Brief encounter networks

1 Brief encounter networks Vassilis Kostakos,* Eamonn O’Neill,* Alan Penn+ * Department of Computer Science, University of Bath, Bath BA2 7AY, UK. (email {vk,eamonn}@cs.bath.ac.uk) + The Bartlett, University College London, UK, WC1E 6BT (email a.penn@ucl.ac.uk) Many complex human and natural phenomena can usefully be represented as networks describing the relationships between individuals1,2,3,4. While these relationships are typically intermittent, previous research has used network representations that aggregate the relationships at discrete intervals5. However, such an aggregation discards important temporal information, thus inhibiting our understanding of the network’s dynamic behaviour and evolution. We have recorded patterns of human urban encounter using Bluetooth technology (Figure 1) thus retaining the temporal properties of this network. Here we show how this temporal information influences the structural properties of the network. We show that the temporal properties of human urban encounter are scale-free, leading to an overwhelming proportion of brief encounters between individuals. While previous research has shown preferential attachment to result in scale-free connectivity in aggregated network data11, we found that scale-free connectivity results from the temporal properties of the network. In addition, we show that brief encounters act as weak social ties6,7 in the diffusion of non-expiring information, yet persistent encounters provide the means for sustaining time- expiring information through a network. Our earlier work indicates that about 7.5% of observed pedestrians carry discoverable Bluetooth devices in the city of Bath8, giving us an approximation of the proportion of the public our technique captures. In Table 1 we list the structural properties of our observation data (Bath), as well as four distinct subsets. The networks exhibit small average paths ! and high clustering coefficients C, indicative of small-world networks9. Furthermore, the Pareto distribution10 of degree P(k) across the whole dataset follows an approximate power law with "!1 ! 1.5 (Figure 2a), which is characteristic of scale-free networks11. Finally, clustering in our dataset follows the approximate relationship C(k) ! 1/k (Figure 2b), which suggests an underlying modularisation of our data12,13. The structural properties of the sub-networks tell a story which intuitively makes sense. For instance we observe the highest C and smallest ! in the office rather than the street. Correspondingly, we would expect an office environment to be much more clustered than, say, the street. Furthermore, we see that the street network has the lowest density, while the campus network, being of much smaller size than the street network, has double the number of edges. Although an examination of the structural properties of encounter networks can provide interesting insights, an aggregated network representation discards valuable temporal information. Techniques have been developed to describe the dynamics of complex networks such as the Brazilian soccer network2, online dating networks3 and student affiliation networks4. However, such work typically relies on the analysis of a limited number of discrete snapshots of the complex networks.5 Our data, on the other hand, 2 consists of a chain of events that allows for a minute-by-minute evolving description of the network as people move into and out of contact with each other and our scanners (Figure 1). Here we explore the temporal properties of our network by focusing on three key aspects: presence and frequency of nodes, presence and frequency of links, and temporal order of events. While in Figure 1c all nodes are visible, in fact they were available sporadically, and only when the corresponding individuals were at a scanning location. We call this availability node presence (np), calculated as the total amount of time an individual spent near one of our scanners during the study. In Figure 3a (black solid line) we see that np follows a power law with "!1 ! 0.9. Thus, whilst most individuals were seen only for a few seconds, others accumulated a presence of more than a month during their visits near our scanners. A further temporal aspect, node frequency (nf), describes the number of distinct instances a person came near a scanner. In Figure 3b we see that nf follows a power law with "!1 ! 1.6. Thus, most individuals were seen only once, while others were seen on more than a thousand occasions. Finally, we observed that np and nf are not correlated. When considering human encounters, node availability is a prerequisite for establishing links: a person gains links by being near a scanner and “waiting” for others to show up. Additionally, this attachment is not driven by degree k: an individual is attached to all other co-present individuals, regardless of their k (as described in Figure 1b).

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