The Maximum Neighborhood Component (MNC) centrality quantifies the importance of a node based on the internal connectivity structure among its immediate neighbors [2].
For a given node \( i \), let its neighborhood be denoted by \( \mathcal{N}(i) \), that is, the set of nodes directly connected to \( i \).
The neighborhood \( \mathcal{N}(i) \) induces a subgraph \( G_{\mathcal{N}(i)} \) composed solely of these neighboring nodes and the edges between them. The MNC centrality \( c_{\mathrm{MNC}}(i) \) of node \( i \) is then defined as the size of the largest connected component within this induced subgraph, formally expressed as:
\[
c_{\mathrm{MNC}}(i)
= \max_{\substack{C \subseteq \mathcal{N}(i)\\ C\text{ is connected in } G_{\mathcal{N}(i)} }}|C|.
\]
Intuitively, the MNC centrality measures how well the neighbors of a node are connected to each other.
Nodes whose neighbors form a densely connected group (i.e., a large maximum connected component) receive higher MNC scores, reflecting their structural significance within the network.

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] Lin, C. Y., Chin, C. H., Wu, H. H., Chen, S. H., Ho, C. W., & Ko, M. T. (2008). Hubba: hub objects analyzer—a framework of interactome hubs identification for network biology. Nucleic acids research, 36, W438-W443. doi: 10.1093/nar/gkn257.