Support measures the ability of an individual to exchange favors and safely transact with others, based on a combination of network position and repeated interactions [2]. A relationship between nodes \(i\) and \(j\) is considered supported if they have at least one friend in common.
The support of node \(i\), denoted \(c_{\mathrm{sup}}(i)\), is defined as the number of neighbors that share at least one common neighbor with \(i\):
\[
c_{\mathrm{sup}}(i) = \left| \{ j \in \mathcal{N}(i) : (A^2)_{ij} > 0 \} \right|,
\]
where \(A\) is the adjacency matrix of the network and \(\mathcal{N}(i)\) is the set of neighbors of node \(i\). The support measure captures the extent to which a node’s relationships are reinforced through shared connections, reflecting trust and reliability in 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] Jackson, M. O. (2020). A typology of social capital and associated network measures. Social choice and welfare, 54(2), 311-336. doi: 10.1007/s00355-019-01189-3.