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In the computer science/graph theory literature, at least, "dense"
and "sparse" are technically characteristics of families of graphs,
rather than of individual graphs: they are terms that describe how
the number of edges of a graph changes as the number of nodes increases.
As a point of departure, though, "sparse" generally means a graph
that has a number of edges (ties) that is bounded above by a constant
multiple of the number of nodes, whereas "dense" generally means a
graph that has a number of edges that is a constant multiple of the
square of the number of nodes.
Thus, for example, a graph of n nodes whose average degree was 3 or 4
would be considered sparse; a graph of n nodes with average degree n/
3 or n/4 would be considered dense.
These references might be useful:
Hope this helps.
On 13 Mar 2006, at 15:48, [log in to unmask] wrote:
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> I need to justify when you call a network dense and need a cite or
> "expert" opinion...
> I have two networks (venture capitalists, afflilation network
> linked by funding companies together although only retained the
> ties between venture capital firms, similiar to actor/movie network
> with essentially the same Log transformation of frequency of in
> degree plot shape including the slight left drop off), one
> component each. In addition the biger network has 17isolates and 4
> dyad pairs not connected to the main component (too bad was hoping
> for more components as this trashed a few hypotheses), and the
> smaller network has fewer isolates, 3 dyad pairs and one pair of 4
> not connected to the main componet.
> Removing the isolates and unconnected dyads/group of 4 here is the
> In the first one I have 277 nodes, 31,087 ties and the possible
> number of ties would be 76,452 so that dividing ties have by ties
> total I get 0.4066 for the network density.
> In the second network I have 191 nodes, 13,485 ties, 36,290
> possible ties and so get a density of 0.3716.
> The drawing of each network looks like a tightly wound ball of yarn
> without much of a periphery although the smaller network has a bit
> more periphery but still the bulk of it looks like a tight ball.
> I need to make a statement about whether these networks are dense
> or not and justify it with a reference that gives when you can call
> something dense or an expert who I can cite...
> U of ID
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