A Measure of Polarization on Social Media Networks based on Community Boundaries

Many societal issues lend themselves to polarization: same-sex marriage, abortion, and gun control, for instance, are all topics that induce antagonism and opposition among people. Given a social network and its division into communities, we ask the question, how can we identify if there is polarization (i.e. segregation) among the sub-groups? This answer is important not only from a sociological standpoint, but also because polarization can be a key piece of information for tasks such as opinion analysis, as conflicting groups may carry biased opinions.

While this is certainly a salient question, we demonstrate that it has not been properly addressed by prior research for a simple reason: most prior research examine networks emerging from topics which are previously known to induce polarization in communities (especially Politics). To really understand the structural characteristics of polarized networks, we need to compare them against non-polarized networks. This is one of the key contributions of our work.

Modularity is a metric widely employed to measure separation in a social network; it roughly characterizes the strength of a division of a community into groups. We find that it is not a good metric to measure polarization because it can’t represent whether this division is a result of homophily within groups or antagonism between groups (or both).


A polarized network of political discussion in Twitter (right) is more modular than a Facebook friendship network divided into two communities (graph on the left – college and high school friends), but how ‘much’ modularity implies polarization?

In the two networks above, the separation between the two groups achieves a modularity score of 0.24 for the first network and 0.42 for the second. The ‘more’ divided group, a friendship network, however, has no polarization at all! These are two groups that share different interests without truly opposing one another. In this way, modularity is not effective for differentiating polarization from the absence of polarization!

To tackle this issue, we propose a new measure of polarization that, unlike modularity, focuses on the existence (or absence) of antagonism between the groups. We compare nodes’ propensity towards connecting to users in the other (potentially opposing) group to their propensity to connecting to members within their own group – we thus measure antagonism by looking to see if members of a group avoid connecting with members of the other group.

We show the usefulness of our novel metric on the analysis of the social network of retweets that emerged during the gun control debate due the shootings on Newtown, CT, on December 2012.

Want to learn more? See our full paper: A Measure of Polarization on Social Media Networks based on Community Boundaries

Pedro Calais Guerra, UFMG, Brazil
Wagner Meira Jr., UFMG, Brazil
Claire Cardie, Cornell University
Robert Kleinberg, Cornell University