Human interactive patterns in temporal networks

Yi-Qing Zhang, Xiang Li, Jian Xu, Athanasios V. Vasilakos

IEEE Transactions on Systems, Man, and Cybernetics: Systems 45(2): 214 to 222, February 2015 published

Phone logs, Wi-Fi logs and badge sensors record not just who interacts with whom but in what order. An ordinary network diagram throws that order away. This paper keeps it by counting temporal motifs: small groups of interactions that follow closely one after another and share people. Across six datasets, three shapes dominate: one person contacting three others in turn (a Leader), contact passing down a line of people (a Queue), and two people messaging back and forth (Feedback). The gaps between these interactions are bursty, and each pattern has its own time scale, from three minutes for text replies to seven days on an online forum.

Diagrams of the three dominant motifs, Star, Ordered-chain and Ping-Pong, each shown as a four-event version equal to two overlapping three-event versions. — Fig. 7. The three dominant shapes: Star (Leader), Ordered-chain (Queue) and Ping-Pong (Feedback). Their four-event versions are two overlapping copies of the three-event motif. The section icons on this site are drawn from these shapes.

Abstract

Modern information and communication technologies provide digital traces of human interactive activities, which offer novel avenues to map and analyze temporal features of human interaction networks. This paper explores mesoscopic patterns of human interactive activities from six real-world interaction networks with temporal-topological isomorphic subgraphs, i.e., temporal motifs. We discover two dominant mutual motifs, “Star,” “Ordered-chain,” and one dominant directed motif, “Ping-Pong,” which characterize the interactive patterns of “Leader,” “Queue,” and “Feedback,” respectively. Moreover, temporal dynamics shows that bursts are universal in human mesoscopic patterns, and the evolution of three dominant temporal motifs indicates the existence of characteristic time. Finally, we analyze temporal robustness and generalization to verify that 3-event temporal motifs are a simple yet powerful tool to capture the mesoscopic patterns of human interactive activities.

What a temporal motif is

An event is one timed interaction between two people. Two events are adjacent if they share a person and the second starts within a time window Δt of the first ending. A temporal motif is a group of events linked this way, with nobody interacting with anyone else in between. Motifs are told apart by their shape and by the order of their events, which is why the diagrams number the edges 1, 2, 3.

The six datasets

Dataset	What an interaction is	People	Events	Days
FudanWiFi09	two people on the same campus Wi-Fi access point	17,881	209,137	84
Sex6yr	contacts between sellers and buyers on a Brazilian online forum	16,102	42,851	2,232
HT09	face-to-face conversations at a conference, from RFID badges	113	8,641	3
SGinfectious	face-to-face conversations at a museum exhibition, from RFID badges	10,924	138,567	81
SMS1	text messages, one mobile operator	9,259	22,771	1
SMS2	text messages, a second operator	12,001	25,543	1

What we found

Three shapes dominate. Star and Ordered-chain lead in the four proximity and face-to-face datasets; Ping-Pong leads in both text-message datasets.
Without timing, the patterns disappear. In the same data with time order removed, the static chain outnumbers the static star, so the Leader pattern is hidden; in text messages the back-and-forth of Ping-Pong vanishes entirely.
Bursts everywhere. Gaps between events inside each dominant motif are bursty in all six datasets, fitting a power law with an exponential cutoff far better than an exponential.
Each pattern has a characteristic time. Leader: 20 minutes on campus Wi-Fi and 7 days on the forum. Queue: 26 and 21 minutes at the two badge-sensor venues. Feedback: 3 minutes in both text-message datasets.
The results are robust. Motif shares barely change when 90% of events are removed at random or only part of the collection period is used.

Figures

Timelines of interactions, the temporal networks built from them, and catalogs of one-, two- and three-event motifs. — Fig. 1. From interactions to motifs: timed interactions (a) become a temporal network (b), and closely spaced groups of events form motifs (c), numbered in the order they happen.

Line charts of the share of each three-event motif against the time window, for six datasets. — Fig. 2. Share of each three-event motif as the time window grows, in all six datasets.

Step plots of the excess of the dominant motif over the runner-up against the time window, for six datasets. — Fig. 5. When does each pattern win? The curve is above zero where the dominant motif outgrows the runner-up.

Cumulative distributions of gaps between events inside the dominant motif for six datasets, with fitted curves. — Fig. 4. Gaps between interactions inside each dominant motif are bursty: short flurries separated by long quiet spells.

Bar and line charts of static three- and four-node motif densities for each dataset. — Fig. 3. Without timing the same data look different: the static chain outnumbers the static star.

Motif densities from full data, ten percent samples and sub-periods, nearly overlapping. — Fig. 6. Motif shares barely move when 90% of events are removed or only part of the period is used.

Cite

@article{zhang2015human,
  title   = {Human Interactive Patterns in Temporal Networks},
  author  = {Zhang, Yi-Qing and Li, Xiang and Xu, Jian and Vasilakos, Athanasios V.},
  journal = {IEEE Transactions on Systems, Man, and Cybernetics: Systems},
  volume  = {45},
  number  = {2},
  pages   = {214--222},
  year    = {2015},
  doi     = {10.1109/TSMC.2014.2360505}
}