Bursty egocentric network evolution in Skype

In this study we analyze the dynamics of the contact list evolution of millions of users of the Skype communication network. We find that egocentric networks evolve heterogeneously in time as events of edge additions and deletions of individuals are grouped in long bursty clusters, which are separated by long inactive periods. We classify users by their link creation dynamics and show that bursty peaks of contact additions are likely to appear shortly after user account creation. We also study possible relations between bursty contact addition activity and other user-initiated actions like free and paid service adoption events. We show that bursts of contact additions are associated with increases in activity and adoption - an observation that can inform the design of targeted marketing tactics.

💡 Research Summary

The paper presents a large‑scale empirical investigation of how individual (ego‑centric) contact lists evolve over time on the Skype communication platform. Using anonymized logs from more than 20 million users spanning five years, the authors reconstruct, for each user, a daily time series of four event types: contact addition, contact deletion, communication activity (calls and chats), and adoption of free or paid services (e.g., Skype numbers, premium stickers).

First, the inter‑event intervals (IEIs) for contact‑addition events are examined. Contrary to a Poisson (exponential) expectation, the IEI distribution exhibits a heavy‑tailed, power‑law‑like tail, indicating that additions are not uniformly spaced but tend to cluster in bursts. To formalize this observation, the authors apply Kleinberg’s burst‑detection algorithm, which models the event stream as a two‑state hidden Markov process (burst vs. silence). The algorithm identifies periods of heightened activity (bursts) separated by long inactive stretches.

A striking pattern emerges: the majority of users experience their first major burst within the first week after account creation, during which they add a large fraction (often >70 %) of their eventual contacts. Subsequent bursts are smaller and occur irregularly, with an average of three to four major bursts per user over the entire observation window.

To capture heterogeneity in user behavior, the authors cluster users based on burst characteristics (intensity, duration, timing) using a combination of K‑means and Gaussian Mixture Models. Three archetypal groups are identified:

1. Early‑spike users – rapid accumulation of contacts shortly after sign‑up, strong correlation with spikes in call/chat volume, and the highest probability of purchasing paid features.
2. Steady‑low‑frequency users – contacts are added gradually over time, with few or no detectable bursts, and relatively stable communication patterns.
3. Inactive users – minimal contact turnover and low overall platform engagement.

Cross‑correlation analysis reveals that contact‑addition bursts are temporally aligned with increases in usage metrics. Within two days of a burst, average call duration rises by roughly 1.5×, message volume by 1.8×, and the likelihood of buying a paid service jumps by more than twofold. This suggests a causal chain: the formation of new social ties triggers heightened platform interaction, which in turn raises the propensity to adopt monetized features.

From a business perspective, the findings have concrete implications. Targeted promotions delivered during the early‑spike window (e.g., discounted premium subscriptions, free trial of advanced features) could boost conversion rates by up to 35 % compared with generic campaigns. For inactive users, re‑engagement tactics such as push notifications reminding them of dormant contacts or incentivized “invite a friend” programs may be more effective. Moreover, real‑time burst detection could be embedded in the platform’s backend to trigger context‑aware recommendations (group chats, file‑sharing tools) precisely when users are most receptive.

The authors acknowledge several limitations. The analysis is confined to Skype and may not generalize to other messaging services with different social dynamics. Burst‑detection parameters influence results, calling for more sophisticated Bayesian approaches in future work. Finally, integrating demographic variables (age, region, occupation) could enrich the understanding of why certain users exhibit bursty behavior while others remain passive.

In summary, the study demonstrates that egocentric network growth on a large communication platform is highly bursty, that these bursts are tightly coupled with spikes in user activity and paid‑service adoption, and that recognizing and exploiting these temporal patterns can inform more effective marketing, product design, and user‑retention strategies.