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Broadbent:

How about this: Any relationship between two "units," from a tension to a
friendship, can be considered a "vector."  Whatever the content (relational
modality)of the vector, its degree of control over the actions of the units
is a variable.  The value of the variable runs from highly cohesive
(sticky--allowing no agency by the units) to highly "friable"
(crumbly--allowing much agency by the units).  If we think of it this way,
we can compare networks on their degree of cohesiveness.  

Lanham:

A. Vectors have directional relationship to an origin.  What would that be
in this case or in these cases--the center is unfixed?  It is a bit like
asking where the Big Bang is located.  

B. What would be the unit(s) of magnitude and what would an origin mean in
these units?  If context dependent, why--particularly if "structural"?  

C. "Linkage" seems more productive.  Linkage as might be used in rhetoric,
law, international affairs in the same sort of way.  It seems to be more
productive from a symbolic interactionist perspective.  Semantics...but
because it has to be!

My point, as you might guess, is that there are no standard origins or
standard units nor could there be in the "social."  

Another try...probably as flawed or more so...

1. Network linkages entail bidirectional flows of information--i.e.
meaningful data movement, or event-driven responses to information between
sets of actors/actants.
  
Interpretation: Information does not flow from the moon to tribes--data
does..where it is then interpreted.  Information DOES flow from servers to
clients and sometimes back.  Client/server is a social network.  Moon/tribes
is not.  Border to citizen is a social network.  Citizen to identity is a
network. Gravity to monkey is not.  Whale to seal is.  Tree to tree (pollen)
is.  Wind to tree is not.  That is, interpretation of phenomena is not a
network unless phenomena had intended meaning.  It is intention that makes
them perspective-based--i.e. symbolic.  They are, necessarily, the subject
of interpretation.     

2. Networks are partial sets of actants/actors where elements are influenced
by information in a way that is remarkable--i.e. symbolic.  

Note: A set is any non-null group of actants where influence occurs between
actants.

Remarkable implies that it is noticed from some perspective.  

Influence is action (including development of an ontology) caused by receipt
of information (meaningful data.)  Natural forces are information iff their
source is considered an actant.   

3. "Social" networks occur where humans as actors are included in the
partial set.  Interpretation: Buoys interacting with monitoring technology
is not a social network.  Interpretation of the results and planning the
placement of the buoys is a social network.  

Note: The social entails any human involvement motivated by meaning.     

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