Skip to main content Accessibility help
Hostname: page-component-79b67bcb76-bntjx Total loading time: 0.305 Render date: 2021-05-16T08:40:09.659Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Impact of degree truncation on the spread of a contagious process on networks

Published online by Cambridge University Press:  30 October 2017

Department of Global Health and Population, Harvard T.H. Chan School of Public Health, 655 Huntington Ave, Boston, MA 02115, USA (e-mail:
Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Avenue, Boston, MA 02115, USA (e-mail:
Rights & Permissions[Opens in a new window]


Understanding how person-to-person contagious processes spread through a population requires accurate information on connections between population members. However, such connectivity data, when collected via interview, is often incomplete due to partial recall, respondent fatigue, or study design, e.g. fixed choice designs (FCD) truncate out-degree by limiting the number of contacts each respondent can report. Research has shown how FCD affects network properties, but its implications for predicted speed and size of spreading processes remain largely unexplored. To study the impact of degree truncation on predictions of spreading process outcomes, we generated collections of synthetic networks containing specific properties (degree distribution, degree-assortativity, clustering), and used empirical social network data from 75 villages in Karnataka, India. We simulated FCD using various truncation thresholds and ran a susceptible-infectious-recovered (SIR) process on each network. We found that spreading processes on truncated networks resulted in slower and smaller epidemics, with a sudden decrease in prediction accuracy at a level of truncation that varied by network type. Our results have implications beyond FCD to truncation due to any limited sampling from a larger network. We conclude that knowledge of network structure is important for understanding the accuracy of predictions of process spread on degree truncated networks.

