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NETWORKS > EGO NETWORKS > STRUCTURAL HOLES


PURPOSE Compute measures of structural holes.

 
DESCRIPTION Compute several measures of structural holes, including all of the measures developed by Ron Burt. The measures are computed for all nodes in the network, treating each one in turn as ego. There are two options the first is to treat each actor as an ego and consider the ego network as if the rest of the network did not exist so that ties beyond alters have no effect. Hence we only consider alter-alter ties as originally suggested by Burt.  The second method is to look at all of the alters connections in the network whether they are tied to ego or not. The former is called the ego network model the latter is the whole network model. 

PARAMETERS 
Input dataset: 
Name of file containing network to analyze. Data type: Directed Graph.

Method
Choices are:
Ego network model -- ties beyond egonet have no effect consideration is only given to alter ties with other alters.
Whole network model -- includes alter ties outside of egonet in caculating the measures account is taken of all of alters ties whether they are connected to ego or not.

Undefined values (Default =na)
What value to use for any undefined measure, the default is to report these as missing values but the user can select others such as zero.

Ouput dyadic redundancy (Default=<inputfilename>-DR)
Name of actor-by-actor matrix that indicates the extent to which the column actor (an alter) is a redundant contact for the row actor (ego). 

Ouput dyadic constraint (Default=<inputfilename>-DC)
Name of actor-by-actor matrix that indicates the extent to which the row actor (ego) is constrained by each other actor in its ego network.

Node level measures: (Default=<inputfilename>-SH)
Name of actor-by-variable matrix to hold structural hole measures.

How to define ego net
Radio buttons so that selected alters can either be just out going ties from ego, in comming ties to ego or both which would mean all ties.


LOGFILE 
Three tables are output. First is the set of monadic (nodal) structural hole measures based on redundancy and constraint. The following measures are displayed:

effsize. Burt's measure of the effective size of ego's network (essentially, the number of alters minus the average degree of alters within the ego network, not counting ties to ego). 

efficiency. The effective size divided by the number of alters in ego's network.

constraint. Burt's constraint measure (equation 2.4, pg. 55 of Burt, 1992). Essentially a measure of the extent to which ego is invested in people who are invested in other of ego's alters. 

hierarchy. Burt's adjustment of constraint (equation 2.9, pg 71), indicating the extent to which constraint on ego is concentrated in a single alter.

The second table is the dyadic redundancy matrix. For each ego (rows) it gives the extent to which each of its alters are tied to all of ego's other alters (i.e., the extent to which the alter is redundant).

The third table is the dyadic constraint matrix. For each ego (rows) it gives the extent to which it is constrained by each of its alters. Ego is contained by alter j if (a) j represents a large proportion of ego's relational investment, and (b) if ego is heavily invested in other people who are in turn heavily invested in j. In short,  j constrains Ego if ego is heavily invested in j directly and indirectly.

TIMING O(N^3)

REFERENCES Burt, R.S. 1992. Structural Holes: The social structure of competition. Cambridge: Harvard University Press.