Dear Alfonso,

I have explored for links between brain regions and clinical data using graph theory. I have correlations with average path length and global efficiency of two different regions (but not the other measures including local efficiency, degree, clustering coefficient, cost, etc).

If I understand correctly, average path length and global efficiency are measures of centrality (from your CONN handbook).

Is the following interpretation of centrality correct: ""Centrality" describes the number of short-range connections for each node. Nodes with higher centrality contribute more to the overall efficiency of the network" (from Lv et al 2018 AJNR Am J Neuroradiol). 

Would it be safe to say that the overall brain network displays more random properties, as opposed to small world properties?

Also, could you please clarify why global efficiency is calculated as the inverse of average path length? 

Thank you,
Best,
Amy