Complex hypergraph analysis of Australian MPs' professional connections, 1947-2019

TL;DR

The paper addresses how MPs' professional backgrounds relate to their networked connections and recruitment. It introduces an attributes-as-networks framework that uses graphs and hypergraphs, mapped to s-line graphs, and analyzes connectivity with two statistics, the average maximal flow $averF$ and transitivity $T(G)$, against random-baseline simulations. Empirically, it analyzes Australian MPs from 1947–2019 (ALP and LP) and finds bouquet structures among Labor pre-1980s and more homogeneous Liberal early, followed by convergence in network structure after the 1980s consistent with cartellised recruitment. The work demonstrates the method's potential for broad study of political representation and elite networks in diverse political systems.

Abstract

We propose a suit of methods to analyse the professional networks of MPs, showing how to analyse weak-tie connections between legislators and the connections between background charactersitic attributes. Applied to a novel dataset on the backgrounds of Australian MPs in the Australian Labor Party and the Liberal Party of Australia (1947-2019), we show that our approach can help to describe and explain the decline in working-class and trade unionist MPs from the Labor Party, the homogeneous elitism of the mid-20 century Liberal Party, and the increasing similarity of both parties' professional networks, occuring in the period of party cartellisation from the 1980s onward. Our paper's finding show that our method has clear potential for broader applications in the study of political representation, diversity, and elite political networks.

Figures (10)

• Figure 1: This scheme describes both the graph set-up for MP networks and the hypergraph setup for the attribute networks. Both the MP networks and the attribute hypergraphs have MPs as nodes and shared attributes as edges. The attribute hypergraphs are mapped to two sets of s-line graphs. The first set is undirected s-line graphs, and the second set is directed s-line graphs.
• Figure 2: (a) an example of a bouquet structure, with one node connecting two complete networks. (b) an example of a satellite structure, with a compact structure in the middle and scattered disconnected components. (c) asymmetrical bonding between a large edge and a small edge, where N1 and N2 represent the number of nodes the edges possess and $N1 << N2$ and n is the number of nodes that are in the overlap region.
• Figure 3: (a) and (b) show the comparison between the simulation (free choice) and real MP networks for average maximal flow and transitivity respectively. The error bars on the simulation data are the standard deviations of the 100 simulations calculated for each year, with the simulation line being the average of the 100 simulations. (c) and (d) show the same comparison with (a) and (b) except against the shuffle simulations. (e) the MP network for ALP in 1960. The bouquet structure is obvious with one end being the trade unionists. (f) the slight clustering structure caused by many bouquet sub-structures (the LP MP network at 2003).
• Figure 4: The diagrams (a)-(c) and (g)-(i) show the comparison between simulation and real attribute networks in terms of changes of average maximum flow over the years for both Liberal and Labor parties for free choice simulation, s=0,2, and edge weight being uniform, normalised and directed normalised weight from left to right. The diagrams (d) - (f) and (j) - (l) show the similar set of comparisons with shuffle simulation. The error bars on the simulation data are the standard deviations of the 100 simulations calculated for each year, with the simulation line being the average of the 100 simulations.
• Figure 5: The diagrams (a) - (b) show the comparison between transitivity of s-line graphs with s being 0 and 2 respectively for real and free choice simulated data. The diagrams (c) - (d) show the same comparison with simulation shuffle.