Temporal motifs reveal collaboration patterns in online task-oriented networks

Real networks feature layers of interactions and complexity. In them, different types of nodes can interact with each other via a variety of events. Examples of this complexity are task-oriented social networks (TOSNs), where teams of people share tasks towards creating a quality artifact, such as academic research papers or software development in commercial or open source environments. Accomplishing those tasks involves both work, e.g., writing the papers or code, and communication, to discuss and coordinate. Taking into account the different types of activities and how they alternate over time can result in much more precise understanding of the TOSNs behaviors and outcomes. That calls for modeling techniques that can accommodate both node and link heterogeneity as well as temporal change. In this paper, we report on methodology for finding temporal motifs in TOSNs, limited to a system of two people and an artifact. We apply the methods to publicly available data of TOSNs from 31 Open Source Software projects. We find that these temporal motifs are enriched in the observed data. When applied to software development outcome, temporal motifs reveal a distinct dependency between collaboration and communication in the code writing process. Moreover, we show that models based on temporal motifs can be used to more precisely relate both individual developer centrality and team cohesion to programmer productivity than models based on aggregated TOSNs.

Figure 1

Sketch of a typical TOSN, with two types of nodes and links, i.e., a group of people collaborating to process a number of artifacts, while they communicate with each other to coordinate their work.

Figure 2

(a) A TOSN with six developers (red circles) and seven files (blue squares). (b) Four typical temporal motifs: plan before temporal collaboration (TAB/TBA), call for participation (ATB/BTA), discussion after temporal cocommits (ABT/BAT), and temporal cocommits without communications by email (AB/BA). (c) The ordered sequence of activities, which is divided into a subsequence at the interactivity intervals larger than a given threshold $\theta$. (d) The subsequences after combining the same successive elements. (e) Counting temporal motifs in the resulting subsequence.

Figure 3

The average numbers of three-motifs $M_1,M_2$, and $M_3$ and two-motifs $M_4$ for the 31 TOSNs at different time threshold $\theta$, varying from three hours to three days.

Figure 4

Aggregate motif networks for six OSS projects: (a) Ant, (b) Axis2_java, (c) Cxf, (d) Derby, (e) Lucene, and (f) Openejb, with time threshold set to $\theta =3$ (h). Here the red circles represent developers and the blue diamonds represent files; the red solid lines represent the communications between developers, and the gray dashed lines represent the developer commits to files.

Figure 5

Correlation between collaborative and social weights, calculated by Eq. (4), obtained from the aggregate TOSN and the corresponding aggregate motif networks for all 31 OSS projects (the mean value and the error bars are shown), as functions of the time threshold $\theta$.