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Dekker MM, Schram RD, Ou J, Panja D. Hidden dependence of spreading vulnerability on topological complexity. Phys Rev E 2022; 105:054301. [PMID: 35706267 DOI: 10.1103/physreve.105.054301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Accepted: 04/08/2022] [Indexed: 06/15/2023]
Abstract
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time-commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its "spreading vulnerability," is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the "entropy of temporal entanglement" as a quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological, and engineered systems.
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Affiliation(s)
- Mark M Dekker
- Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Raoul D Schram
- Information and Technology Services, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands
| | - Jiamin Ou
- Department of Sociology, Utrecht University, Padualaan 14, 3584 CH Utrecht, Netherlands
| | - Debabrata Panja
- Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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Badie-Modiri A, Rizi AK, Karsai M, Kivelä M. Directed percolation in random temporal network models with heterogeneities. Phys Rev E 2022; 105:054313. [PMID: 35706217 DOI: 10.1103/physreve.105.054313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 04/07/2022] [Indexed: 06/15/2023]
Abstract
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similarly to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and, otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low-dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limited-time reachability of temporal networks.
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Affiliation(s)
- Arash Badie-Modiri
- Department of Computer Science, School of Science, Aalto University, FI-0007, Finland
| | - Abbas K Rizi
- Department of Computer Science, School of Science, Aalto University, FI-0007, Finland
| | - Márton Karsai
- Department of Network and Data Science Central European University, 1100 Vienna, Austria
- Alfréd Rényi Institute of Mathematics, 1053 Budapest, Hungary
| | - Mikko Kivelä
- Department of Computer Science, School of Science, Aalto University, FI-0007, Finland
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Dekker MM, Blanken TF, Dablander F, Ou J, Borsboom D, Panja D. Quantifying agent impacts on contact sequences in social interactions. Sci Rep 2022; 12:3483. [PMID: 35241710 PMCID: PMC8894368 DOI: 10.1038/s41598-022-07384-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 02/10/2022] [Indexed: 01/12/2023] Open
Abstract
Human social behavior plays a crucial role in how pathogens like SARS-CoV-2 or fake news spread in a population. Social interactions determine the contact network among individuals, while spreading, requiring individual-to-individual transmission, takes place on top of the network. Studying the topological aspects of a contact network, therefore, not only has the potential of leading to valuable insights into how the behavior of individuals impacts spreading phenomena, but it may also open up possibilities for devising effective behavioral interventions. Because of the temporal nature of interactions—since the topology of the network, containing who is in contact with whom, when, for how long, and in which precise sequence, varies (rapidly) in time—analyzing them requires developing network methods and metrics that respect temporal variability, in contrast to those developed for static (i.e., time-invariant) networks. Here, by means of event mapping, we propose a method to quantify how quickly agents mingle by transforming temporal network data of agent contacts. We define a novel measure called contact sequence centrality, which quantifies the impact of an individual on the contact sequences, reflecting the individual’s behavioral potential for spreading. Comparing contact sequence centrality across agents allows for ranking the impact of agents and identifying potential ‘behavioral super-spreaders’. The method is applied to social interaction data collected at an art fair in Amsterdam. We relate the measure to the existing network metrics, both temporal and static, and find that (mostly at longer time scales) traditional metrics lose their resemblance to contact sequence centrality. Our work highlights the importance of accounting for the sequential nature of contacts when analyzing social interactions.
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Affiliation(s)
- Mark M Dekker
- Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands. .,Centre for Complex Systems Studies, Utrecht University, Minnaertgebouw, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands.
| | - Tessa F Blanken
- Department of Psychological Methods, University of Amsterdam, Nieuwe Achtergracht 129-B, 1018 VZ, Amsterdam, The Netherlands
| | - Fabian Dablander
- Department of Psychological Methods, University of Amsterdam, Nieuwe Achtergracht 129-B, 1018 VZ, Amsterdam, The Netherlands
| | - Jiamin Ou
- Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands.,Department of Sociology, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands
| | - Denny Borsboom
- Department of Psychological Methods, University of Amsterdam, Nieuwe Achtergracht 129-B, 1018 VZ, Amsterdam, The Netherlands
| | - Debabrata Panja
- Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands.,Centre for Complex Systems Studies, Utrecht University, Minnaertgebouw, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands
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Holme P. Fast and principled simulations of the SIR model on temporal networks. PLoS One 2021; 16:e0246961. [PMID: 33577564 PMCID: PMC7880429 DOI: 10.1371/journal.pone.0246961] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Accepted: 01/28/2021] [Indexed: 01/16/2023] Open
Abstract
The Susceptible-Infectious-Recovered (SIR) model is the canonical model of epidemics of infections that make people immune upon recovery. Many of the open questions in computational epidemiology concern the underlying contact structure's impact on models like the SIR model. Temporal networks constitute a theoretical framework capable of encoding structures both in the networks of who could infect whom and when these contacts happen. In this article, we discuss the detailed assumptions behind such simulations-how to make them comparable with analytically tractable formulations of the SIR model, and at the same time, as realistic as possible. We also present a highly optimized, open-source code for this purpose and discuss all steps needed to make the program as fast as possible.
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Affiliation(s)
- Petter Holme
- Tokyo Tech World Research Hub Initiative (WRHI), Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan
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