Research Article
Copyright © Cambridge University Press 2017 


Badham, J., & Stocker, R. (2010). The impact of network clustering and assortativity on epidemic behaviour. Theoretical Population Biology, 77 (1), 7175.CrossRefGoogle ScholarPubMed
Banerjee, A., Chandrasekhar, A. G., Duflo, E., & Jackson, M. O. (2013a). The diffusion of microfinance. (V9). Retrieved from Scholar
Banerjee, A., Chandrasekhar, A. G., Duflo, E., & Jackson, M. O. (2013b). The diffusion of microfinance. Science, 341 (6144), 1236498.CrossRefGoogle ScholarPubMed
Barrat, A., Barthelemy, M., & Vespignani, A. (2008). Dynamical processes on complex networks. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Blondel, V. D., Decuyper, A., & Krings, G. (2015). A survey of results on mobile phone datasets analysis. EPJ Data Science, 4 (1), 10.CrossRefGoogle Scholar
Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008 (10), P10008.CrossRefGoogle Scholar
Boguñá, M., Pastor-Satorras, R., & Vespignani, A. (2003). Absence of epidemic threshold in scale-free networks with degree correlations. [Research Support, Non-U.S. Gov't]. Physical Review Letters, 90 (2), 028701.CrossRefGoogle Scholar
Burt, R. S. (1984). Network items and the general social survey. Social Networks, 6 (4), 293339.CrossRefGoogle Scholar
Burt, R. S. (2004). Structural holes and good ideas1. American Journal of Sociology, 110 (2), 349399.CrossRefGoogle Scholar
Campbell, K. E., & Lee, B. A. (1991). Name generators in surveys of personal networks. Social Networks, 13 (3), 203221.CrossRefGoogle Scholar
Eames, K. T. (2008). Modelling disease spread through random and regular contacts in clustered populations. Theoretical Population Biology, 73 (1), 104111.CrossRefGoogle ScholarPubMed
Ebbes, P., Huang, Z., & Rangaswamy, A. (2015). Sampling designs for recovering local and global characteristics of social networks. International Journal of Research in Marketing, 33 (3), 578599.CrossRefGoogle Scholar
Fernholz, D., & Ramachandran, V. (2007). The diameter of sparse random graphs. Random Structures & Algorithms, 31 (4), 482516.CrossRefGoogle Scholar
Fortunato, S. (2010). Community detection in graphs. Physics Reports, 486 (3), 75174.CrossRefGoogle Scholar
Frank, O. (2011). Survey sampling in networks. In Scott, J. & Carrington, P. J. (Eds.), The SAGE Handbook of Social Network Analysis, (pp. 389403). London: SAGE Publications.Google Scholar
Goyal, R., Blitzstein, J., & de Gruttola, V. (2014). Sampling networks from their posterior predictive distribution. Network Science, 2 (01), 107131.CrossRefGoogle ScholarPubMed
Granovetter, M. (1976). Network sampling: Some first steps. American Journal of Sociology, 81 (6), 12871303.CrossRefGoogle Scholar
Granovetter, M. S. (1973). The strength of weak ties. American Journal of Sociology, 78 (6), 13601380.CrossRefGoogle Scholar
Gupta, S., Anderson, R. M., & May, R. M. (1989). Networks of sexual contacts: Implications for the pattern of spread of HIV. AIDS, 3 (12), 807818.CrossRefGoogle ScholarPubMed
Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM review, 42 (4), 599653.CrossRefGoogle Scholar
Holland, P. W., & Leinhardt, S. (1973). The structural implications of measurement error in sociometry. Journal of Mathematical Sociology, 3 (1), 85111.CrossRefGoogle Scholar
Jenness, S., Goodreau, S. M., & Morris, M. (2015). EpiModel: Mathematical Modeling of Infectious Disease. R package version 1.2.1. Retrieved from Scholar
Keeling, M. (2005). The implications of network structure for epidemic dynamics. Theoretical Population Biology, 67 (1), 18.CrossRefGoogle ScholarPubMed
Keeling, M. J., & Eames, K. T. (2005). Networks and epidemic models. Journal of The Royal Society Interface, 2 (4), 295307.CrossRefGoogle ScholarPubMed
Kogovsek, T., Mrzel, M., & Hlebec, V. (2010). “Please name the first two people you would ask for help”: The effect of limitation of the number of alters on network composition. Advances in Methodology & Statistics/Metodoloski zvezki, 7 (2), 95106.Google Scholar
Kossinets, G. (2006). Effects of missing data in social networks. Social networks, 28 (3), 247268.CrossRefGoogle Scholar
Krings, G., Karsai, M., Bernhardsson, S., Blondel, V. D., & Saramäki, J. (2012). Effects of time window size and placement on the structure of an aggregated communication network. EPJ Data Science, 1 (4), 116.CrossRefGoogle Scholar
Lee, S. H., Kim, P.-J., & Jeong, H. (2006). Statistical properties of sampled networks. Physical Review E, 73 (1), 016102.CrossRefGoogle ScholarPubMed
Louch, H. (2000). Personal network integration: Transitivity and homophily in strong-tie relations. Social Networks, 22 (1), 4564.CrossRefGoogle Scholar
Lusher, D., Koskinen, J., & Robins, G. (2012). Exponential random graph models for social networks: Theory, methods, and applications. New York: Cambridge University Press.CrossRefGoogle Scholar
