Talk:Clustering coefficient

message: If you consider a network with overlapping community structure, then there will be many triangles and hence a reasonably high clustering coefficient. But I suspect many people take 'clustering' to imply a non-overlapping partitioning. A more extreme example is a ring lattice - a ring lattice has high clustering coefficient, but it doesn't have anything that can be reasonably called community structure (overlapping or otherwise).
Is it possible to concisely clear this up at the top of the article?  Aaron McDaid (talk - contribs)  10:47, 16 July 2011 (UTC)
replies: text: I agree that it is often overlooked that a network with a high clustering coefficient might have no clusters in it. On the other hand, a network with many clusters, even one that consists entirely of network clusters, could have a low clustering coefficient.  Consider a large, undirected graph, say with hundreds of billions of nodes.  Consider that every node belongs to one hundred cliques (i.e., complete subgraphs) of size eleven that are randomly selected.  Thus all edges in the graph are embedded in a clique of size eleven.  Yet the clustering coefficient will be pretty low. To see this, imagine the egocentric neighborhood of any given node.  Each node is connected to ten cliques of ten, so (ignoring the small chance that any of those ten cliques shares members) there is the potential for 500k edges between the alters of any ego, however, only 4500 of these connections actually exist.  This example also illustrates the clustering coefficients of graphs with different sizes should not be compared without some kind of suitable normalization (I'm not aware of one).--Conradl (talk) 23:14, 14 September 2011 (UTC)
thread_title:  'clustering coefficient' has little to do with 'clustering' 

message: The article claims that these are two separate concepts, but the definitions seem to be identical. What am I missing?
Also: why is it called a transitivity ratio?  — Preceding unsigned comment added by 84.94.180.144 (talk) 15:30, 13 March 2014 (UTC)
replies: text: Let T = the number of triangles, P = the number of two-edge paths, and C = the number of connected triples of vertices. Then , because a connected triple that is not a triangle contributes one to the P term while a triangle contributes 3 to the P term and −2 from the other term, so that its contribution is also one. My understanding is that the transitivity ratio is 3T/P and that the clustering coefficient is T/C. So they both give the same information (one is a function of the other) but have different values. But this is not clearly explained in the article and the formula in the transitivity ratio says it is equal to two different things. As for why: because transitivity (a friend of a friend is automatically a friend) would imply that , and the transitivity ratio measures how close this is to being true. —David Eppstein (talk) 16:04, 13 March 2014 (UTC)
replies: text: Thanks! That cleared it up. I think I'll try to incorporate all that into the article, as long as I'm here.  — Preceding unsigned comment added by 84.94.180.144 (talk) 20:40, 16 March 2014 (UTC)

text: This has me confused. Among the sources i've found that are careful with their definitions, most define the (global) clustering coefficient as 3T/P, while the rest call this the transitivity ratio and define the (global) clustering coefficient as the mean local clustering coefficient. I have not been able to find a source that defines anything as T/C, though some sources (e.g. ) use phrases like "connected triples" but make it clear from examples or further exposition that the calculation they're performing is 3T/P. If anyone has a source for the T/C definition, i would love to see it! In the meantime (as written, though perhaps even if it were written more clearly) i worry that the distinction causes more confusion than clarity. 155.37.131.50 (talk) 21:17, 4 June 2014 (UTC)

text: Thanks, Tore. However, another source of confusion for me is the Luce–Perry citation. Can you say where in their paper they attempt to compute or describe (using their terms) the proportion of symmetric 3-chains in a matrix that are redundant? I have read through it and have not found such a comment, so i don't understand why the paper is being cited. 155.37.131.50 (talk) 19:10, 7 September 2014 (UTC)
thread_title:  Global clustering coefficient vs. Transitivity ratio 

message: I think it would be worth having a section about algorithms to generate clustered networks.
If there's agreement: I'd go ahead with the standard small-worlds network algorithm and also the random clustered graphs introduced (separately) by Miller and Newman.  Since I'm "Miller", I want to be careful not to be biased on this, so seeking feedback before I do any such changes.  If no-one has comments on this, I may go ahead and do the changes (eventually).
I'd be interested in including other algorithms as well. Please give suggestions.  Joelmiller (talk) 02:39, 19 March 2015 (UTC)
thread_title:  Algorithms to generate clustered networks