Centrality Score: Understanding average clustering

Hi there,
I use squidpy to analyse Chip cytometry data. I have some issues with understanding the average clustering coefficient…
After running sq.gr.centrality_scores() and plotting the centrality scores via sq.pl.centrality_scores() one also gets an overview of the average clustering (please view the graphs at the very end of this tutorial: Analyze Imaging Mass Cytometry data — Squidpy main documentation).
I now have some problems understanding the average clustering graph. It seems to me that populations that form more uniform clusters get a lower average clustering value… If someone could briefly explain the average clustering coefficient and how it is interpreted I would be really happy.
Thanks a lot!

Hi @Nicolas

The average clustering coefficient for a Graph G is the average of all clustering coefficients for each node n in G.

So first the clustering coefficients of each node are calculated as seen here and then the average clustering coefficient across all clustering coefficients is computed as shown here.

If the average clustering coefficient of a graph is low, that means the clustering coefficients of the nodes are low on average, which is related to the amount of triangles and degree of the nodes. E.g. if the node has a high degree (many edges connecting to this node), but only few triangles (a triangle is a graph with 3 nodes and 3 edges in the form of a triangle, so “few triangles” mean that the node is only part of few triangles), then the clustering coefficient will be low.

Regarding interpretation, I’m not sure exactly since I don’t know the data, but a low average clustering coefficient should mean that most nodes aren’t really clustering together (will update if I have a better interpretation).