[FEAT] Cluster IDs based on node centrality

[samnlindsay]

Is your proposal related to a problem?

Related to discussion in https://github.com/moj-analytical-services/data_linking/issues/329 and #1677

Cluster IDs in splink used to be integers and are now (v3) the min ID in the cluster (e.g. dataset_a-__-0001 for the cluster containing records 0001 and 0004 from dataset_a, and several records from dataset_b and dataset_c).

This change itself is an improvement in terms of the same cluster often being assigned the same ID when re-linked in future. However, it can be misleading that a node label is used as a cluster ID, especially as that node is not necessarily representative of the cluster as a whole.

Describe the solution you'd like

Once more graph properties have been included in the cluster generation outputs, node centrality or node degree would be relatively simple metrics for defining the "central" node after which the cluster should be named.

Low threshold	Medium threshold	High threshold
Cluster ID: 1014014	Cluster ID: 1014014	Cluster ID: 1015600
Node ID (max degree): 1015600	Node ID (max degree): 1015600	Node ID (max degree): 1015600

Currently, cluster ID is subject to change as nodes are added or removed, dependent only on the alphabetical ordering of the IDs. The most central node, however, should be least susceptible to change and therefore be a more consistent basis of the cluster ID.

Describe alternatives you've considered

See discussion here - https://github.com/moj-analytical-services/data_linking/issues/329