Academic team formation as evolving hypergraphs

Abstract

This paper quantitatively explores the social and socio-semantic patterns of constitution of academic collaboration teams. To this end, we broadly underline two critical features of social networks of knowledge-based collaboration: first, they essentially consist of group-level interactions which call for team-centered approaches. Formally, this induces the use of hypergraphs and n-adic interactions, rather than traditional dyadic frameworks of interaction such as graphs, binding only pairs of agents. Second, we advocate the joint consideration of structural and semantic features, as collaborations are allegedly constrained by both of them. Considering these provisions, we propose a framework which principally enables us to empirically test a series of hypotheses related to academic team formation patterns. In particular, we exhibit and characterize the influence of an implicit group structure driving recurrent team formation processes. On the whole, innovative production does not appear to be correlated with more original teams, while a polarization appears between groups composed of experts only or non-experts only, altogether corresponding to collectives with a high rate of repeated interactions.

Appendix: Weighting functions

A weighted hypergraphic repetition rate could be written as follows:

$$ r_t({\mathfrak{e}})={\frac{\sum_{\mathop{{\mathfrak{e}}^{\prime}\subseteq {\mathfrak{e}}}\limits_{ |{\mathfrak{e}}^{\prime}|\geq 2}}w_{\mathfrak{e}}(|{\mathfrak{e}}^{\prime}|)\cdot \rho_t({\mathfrak{e}}^{\prime})} {\sum_{i\in\{2,\ldots,|{\mathfrak{e}}|\}}{w_{{\mathfrak{e}}}(i){|{\mathfrak{e}}|\choose i}}}} $$

where w _. is a weight function (given ${\mathfrak{e}}, w_{{\mathfrak{e}}}:{\mathbb{N}}\rightarrow{\mathbb{R}}$) which makes it possible to give more or less weight to particular subset sizes.

For instance:

• taking $w_{{\mathfrak{e}}}(i)=1,$ i.e. actually no weighting as has been used in the paper,

  $$ r_t({\mathfrak{e}})={\frac{1}{2^{|{\mathfrak{e}}|}-|{\mathfrak{e}}|-1}} \sum_{\mathop{{\mathfrak{e}}^{\prime}\subseteq {\mathfrak{e}}}\limits_{|{\mathfrak{e}}^{\prime}|\geq 2}}\rho_t({\mathfrak{e}}^{\prime}) $$

• if instead $w_{{\mathfrak{e}}}(i)=i,$ i.e. weighting proportional to the size of the considered subset,

  $$ r_t({\mathfrak{e}})={\frac{1}{|{\mathfrak{e}}|(2^{|{\mathfrak{e}}|-1}-1)}} \sum_{\mathop{{\mathfrak{e}}^{\prime}\subseteq {\mathfrak{e}}}\limits_{|{\mathfrak{e}}^{\prime}|\geq 2}}|{\mathfrak{e}}^{\prime}|\rho_t({\mathfrak{e}}^{\prime}) $$

• if finally $w_{{\mathfrak{e}}}(i)={|{\mathfrak{e}}|\choose i}^{-1},$ i.e. weighting proportional to the number of possible subsets of size $|{\mathfrak{e}}|$ in a set of size i,

  $$ r_t({\mathfrak{e}})=\sum_{\mathop{{\mathfrak{e}}^{\prime}\subseteq {\mathfrak{e}}}\limits_{ |{\mathfrak{e}}^{\prime}|\geq 2}}{\frac{\rho_t({\mathfrak{e}}^{\prime})} {{|{\mathfrak{e}}|\choose|{\mathfrak{e}}^{\prime}|}}} $$