Similarity Forces and Recurrent Components in Human Face-to-Face Interaction Networks

Marco Antonio Rodríguez Flores and Fragkiskos Papadopoulos

Phys. Rev. Lett. 121, 258301 – Published 18 December 2018

Abstract

We show that the social dynamics responsible for the formation of connected components that appear recurrently in face-to-face interaction networks find a natural explanation in the assumption that the agents of the temporal network reside in a hidden similarity space. Distances between the agents in this space act as similarity forces directing their motion towards other agents in the physical space and determining the duration of their interactions. By contrast, if such forces are ignored in the motion of the agents recurrent components do not form, although other main properties of such networks can still be reproduced.

Received 3 August 2018
Revised 1 November 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.258301

Physics Subject Headings (PhySH)

Collective behavior in networks Community structure Network formation & growth Topological tools

Networks

Authors & Affiliations

Marco Antonio Rodríguez Flores^* and Fragkiskos Papadopoulos^†

Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 33 Saripolou Street, 3036 Limassol, Cyprus and Social Computing Research Centre (SCRC), Cyprus University of Technology, 3036 Limassol, Cyprus

^*mj.rodriguezflores@edu.cut.ac.cy
^†f.papadopoulos@cut.ac.cy

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Issue

Vol. 121, Iss. 25 — 21 December 2018

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Images

Figure 1
Recurrent component patterns and distributions of contact durations and of times between consecutive contacts in three real-world data sets and in simulated networks. (a)–(c) Components found in the first activity cycle of the hospital, primary school, and high school (6, 8.6, and 5 h, respectively). (d) Components found in a simulation of the attractiveness model with the same duration as in (a). (e) Same as (d) but with the FDM (force-directed motion) model. (f),(g) Distribution of contact duration and of time between consecutive contacts in real and simulated networks. (h) Average number of recurrent components where an agent participates as a function of its total number of interactions in real and simulated networks. The blue lines in (a)–(e) correspond to recurrent components while the black lines to components appearing for the first time, i.e., to the unique components. The $x$ axis is binned into 30 min intervals, while the $y$ axis shows the component IDs observed in each bin; all components consist of at least three nodes. The simulations with the models use the parameters of the hospital (Table 1 and Supplemental Material [19], Sec. IV). In (f)–(h) the results with the models are averages over 10 simulation runs. Results for all activity cycles, the conference data set, and for the simulated counterparts of the rest of the real networks are found in Supplemental Material [19], Secs. II, III.
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Figure 2
Formation of components in the FDM. (a) Number of components formed (total and unique) in deterministic motion ( $v = 0$ ) for pairs of parameters $μ_{2}$ (bottom $x$ axis) and $F_{0}$ (top $x$ axis). (b) Same as (a) but for pairs of $F_{0}$ and $v \geq 0$ . In both (a),(b) as one parameter increases the other decreases so that the expected agent displacement per slot is always $\approx d = 1$ . The insets show the maximum and average size across all components. In both plots $N = 242$ , in (b) $μ_{2} = 1$ . See also Supplemental Material [19], Sec. IV.
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Figure 3
Average percentage of infected agents per time slot (prevalence) of the SIS model as a function of the infection probability $α$ in real and simulated networks (circles and triangles, respectively), for two recovery probabilities $β$ . In the SIS each agent can be in one of two states, susceptible or infected. At any time slot an infected agent recovers with probability $β$ and becomes susceptible again, whereas infected agents infect the susceptible agents with whom they interact, with probability $α$ . To simulate the SIS process on temporal networks we use the dynamic SIS implementation of the Network Diffusion Library [27]. See Supplemental Material [19], Sec. VII, for further details.
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Figure 4
Average Euclidean distance and number of interactions between two agents as a function of their similarity distance, in simulated counterparts of the Hospital, primary school, and high school. The inset in (a) is an enlarged view of similarity distances up to 5.
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