A second look at Krackhardt's graph theoretical dimensions of informal organizations

► We prove Krackhardt's graph dimensions imply an arborescence. ► We look at the modelling implications of the dimensions. ► We suggest relaxations. ► We give examples of situations in which the relaxations are appropriate. Krackhardt (1994) proposed four dimensions to describe and measure the...

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Bibliographic Details
Published in:Social networks 2012-05, Vol.34 (2), p.159-163
Main Authors: Everett, Martin G., Krackhardt, David
Format: Article
Language:English
Subjects:
Arborescence
Connectedness
Graph efficient
Graph hierarchic
Graph theory
Graph-theoretic dimensions
Hierarchy
Informal groups
Least upper boundedness
Network analysis
Networks
Organization theory
Out-tree
Sociology
Sociology of organizations and enterprises. Bureaucracy and administration
Sociology of work and sociology of organizations
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Summary:► We prove Krackhardt's graph dimensions imply an arborescence. ► We look at the modelling implications of the dimensions. ► We suggest relaxations. ► We give examples of situations in which the relaxations are appropriate. Krackhardt (1994) proposed four dimensions to describe and measure the amount of hierarchy in networks of informal organizations. We examine these conditions, suggest some relaxations and prove that they are both necessary and sufficient to guarantee an arborescence (or out-tree). In addition we suggest situations some of which are outside of informal organizations in which fewer of the conditions can be used to capture the hierarchical tree structure.
ISSN:0378-8733
1879-2111
DOI:10.1016/j.socnet.2011.10.006