Hello,
when comparing clustering coefficient of networks with unequal number of nodes (I am interested in small networks with approximately 20-30 nodes), should the number of nodes be controlled for? If yes, what is the best way?
Thank you!
M.
clustering coefficient and nertwork size values have many meanings. Small world phenomena is proved by these two values. however, the same network with different number of links may have different cluster coefficinet value.
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comparison across networks of different sizes is a touchy topic ; see
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0013701
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the idea of investigating the scaling of a given quantity when randomly removing edges or nodes seems quite interesting
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Furthermore, it depends on what clustering coefficient you consider. The average clustering coefficient that averages the local clustering coefficient is different from the global clustering coefficient calculated using the triangles number. Those two cannot be compared...
In general there is no scaling. There may be a different coefficient amongst different parts of the network for various sized components but the clustering component is more like an intensive property of a graph and may not scale with size.
Tricky one. It depends on the type of network you're investigating, there are cases (especially in networks of individuals) where one would theorethically expect different levels of global clustering coefficients due to differences in network size (given the nature of the investigated relation). My advice would be to focus on the local clustering coefficients and their distributions in each network, which should give you the more detailed insight into the potential differences between networks of different sizes.
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