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I'm afraid I have no bibliographical suggestions to offer you because
I've never seen published anything like what you're requesting (at
least in the graph theory and math-sociological social networks
literature). However, I take the liberty to describe to you some
related formal ideas along which I'm working this period hoping that
they might somehow touch your problem too.
My starting point is the remark that Mark Newman's assortativity
coefficient is solely an edge-count-based measure, i.e., a measure
which solely depends on the count of edges connecting nodes over which
certain characteristics are distributed. For instance, if you have two
networks both with the same number of edges (although with different
number of nodes) that exhibit exactly the same number of nodal
characteristics such that you have the same count of edges inside and
among groups formed by the characteristics in both networks, then
these two networks share a common assortativity coefficient. This is
the case even if one of them is just composed of disconnected dyads.
For instance, the first network might be a triangle with two blue
nodes and one red node, while the second might be composed of three
dyads (not linked to each other), one dyad between two blue nodes and
two dyads between a blue and a red node.
This is why I was thinking that an alternative formal construction
measuring mixing patterns would be to consider a sort of a path-based
assortativity coefficient, because in principle (connected) n-paths
(where n > 1) might weld together more tightly different groups in a
network than what would do sheer edges, which are just 1-paths. Notice
that since strings of such paths might cross the contact layers (the
interface) among groups they would contain two kinds of substrings.
The first kind is just (heterogeneous) interfacial
contact-layer-crossing edges (among different groups) and the second
is (homogeneous) connected strings inside each group. The difference
now is that interfacial edges could be connected to intra-group
strings, while in Mark's assortativity computation this might not be
the case. This means that an appropriate measure of path-based
assortativity coefficient (and mixing as well) might be more
illustrative (in certain cases) than the standard measure of
edge-based assortativity, although undoubtedly Mark's definition of
the latter is quite simple and it can be easily implemented in all
sorts of mixed networks to give a direct assessment of how (well)
groups are intermingled in mixed networks.
Unfortunately the previous is just my current work on progress and I
have not yet completed anything that I could share with you in case
you find it relevant and interesting to your investigations.
Department of Mathematics
University of Patras, Greece
On Sat, Mar 9, 2013 at 4:50 AM, Yong Min <[log in to unmask]> wrote:
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> Deaer all,
> In our recent paper:
> we find even with the same community modularity (the metric from Mark
> Newman's works), the network could display different mixing styles of
> communities, and lead to a different capacity in spreading pathogens or
> I want to extend the result to find out a new community metric, which
> could include the influence of mixing styles of communites.
> I would appreciate if you could provide some references about the topic?
> I found I cannot find closely relative paper about the topic, but I
> think there must be some previous works about the topic.
> I also want to discuss with anyone about the scientific value of the topic?
> Thank you very much!
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