Contact Patterns in a High School: A Comparison between Data Collected Using Wearable Sensors, Contact Diaries and Friendship Surveys

Abstract

Given their importance in shaping social networks and determining how information or transmissible diseases propagate in a population, interactions between individuals are the subject of many data collection efforts. To this aim, different methods are commonly used, ranging from diaries and surveys to decentralised infrastructures based on wearable sensors. These methods have each advantages and limitations but are rarely compared in a given setting. Moreover, as surveys targeting friendship relations might suffer less from memory biases than contact diaries, it is interesting to explore how actual contact patterns occurring in day-to-day life compare with friendship relations and with online social links. Here we make progresses in these directions by leveraging data collected in a French high school and concerning (i) face-to-face contacts measured by two concurrent methods, namely wearable sensors and contact diaries, (ii) self-reported friendship surveys, and (iii) online social links. We compare the resulting data sets and find that most short contacts are not reported in diaries while long contacts have a large reporting probability, and that the durations of contacts tend to be overestimated in the diaries. Moreover, measured contacts corresponding to reported friendship can have durations of any length but all long contacts do correspond to a reported friendship. On the contrary, online links that are not also reported in the friendship survey correspond to short face-to-face contacts, highlighting the difference of nature between reported friendships and online links. Diaries and surveys suffer moreover from a low sampling rate, as many students did not fill them, showing that the sensor-based platform had a higher acceptability. We also show that, despite the biases of diaries and surveys, the overall structure of the contact network, as quantified by the mixing patterns between classes, is correctly captured by both networks of self-reported contacts and of friendships, and we investigate the correlations between the number of neighbors of individuals in the three networks. Overall, diaries and surveys tend to yield a correct picture of the global structural organization of the contact network, albeit with much less links, and give access to a sort of backbone of the contact network corresponding to the strongest links, i.e., the contacts of longest cumulative durations.

Fig 1. Facebook local networks.

The local Facebook friendship networks provided by students A and B are shown in black. In particular, we know that i and j are friends on Facebook but not j and k, as i and j are both friends of A and j and k are both friends of B. On the other hand, we do not know if i and k are friends or not: the red dashed line represents the lack of knowledge about the potential existence of this relationship.

Fig 2. Venn diagrams representing the sets of students concerned by the various data collection efforts.

Fig 3. Contact matrices of link densities.

We compare here the contact matrices of link densities built from (a) the network of contacts obtained using the sensor data collected on Dec. 5^th and (b) the network of contacts as reported in the contact diaries. We discarded here the data corresponding to the MP*1, PC* and PSI* classes as too few students from these classes filled in a contact diary (2 for MP*1, 0 for PC* and PSI*). The similarity between these two matrices is of 97%.

Fig 4. Sensors vs. contact diaries: distributions of cumulative durations registered by the sensors.

(a) Cumulative distributions of the aggregate durations of contacts registered by the sensors for (i) all 488 links between the 109 nodes belonging to both networks; (ii) the 202 links that were also reported in the diaries; (iii) the 286 links that were not reported in the diaries. (b) Cumulative distribution of aggregate durations of contacts registered by the sensors for the different categories of links reported in the diaries.

Fig 5. Contact and friendship networks.

The three layers of the multiplex are shown using exactly the same layout: each node is placed at the same position in the three panels. The color of each node represents its class and size represents its degree in the corresponding network (here we consider a symmetrized version of the network of reported friendships). * Strictly speaking, the Facebook data do not provide a network as we do not have information about the presence or absence of a link between many pairs of nodes (see Fig 1). Figure created using the Gephi software http://www.gephi.org.

Fig 6. Comparison of the networks of contacts and friendships.

(a) Shortest path length distributions for both networks; (b) Distributions of aggregate durations, as measured by the sensors, for different kinds of links in the contact network: (i) all links, (ii) links i − j for which only one of i or j reported a friendship with the other, (iii) links for which both students reported the friendship, and (iv) links for which no friendship was reported; (c) and (d): Contact matrices of link densities. We compare here the contact matrices of link densities built from (c) the global aggregated network of contacts obtained using the sensor data and (d) the symmetrized network of reported friendships. The similarity between these two matrices is ≈ 95%.

Fig 7. Fraction of friendship and contact links as a function of the number of features shared by two students.

Fig 8. Contact vs. Facebook links.

a) Distribution of aggregate durations for the different sets of links. b) Fractions of pairs of students belonging to specific groups (no link, link in both the contact network and Facebook, link in only one of the two) as a function of the number of common features.

Fig 9. Multiplex Analysis.

(a) Conditional probability to find a link in one layer (row index) given its existence in another one (column index); “C” stands for contact network, “FS” for friendship survey, “FB” for Facebook; (b) Distribution of aggregate durations in the contact network for different sets of links.