Self- and Cross-Excitation in Stack Exchange Question & Answer Communities

In this paper, we quantify the impact of self- and cross-excitation on the temporal development of user activity in Stack Exchange Question & Answer (Q&A) communities. We study differences in user excitation between growing and declining Stack Exchange communities, and between those dedicated to STEM and humanities topics by leveraging Hawkes processes. We find that growing communities exhibit early stage, high cross-excitation by a small core of power users reacting to the community as a whole, and strong long-term self-excitation in general and cross-excitation by casual users in particular, suggesting community openness towards less active users. Further, we observe that communities in the humanities exhibit long-term power user cross-excitation, whereas in STEM communities activity is more evenly distributed towards casual user self-excitation. We validate our findings via permutation tests and quantify the impact of these excitation effects with a range of prediction experiments. Our work enables researchers to quantitatively assess the evolution and activity potential of Q&A communities.