Marsden, P. V. (1987). Core discussion networks of Americans. American Sociological Review, 122–131.CrossRefGoogle Scholar
Marsden, P. V. (2005). Recent developments in network measurement. In Carrington, P. J., Scott, J., & Wasserman, S. (Eds.), Models and methods in social network analysis (pp. 830). New York: Cambridge University Press.CrossRefGoogle Scholar
McCarty, C., Killworth, P. D., & Rennell, J. (2007). Impact of methods for reducing respondent burden on personal network structural measures. Social Networks, 29 (2), 300315.CrossRefGoogle Scholar
Miller, J. C. (2009). Spread of infectious disease through clustered populations. Journal of The Royal Society Interface, 6 (41), 11211134.CrossRefGoogle ScholarPubMed
Molina, C., & Stone, L. (2012). Modelling the spread of diseases in clustered networks. Journal of Theoretical Biology, 315, 110118.CrossRefGoogle ScholarPubMed
Molloy, M., & Reed, B. A. (1995). A critical point for random graphs with a given degree sequence. Random Structures and Algorithms, 6 (2/3), 161180.CrossRefGoogle Scholar
Moore, C., & Newman, M. E. J. (2000). Epidemics and percolation in small-world networks. Physical Review E, 61 (5), 5678.CrossRefGoogle ScholarPubMed
Newman, M. E. J. (2002). Spread of epidemic disease on networks. Physical Review E, 66 (1), 016128.CrossRefGoogle ScholarPubMed
Newman, M. E. J. (2003a). Mixing patterns in networks. Physical Review E, 67 (2), 026126.CrossRefGoogle ScholarPubMed
Newman, M. E. J. (2003b). Properties of highly clustered networks. Physical Review E, 68 (2), 026121.CrossRefGoogle ScholarPubMed
Newman, M. E. J. (2010). Networks: An introduction. Oxford: Oxford University Press.CrossRefGoogle Scholar
Onnela, J.-P., & Christakis, N. A. (2012). Spreading paths in partially observed social networks. Physical Review E, 85 (3), 036106.CrossRefGoogle ScholarPubMed
Onnela, J.-P., Saramäki, J., Hyvönen, J., Szabó, G., De Menezes, M. A., Kaski, K.,. . . Kertész, J. (2007a). Analysis of a large-scale weighted network of one-to-one human communication. New Journal of Physics, 9 (6), 179.CrossRefGoogle Scholar
Onnela, J.-P., Saramäki, J., Hyvönen, J., Szabó, G., Lazer, D., Kaski, K.,. . . Barabási, A.-L. (2007b). Structure and tie strengths in mobile communication networks. Proceedings of the National Academy of Sciences, 104 (18), 73327336.CrossRefGoogle ScholarPubMed
Pastor-Satorras, R., & Vespignani, A. (2002). Immunization of complex networks. Physical Review E, 65 (3), 036104.CrossRefGoogle ScholarPubMed
Pastor-Satorras, R., Castellano, C., Van Mieghem, P., & Vespignani, A. (2015). Epidemic processes in complex networks. Reviews of Modern Physics, 87 (3), 925979.CrossRefGoogle Scholar
Porter, M. A., Onnela, J.-P., & Mucha, P. J. (2009). Communities in networks. Notices of the AMS, 56 (9), 10821097.Google Scholar
Reid, F., & Hurley, N. (2011). Diffusion in networks with overlapping community structure. 2011 IEEE 11th International Conference on, Paper presented at the Data Mining Workshops (ICDMW),.CrossRefGoogle Scholar
Salathé, M., & Jones, J. H. (2010). Dynamics and control of diseases in networks with community structure. PLoS Computational Biology, 6 (4), e1000736.CrossRefGoogle ScholarPubMed
Staples, P. C., Ogburn, E. L., & Onnela, J.-P. (2015). Incorporating contact network structure in cluster randomized trials. Scientific Reports, 5, 17581.CrossRefGoogle ScholarPubMed
Vázquez, A., & Moreno, Y. (2003). Resilience to damage of graphs with degree correlations. Physical Review E, 67 (1), 015101.CrossRefGoogle ScholarPubMed
Volz, E. M., Miller, J. C., Galvani, A., & Meyers, L. A. (2011). Effects of heterogeneous and clustered contact patterns on infectious disease dynamics. PLoS Computational Biology, 7 (6), e1002042.CrossRefGoogle ScholarPubMed
Vynnycky, E., & White, R. (2010). An introduction to infectious disease modelling. New York: Oxford University Press.Google Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’networks. Nature, 393 (6684), 440442.CrossRefGoogle Scholar
Supplementary material: PDF

Harling and Onnela supplementary material

Harling and Onnela supplementary material 1

Download Harling and Onnela supplementary material(PDF)
You have Access

Send article to Kindle

To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Impact of degree truncation on the spread of a contagious process on networks
Available formats

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Impact of degree truncation on the spread of a contagious process on networks
Available formats

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Impact of degree truncation on the spread of a contagious process on networks
Available formats

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *