Table 2 Null models identify memory as a mechanism for reciprocity. Signed (one-tailed) p-values of the temporal reciprocity measures \(p(E_{rec})\) and \(p(l_{rec})\) between the studied datasets and four null models shuffling interaction events. Symbols are ■ (\(p < 0.03 \)), △ (\(0.03 < p < 1\)), and ∘ (\(p = 1\)), with filled symbols indicating a statistical significant difference between model and data (significance level \(\alpha = 0.03\)). The sign of the p-value is chosen with respect to median values: for positive (green) p-values, empirical measures are higher than the median of shuffling results, and viceversa for the negative (red) p-values (see Additional file 1 Section S4 for details). Null models are denoted by NTS (Network Shuffling Timestamps), NDS (Node Shuffling Timestamps), NTSR (Network Rewiring and Shuffling Timestamps), and NDSR (Node Rewiring and Shuffling Timestamps) (Additional file 1 Section S4). The calls dataset is not included due to its small size after filtering (Additional file 1 Section S3). We see more positive than negative statistically significant p-values, implying that temporal reciprocity is not reproduced by random mechanisms. The NTSR model randomizes the timeline of social interactions of an individual and the identities of its neighbours, erasing its structural and temporal memory. Positive p-values for NTSR thus suggest memory as a potentially relevant mechanism for reciprocal interaction in social communication. There is also a notable difference in p-value sign between conversation (sms, msg, email) and broadcasting (retweets, mentions) channels, pointing to the distinct roles of bidirectional vs. unidirectional exchange

From: Temporal patterns of reciprocity in communication networks