hello,
i want to know about the relationship between average clustering coefficient of the graph and community detection. can we say that average clustering of the graph reflects the community structure of it?
To some extent, the average clustering coefficient of a graph does represent the community structure of the graph but how useful it is will depend on your application. The clustering coefficient of a vertex is a very local property, measuring the "completeness" of its neighborhood. When you average that over all vertices, it is a very global combination of very local information. If you're broadly looking for small dense communities, this might be a good approach. If you're looking for mid-sized communities in a large graph, where the communities may be spread out, it may not help much.
Nice question! I'd be interested to see what others have to say on this topic, even if it contradicts what I said. :-)
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