrossRefGoogle ScholarPubMed
Boorman, S. A., & White, H. C. (1976). Social structure from multiple networks. II. Role structures. American Journal of Sociology, 81(6), 1384–1446.CrossRefGoogle Scholar
Borgatti, S. P., & Halgin, D. S. (2011). Analyzing affiliation networks. The Sage Handbook of Social Network Analysis, 1, 417–433.Google Scholar
Bullo, F. (2018). Lectures on network systems (1st ed.). CreateSpace. With contributions by Cortés, J., Dörfler, F. and Martnez, S..Google Scholar
Cornwell, B., & Harrison, J. A. (2004). Union members and voluntary associations: Membership overlap as a case of organizational embeddedness. American Sociological Review, 69(6), 862–881.CrossRefGoogle Scholar
Crozier, M. (1964). The bureaucratic phenomenon. Chicago: University of Chicago Press.Google Scholar
DeGroot, M. H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69(345), 118–121.CrossRefGoogle Scholar
Erdös, P., & Rényi, A. (1959). On random graphs, I. Publicationes mathematicae (debrecen), 6, 290–297.Google Scholar
Evans, W. R., & Davis, W. D. (2005). High-performance work systems and organizational performance: The mediating role of internal social structure. Journal of Management, 31(5), 758–775.CrossRefGoogle Scholar
Fienberg, S. E., & Wasserman, S. S. (1981). Categorical data analysis of single sociometric relations. Sociological Methodology, 12, 156–192.CrossRefGoogle Scholar
Fortunato, S. (2010). Community detection in graphs. Physics Reports, 486(3–5), 75–174.CrossRefGoogle Scholar
French, J. R. P. Jr. (1956). A formal theory of social power. Psychological Review, 63(3), 181–194.CrossRefGoogle ScholarPubMed
Friedkin, N. E. (1983). Horizons of observability and limits of informal control in organizations. Social Forces, 62(1), 54–77.CrossRefGoogle Scholar
Friedkin, N. E. (1998). A structural theory of social influence. Structural Analysis in the Social Sciences. New York: Cambridge University Press.CrossRefGoogle Scholar
Friedkin, N. E., & Johnsen, E. C. (2002). Control loss and Fayol’s gangplanks. Social Networks, 24(4), 395–406.CrossRefGoogle Scholar
Galbraith, J. R. (1974). Organization design: An information processing view. Interfaces, 4(3), 28–36.CrossRefGoogle Scholar
Granovetter, M. (1983). The strength of weak ties: A network theory revisited. Sociological Theory, 1(1), 201–233.CrossRefGoogle Scholar
Granovetter, M. S. (1973). The strength of weak ties. American Journal of Sociology, 78(6), 1360–1380.CrossRefGoogle Scholar
Hethcote, H. W. (1978). An immunization model for a heterogeneous population. Theoretical Population Biology, 14(3), 338–349.CrossRefGoogle ScholarPubMed
Holland, P. W., Laskey, K., & Leinhardt, S. (1983). Stochastic blockmodels: First steps. Social Networks, 5(2), 109–137.CrossRefGoogle Scholar
Jackson, M. O. (2010). Social and economic networks. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Jadbabaie, A., & Olshevsky, A. (2017). Scaling laws for consensus protocols subject to noise. IEEE Transactions on Automatic Control, 64(4), 1389–1402.CrossRefGoogle Scholar
Karrer, B., & Newman, M. E. J. (2011). Stochastic blockmodels and community structure in networks. Physical Review E, 83, 016107.CrossRefGoogle ScholarPubMed
Kemeny, J. G., & Snell, J. L. (1976). Finite markov chains. Harrisonburg, VA: Springer.Google Scholar
Lajmanovich, A., & Yorke, J. A. (1976). A deterministic model for gonorrhea in a nonhomogeneous population. Mathematical Biosciences, 28(3), 221–236.CrossRefGoogle Scholar
Likert, R. (1967). The human organization: Its management and values. New York, NY: McGraw-Hill.Google Scholar
Mei, W., Mohagheghi, S., Zampieri, S., & Bullo, F. (2017). On the dynamics of deterministic epidemic propagation over networks. Annual Reviews in Control, 44, 116–128.CrossRefGoogle Scholar
Newman, M. E. J. (2006). Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103(23), 8577–8582.CrossRefGoogle ScholarPubMed
Newman, M. E. J, & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113.CrossRefGoogle ScholarPubMed
Reynolds, E. V., & Johnson, J. D. (1982). Liaison emergence: Relating theoretical perspectives. Academy of Management Review, 7(4), 551–559.CrossRefGoogle Scholar
Sawardecker, E. N., Sales-Pardo, M., & Amaral, L. A. N. (2009). Detection of node group membership in networks with group overlap. The European Physical Journal B, 67(3), 277–284.CrossRefGoogle Scholar
Schaeffer, S. E. (2007). Graph clustering. Computer Science Review, 1(1), 27–64.CrossRefGoogle Scholar
Schwartz, D. F. (1977). Organizational communication network analysis: The liaison communication role. Organizational Behavior and Human Performance, 18(1), 158–174.CrossRefGoogle Scholar
Singhal, A. V., Jha, A., & Gairola, A. (2014). A networking solution for disaster management to address liaison failures in emergency response. Risk Analysis IX, 47, 401.CrossRefGoogle Scholar
Stam, W., & Elfring, T. (2008). Entrepreneurial orientation and new venture performance: The moderating role of intra-and extraindustry social capital. Academy of Management Journal, 51(1), 97–111.CrossRefGoogle Scholar
Tortoriello, M., & Krackhardt, D. (2010). Activating cross-boundary knowledge: The role of simmelian ties in the generation of innovations. Academy of Management Journal, 53(1), 167–181.CrossRefGoogle Scholar
Wang, Y., Chakrabarti, D., Wang, C., & Faloutsos, C. (2003). Epidemic spreading in real networks: An eigenvalue viewpoint. In IEEE International Symposium on Reliable Distributed Systems (pp. 25–34).CrossRefGoogle Scholar
Wang, Y. J., & Wong, G. Y. (1987). Stochastic blockmodels for directed graphs. Journal of the American Statistical Association, 82(397), 8–19.CrossRefGoogle Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442.CrossRefGoogle ScholarPubMed
White, H. C., Boorman, S. A., & Breiger, R. L. (1976). Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology, 81(4), 730–780.CrossRefGoogle Scholar
Williamson, O. E. (1970). Corporate control and business behavior: An inquiry into the effects of organization form on enterprise behavior. Englewood Cliffs, NJ: Prentice Hall.Google Scholar