TY - JOUR

T1 - Detection of Influential Nodes in Network Dynamical Systems from Time Series

AU - De Lellis, Pietro

AU - Porfiri, Maurizio

N1 - Funding Information:
Manuscript received October 11, 2020; revised October 12, 2020; accepted February 3, 2021. Date of publication February 24, 2021; date of current version September 17, 2021. The work of Pietro De Lellis was supported by the Program “STAR 2018” of the Compagnia di San Paolo, Fondazione Banco di Napoli, through Project ACROSS. The work of Maurizio Porfiri was supported in part by the National Science Foundation under Grants CMMI 1561134 and CMMI 1932187 and in part by the program of the region of Murcia (Spain), “Call for Fellowships for Guest Researcher Stays at Universities and OPIS,” under Grant 21144/IV/19. Recommended by Associate Editor M. V. Salapaka. (Corresponding authors: Pietro De Lellis; Maurizio Porfiri.) Pietro De Lellis is with the Department of Information Technology and Electrical Engineering, University of Naples Federico II, 80125 Naples, Italy (e-mail: pietro.delellis@unina.it).
Publisher Copyright:
© 2014 IEEE.

PY - 2021/9

Y1 - 2021/9

N2 - Identifying influential nodes in network dynamical systems requires the manipulation of topological and dynamic characteristics within ideal experiments. However, seldom we have access to experimental settings that could afford targeted interventions or to calibrated mathematical models that could support faithful what/if analyses. Our knowledge of the network dynamical system is often limited to the time series of individual nodes in some real experiments. Using these time series, it is possible to undertake a number of inference tasks, from reconstructing the topology of the network to discovering hidden nodes. Whether time series of real experiments could help pinpoint causal influence within the network is an open question. Here, we address this question in the context of synchronization problems, where the influence of a node is defined as the extent to which adding noise at that particular node affects the overall synchronization of the entire network. For linear time-invariant dynamics and undirected topologies, we demonstrate the possibility of exactly detecting the most influential nodes in the network without a calibrated mathematical model, using only time series of a real experiment, where all nodes are plagued by noise. Beyond illustrating our results on classical and second-order consensus protocols, we consider two real-world datasets: 1) 1) firearm prevalence in the USA and 2) players' movements in a soccer game. Just as our conclusions support the emergence of influential states, which have a less stringent legal environment, they hint at the instrumental role of players, who are critical to the offense strategy of the team.

AB - Identifying influential nodes in network dynamical systems requires the manipulation of topological and dynamic characteristics within ideal experiments. However, seldom we have access to experimental settings that could afford targeted interventions or to calibrated mathematical models that could support faithful what/if analyses. Our knowledge of the network dynamical system is often limited to the time series of individual nodes in some real experiments. Using these time series, it is possible to undertake a number of inference tasks, from reconstructing the topology of the network to discovering hidden nodes. Whether time series of real experiments could help pinpoint causal influence within the network is an open question. Here, we address this question in the context of synchronization problems, where the influence of a node is defined as the extent to which adding noise at that particular node affects the overall synchronization of the entire network. For linear time-invariant dynamics and undirected topologies, we demonstrate the possibility of exactly detecting the most influential nodes in the network without a calibrated mathematical model, using only time series of a real experiment, where all nodes are plagued by noise. Beyond illustrating our results on classical and second-order consensus protocols, we consider two real-world datasets: 1) 1) firearm prevalence in the USA and 2) players' movements in a soccer game. Just as our conclusions support the emergence of influential states, which have a less stringent legal environment, they hint at the instrumental role of players, who are critical to the offense strategy of the team.

KW - Consensus

KW - stochastic systems

KW - synchronization

KW - vulnerability

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U2 - 10.1109/TCNS.2021.3061953

DO - 10.1109/TCNS.2021.3061953

M3 - Article

AN - SCOPUS:85101779220

VL - 8

SP - 1249

EP - 1260

JO - IEEE Transactions on Control of Network Systems

JF - IEEE Transactions on Control of Network Systems

SN - 2325-5870

IS - 3

ER -