If you’re happy and we know it … are your friends?

Do your friends influence your behavior?  Of course they do.  But it’s hard to actually measure their influence.  Social contagion is difficult to distinguish from homophily, the tendency we have to seek relationships with people like ourselves.

In response to the “happiness is contagious” phenomenon promoted by Nicholas Christakis and James Fowler, we here at onehappybird were wondering whether happy Twitter users were more likely to be connected to each other.  In other words, is happiness assortative in the Twitter social network?  (See related work here.)

In the image below, each circle represents a person in the social network of the center node.  We color nodes by the happiness of their tweets during a single week.  Pink colors are happier, gray colors are sadder, and nodes depicted with the color black did not meet our thresholding criteria (50 labMT words).

We established a friendship link between two users if they both replied directly to the other at least once during the week.

As users are added to this network, it quickly becomes difficult to tell whether pink nodes are disproportionately connected to each other, so instead we look at the correlation of their happiness scores.  The plot below shows the Spearman correlation coefficient of the happiness ranks for roughly 100,000 people, with blue squares and green diamonds indicating different word thresholds, and red circles representing the same network but with randomly shuffled happiness scores.

The larger correlation for friends indicates that happy users are likely to be connected to each other, as are sad users. Moving further away from one’s local social neighborhood to friends of friends, and friends of friends of friends, the strength of assortativity decreases as expected.

We also looked at the average happiness of users as a function of their number of friends (degree k). Happiness increases gradually with popularity, with large degree nodes demonstrating a larger average happiness than small degree nodes.

The most popular users used words such as “you,” “thanks,” and “lol” more frequently than small degree nodes, while the latter group used words such as “damn,” “hate,” and “tired” more frequently.  The transition appears to occur near Dunbar’s number (around 150), demonstrating a quantitative difference between personal and professional relationships.

Finally, here we show a visualization of the reciprocal-reply network for the day of October 28, 2008.

The size of the nodes is proportional to their degree, and colors indicate communities detected by Gephi’s community detection algorithm.

For more details, see the publication:

C. A. Bliss, I. M. Kloumann, K. D. Harris, C. M. Danforth, P. S. Dodds.  Twitter Reciprocal Reply Networks Exhibit Assortativity with Respect to Happiness. Journal of Computational Science. 2012. [pdf]

Abstract: Based on nearly 40 million message pairs posted to Twitter between September 2008 and February 2009, we construct and examine the revealed social network structure and dynamics over the time scales of days, weeks, and months. At the level of user behavior, we employ our recently developed hedonometric analysis methods to investigate patterns of sentiment expression. We find users’ average happiness scores to be positively and significantly correlated with those of users one, two, and three links away. We strengthen our analysis by proposing and using a null model to test the effect of network topology on the assortativity of happiness. We also find evidence that more well connected users write happier status updates, with a transition occurring around Dunbar’s number. More generally, our work provides evidence of a social sub-network structure within Twitter and raises several methodological points of interest with regard to social network reconstructions.