Re: [networkx-discuss] Assortativity in metabolic networks

[Chris Myers]

Sanjan,

A couple thoughts about your question:

(1) The complete description (more or less) of a metabolic network is as a bipartite graph connecting two types of nodes: reactions and metabolities. What you have described is one particular choice for condensing that bipartite graph to a unipartite one (reaction ids as nodes and edges in case two reactions share a common metabolite). There are other choices you could have made, e.g., metabolites as nodes that are connected by an edge if they are connected to the same reaction; for example, Huss and Holme 2007 use this latter reduction: "reactant-product pairs were written to an edge-list specifying the connections between the substances". Different reductions of the bipartite graph might yield different graph statistics such as assortativity by degree, and I don't know if there might be useful analyses of the full bipartite graph that would clarify how different reductions impact the graph structure.

(2) The statement that "for biological values r value is expected to be negative" is of course very broad, and it is difficult to imagine that it would hold for all biological networks that one could construct, given the diversity of associations that get captured in different types of networks. I know that Newman 2002 (assortative mixing in networks) makes the claim that "technological and biological networks tend to be disassortative", but that was based on an examination of 3 biological networks. Perhaps others have examined this question in more detail since then; a quick look shows that Piraveenan et al. 2010 quote positive r for metabolic networks, but since they provide no apparent description of how they constructed their networks, it is difficult to know what to do with such claims. (And, for what it's worth, I showed in my 2003 paper on software systems as complex networks that Newman's speculation about technological networks is not entirely correct, since -- for the case of directed software graphs -- the sign of the assortativity by degree depends on whether considers an undirected version of the graph or the actual directed graph, in which case there are 4 separate assortativity coefficients to measure.)

Hope this helps,
Chris



On Feb 16, 2013, at 9:42 AM, Sanjan Tp wrote:

>
> I computed the Pearson correlation coefficient for metabolic networks(which I have modelled as reaction graph i.e reaction ids as nodes and edges in case two reactions share a common metabolite; datasets have been taken from KEGG pathway database). Here's the snippet
> h=nx.Graph(g) #converting the graph to undirected
> r=nx.degree_assortativity_coefficient(h)
> print r
>
> Surprisingly the r values are coming positive and in the range of 0.59 to 0.71 for different organisms whereas for biological networks r value is expected to be negative.Various other analysis that I performed for the same networks viz. centrality measurements,clustering analysis are consistent with those found in literature. I would like to have some hints or directions for troubleshooting.
>
> Thanks.
>
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