CoreHD is a heuristic algorithm for network decycling and dismantling, designed to identify a minimal set of nodes whose removal either eliminates all cycles or breaks the network into small disconnected components [2]. The algorithm generates a sequence of node removals that reflects the importance of each node in sustaining network connectivity. CoreHD operates as follows:


  1. Extract the 2-core of the network, consisting of nodes with degree at least 2.

  2. Remove the highest-degree node within the 2-core.

  3. Recompute the 2-core after removal. If the 2-core becomes empty, perform tree-breaking by removing the node whose removal causes the largest decrease in the size of the largest connected component.

  4. Repeat the above steps until the network is either acyclic or sufficiently fragmented.


By focusing on the 2-core, CoreHD avoids removing peripheral nodes that do not contribute to cycles, thereby achieving near-optimal decycling and dismantling performance. The CoreHD approach has been shown to be effective for enhancing network robustness against failures and attacks.

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Zdeborová, L., Zhang, P., & Zhou, H. J. (2016). Fast and simple decycling and dismantling of networks. Scientific reports, 6(1), 37954. doi: 10.1038/srep37954.