How people make friends in social networking sites - A microscopic perspective

We study the detailed growth of a social networking site with full temporal information by examining the creation process of each friendship relation that can collectively lead to the macroscopic properties of the network. We first study the reciprocal behavior of users, and find that link requests are quickly responded to and that the distribution of reciprocation intervals decays in an exponential form. The degrees of inviters/accepters are slightly negatively correlative with reciprocation time. In addition, the temporal feature of the online community shows that the distributions of intervals of user behaviors, such as sending or accepting link requests, follow a power law with a universal exponent, and peaks emerge for intervals of an integral day. We finally study the preferential selection and linking phenomena of the social networking site and find that, for the former, a linear preference holds for preferential sending and reception, and for the latter, a linear preference also holds for preferential acceptance, creation, and attachment. Based on the linearly preferential linking, we put forward an analyzable network model which can reproduce the degree distribution of the network. The research framework presented in the paper could provide a potential insight into how the micro-motives of users lead to the global structure of online social networks.

💡 Research Summary

This paper presents a fine‑grained empirical study of how friendships are formed on a professional Chinese social networking site, Wealink. The authors have access to a complete, time‑stamped log of every friendship invitation sent and every acceptance recorded between 11 May 2005 and 22 August 2007. In total, 223 482 users generated 273 209 undirected links; only 186 invitations remained unanswered, indicating an almost perfect conversion from invitation to friendship.

Reciprocity dynamics
The time interval between an invitation and its acceptance (the “reciprocity interval”) follows an exponential complementary cumulative distribution, (P_c(t)\sim e^{-0.011t}) (R² = 0.958). Approximately 67 % of all invitations are accepted within 24 hours and 84 % within 30 days. This rapid response contrasts sharply with the heavy‑tailed waiting times observed in email communication, suggesting that the social norm of courtesy on a SNS, together with automatic email notifications, drives a fast, memoryless response process.

Degree‑time correlation
The authors examine whether a user’s degree (number of friends) influences how quickly they respond. Pearson correlation coefficients between degree and reciprocity time are –0.02 for inviters and –0.05 for accepters, indicating only a very weak negative relationship: higher‑degree users tend to reply slightly faster, but degree is not a dominant factor.

User typology
Based on activity, users fall into three categories: (i) “active” users who only send invitations, (ii) “passive” users who only receive them, and (iii) “mixed” users who do both. The majority (≈57 %) belong to the first two groups, reflecting the low average degree (2.53) of this professional network. Mixed users exhibit a moderate positive correlation (0.48) between the number of sent and received invitations, indicating a feedback loop where more active users attract more inbound requests.

Edge classification
Edges are classified as Old‑Old, Old‑New, New‑Old, and New‑New, where “old” denotes a user already present in the network and “new” a user who has just joined. Old‑New (≈30 %) and New‑Old (≈50 %) together account for about 80 % of all links, showing that most friendships are formed by existing members reaching out to newcomers or newcomers responding to existing members. The scarcity of Old‑Old links explains the overall sparsity (density ≈ 1.09 × 10⁻⁵) of the network.

Temporal patterns of link events
The inter‑event times for three types of actions—sending invitations, accepting invitations, and any consecutive event—are all heavy‑tailed with a universal power‑law exponent ≈ 1.89. This deviates from the exponential waiting times of a Poisson process and indicates bursty dynamics: periods of rapid activity are interspersed with long idle intervals. Moreover, distinct peaks appear at multiples of 24 hours, reflecting daily human routines.

Preferential selection
The authors separate “preferential sending” (the probability that a user who has already sent k invitations will send another) and “preferential reception” (the probability that a user who has already received k invitations will receive another). Both follow a linear preferential rule, (Y(k)\propto k^{\beta}) with (\beta\approx1). Using the Simon model, they estimate the rate at which new users appear: (\alpha=0.53) for inviters and (\alpha=0.35) for receivers. Consequently, the cumulative distributions of sent and received invitation counts obey power laws with exponents –2.13 and –1.54, respectively, matching the empirical data.

Linear preferential linking model
Building on the observed linear preferential selection, the authors propose a simple stochastic growth model: at each step a new node appears with probability (\alpha); otherwise an existing node is chosen with probability proportional to its current degree, and a new link is attached. Simulations of this model reproduce the empirical degree distribution of Wealink, confirming that the macroscopic network structure can be explained by microscopic linear preferential attachment combined with a constant influx of new users.

Implications and limitations
The study demonstrates that three microscopic mechanisms—exponential reciprocity, power‑law inter‑event times, and linear preferential selection—jointly shape the global topology of an online social network. By focusing on the elementary “invite‑accept” process rather than on aggregated snapshots, the authors bridge the gap between individual user motives and emergent network properties. However, the analysis is confined to a single, professionally oriented platform; extending the methodology to larger, more heterogeneous networks (e.g., Facebook, Twitter) and incorporating user attributes (age, occupation) would test the generality of the findings.

Conclusion
Through a comprehensive, time‑resolved dataset, the paper uncovers that friendship formation on Wealink is characterized by rapid, memoryless reciprocation, bursty activity with daily periodicity, and linear preferential attachment in both sending and receiving invitations. A parsimonious growth model based on these mechanisms accurately reproduces the observed degree distribution, providing a clear mechanistic link between micro‑level user behavior and the macro‑level structure of online social networks.