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Daniele,

I can offer one approach to this question:

When you say normalize tie strength and ask the question "under what
condition is a tie weak or strong", you are making an implicit comparison to
a null model. For example, you could normalize the w(A,B) tie by
W(A,B)_normalized = w(A,B)/(W_A * W_B)  where W_A=sum_j[w(A,j)] and
W_B=sum_j[w(j,B)] are the respective total activities of the nodes A,B and
are generalizations of degree; you would be comparing the strength of that
tie to its expected strength in a randomized network in which the activities
of each node are preserved.  Here "activity" could be directed or undirected
(as per your example: jetsetters=high activity; homebodies=low activity).

So if your question is really "How do I choose an appropriate null model to
gauge the significance of ties", then I would say it depends on which
features of the network you deem significant.  (For example, in a randomized
model with generalized degree preserved, the clustering/transitivity would
not be preserved).  Thus, if you disclude a feature from your null model you
would be marginalizing ties between individuals that might be exceptional
insomuch as they occur despite the statistical tendency to the contrary.

Dylan Walker
NYU, Stern

-----Original Message-----
Behalf Of Daniele Quercia
Sent: Thursday, June 11, 2009 1:33 PM
Subject: [SOCNET] normalizing tie strength

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Is there any way of normalizing tie strength in the literature? If one
defines tie strength between A and B as the number of times A and B have
seen each other, then tie strengths (for the whole social network) are
not comparable. To see why, consider that A and B have met four times.
Those four times entail completely different meanings in different
situations - for instance, they would reflect either an absent tie (if A
and B are jet setters and go out a lot) or a strong tie (if they are
homebodies and rarely go out). Also, if one normalizes the strength on
A->B based on A's total number of encounters, then one should choose a
threshold that differentiates strong ties from weak ties, and this begs
the question of how to choose that threshold :-)

Daniele.
http://www.cs.ucl.ac.uk/staff/d.quercia/