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"Ron Burt proposed a number of measures for ego networks in his classic book “Structural Holes”. In 1997 Steve Borgatti wrote a short article in connections called unpacking Burt’s redundancy measure. The redundancy measure is relatively easy to disentangle as it is expressed as a fraction. In this talk we attempt to do the same with constraint. Burt’s constraint measure is a lot more challenging as it is expressed as a sum and a squared term. Burt claims it consists of a number of factors that he deems to be important namely size, density and hierarchy. Here I show that if the graph is binary then we can re-write the constraint to explicitly see these contributions. This allows us to do a number of additional things. 1 Calculate max and min for constraint 2 Re-weight how these terms contribute to the measure. 3 Approximate constraint when we know the degrees of the alters without knowing the exact structure. In addition it provides an opportunity to redefine constraint in a way that more evenly balances the three components."
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When examining structural holes, it is possible to calculate the aggregate constraint of an ego. The value of the aggregate constraint is usually between 0 and 1, but it can be greater than 1.
I think I read somewhere that the maximum value possible (greater than 1) has been proved. I have mislaid the reference. Might anyone be able to inform me of the reference? Of the maximum value?
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