Abstract
We quantify a social organization’s potentiality, that is, its ability to attain different configurations. The organization is represented as a network in which nodes correspond to individuals and (multi-)edges to their multiple interactions. Attainable configurations are treated as realizations from a network ensemble. To have the ability to encode interaction preferences, we choose the generalized hypergeometric ensemble of random graphs, which is described by a closed-form probability distribution. From this distribution we calculate Shannon entropy as a measure of potentiality. This allows us to compare different organizations as well as different stages in the development of a given organization. The feasibility of the approach is demonstrated using data from three empirical and two synthetic systems.
Highlights
Social organizations are ubiquitous in everyday life, ranging from project teams, e.g., to produce open source software [1], to special interest groups, such as sports clubs [2] or conference audiences [3]discussed later in this paper
A social organization can be represented by a network ensemble
Real systems are affected by a very large number of constraints and because they are so many, a list stating all of them one by one is unfeasible. We focus on their combined effect, which we extract by applying the generalized hypergeometric ensemble, gHypEG [15], to a given network representation
Summary
Social organizations are ubiquitous in everyday life, ranging from project teams, e.g., to produce open source software [1], to special interest groups, such as sports clubs [2] or conference audiences [3]. Network science allows studying such complex systems in terms of networks, where nodes represent individuals and edges their interactions [4,5] Under this assumption, a social organization can be represented by a network ensemble. We need to decide about a probability distribution suitable for reflecting the interactions and constraints in social organizations. We focus on their combined effect, which we extract by applying the generalized hypergeometric ensemble, gHypEG [15], to a given network representation This allows the encoding of observed interaction preferences among every pair of individuals as biases in the edge formation.
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