Burt (1992) proposed two principal measures of structural holes, effective size and constraint. However, the formulas describing the measures are somewhat opaque and have led to a certain amount of confusion. Borgatti (1997) showed that, for binary data, the effective size formula could be written very simply as degree (ego network size) minus average degree of alters within the ego network. The present paper presents an analogous reformulation of the constraint measure. We also derive minima and maxima for constraint, showing that, for small ego networks, constraint can be larger than one, and for larger ego networks, constraint cannot get as large as one. We also show that for networks with more than seven alters, the maximum constraint does not occur in a maximally dense or closed network, but rather in a relatively sparse “shadow ego network”, which is a network that contains an alter (the shadow ego) that is connected to every other alter, and where no other alter-alter ties exist.

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Published in Social Networks, v. 62.

© 2020 Elsevier B.V.

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© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

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