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. 2016 Sep 19;94(3):032313. doi: 10.1103/PhysRevE.94.032313

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Published by the American Physical Society

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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FIG. 2. — Comparison of the first steps of $k$ -core percolation and the WTM for the karate club graph [40]. Left: $k$ -core percolation with $k = 4$ . Top: the original network. Middle: the first step of $k$ -core percolation. Bottom: the second step. Right: The WTM. Top: thresholds of $d_{u} - 4 + 1$ . Middle: nodes with thresholds $r_{u} \leq 0$ are activated. Bottom: the second step. At each step, the activated nodes of the WTM are exactly the deleted nodes in $k$ -core percolation.