Gramian-Informed Framework for Edge Flow Network Analysis Against Nodal Attacks
Abstract
We study the first-order effects of nodal inputs on edge flows of network systems through controllability Gramians. We consider both discrete- and continuous-time dynamics subject to impulse and step input disturbances. To characterize their impact on network behavior, we introduce the notion of a vulnerability matrix (VM) and provide explicit Gramian-based expressions that reveal the critical role played by the interplay between network topology and dynamics. For the class of directed line networks, we particularize these closed-form expressions in terms of edge weights, input duration, and graph distance to the nodal input. Numerical simulations on directed line and random Erdős-Rényi networks show a tight correspondence between influential nodes identified with the VM and conventional time-domain performance metrics, such as ℋ2 and ℋ∞.
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BibTeX
@misc{chanekar2026gramianinformed,
title = {{Gramian-Informed Framework for Edge Flow Network Analysis Against Nodal Attacks}},
author = {Prasad Vilas Chanekar and Bala Kameshwar Poolla and Jorge Cortés},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06897},
eprint = {2609.06897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06897},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gramian-Informed Framework for Edge Flow Network Analysis Against Nodal Attacks
AU - Prasad Vilas Chanekar
AU - Bala Kameshwar Poolla
AU - Jorge Cortés
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06897
UR - https://arxiv.org/abs/2609.06897
AB - We study the first-order effects of nodal inputs on edge flows of network systems through controllability Gramians. We consider both discrete- and continuous-time dynamics subject to impulse and step input disturbances. To characterize their impact on network behavior, we introduce the notion of a vulnerability matrix (VM) and provide explicit Gramian-based expressions that reveal the critical role played by the interplay between network topology and dynamics. For the class of directed line networks, we particularize these closed-form expressions in terms of edge weights, input duration, and graph distance to the nodal input. Numerical simulations on directed line and random Erdős-Rényi networks show a tight correspondence between influential nodes identified with the VM and conventional time-domain performance metrics, such as ℋ_2 and ℋ_∞.
ER -