  In opinion dynamics, as in general usage, polarisation is subjective. To
understand polarisation, we need to develop more precise methods to measure the
agreement in society. This paper presents four mathematical measures of
polarisation derived from graph and network representations of societies and
information theoretic divergences or distance metrics. Two of the methods,
min-max flow and spectral radius, rely on graph theory and define polarisation
in terms of the structural characteristics of networks. The other two methods
represent opinions as probability density functions and use the Kullback
Leibler divergence and the Hellinger distance as polarisation measures. We
present a series of opinion dynamics simulations from two common models to test
the effectiveness of the methods. Results show that the four measures provide
insight into the different aspects of polarisation and allow real-time
monitoring of social networks for indicators of polarisation. The three
measures, the spectral radius, Kullback Leibler divergence and Hellinger
distance, smoothly delineated between different amounts of polarisation, i.e.
how many cluster there were in the simulation, while also measuring with more
granularity how close simulations were to consensus. Min-max flow failed to
accomplish such nuance.
