On 23.03.2017 11:16, yerali wrote:
My problem with the SBM is that the maximization of internal density is not a desired condition for the separation into blocks. The pattern is very clear in the partition of my figure (without degree correlation), where the nodes of the same colors are connected with the other colors in an equivalent way, but far from being a community.
That is because this is the most significant mixing pattern present in the data. One of the most central features of the SBM is that it admits _any_ mixing pattern, not only assortative ones. For example, it works beautifully well on networks with bipartite or multipartite structures. However, if the network does possess assortative structures, the method _will_ find them. I'd recommend taking a closer look into the SBM literature.
For example, in causality-based networks to know the set of vertex where some flow can be trapped makes sense. The same applies in the case of information flow.
And if these assortative modules exist, they will be picked up by the SBM as well. But see my point below.
I think the network in my figure can be suitably partitioned into communities without being simply noise.
And how do you make this assessment? If you randomize your network, while keeping the degree sequence intact, you will still be able to partition it into communities (that also trap random walks, has high modularity, etc). The point is that this structure is the result of mere statistical fluctuations, not meaningful properties of the generative mechanism behind the network. It is _very_ easy to find structure in random networks. You have to be careful. I recommend taking the SBM result seriously.
Maybe this is a good example for the affirmation of that there is not (yet) a perfect method to detect communities in all kinds of networks. In this sense, I would rather think in the direction of that a partitioning has not a unique and “right” solution.
This is besides my point. Although I agree that there is more than one unique way to represent a network (with the SBM being only one of them), methods that do not distinguish structure from noise result in spurious results, and should be avoided. Best, Tiago -- Tiago de Paula Peixoto <tiago@skewed.de>