Analyzing rich club behavior in open source projects

Editor's Notes

• #3: GitHub is the most popular service to develop and maintain open source software. Each user interacts with many other users in the project development process (commits, issues, pr), defining collaboration networks. Studying collaboration networks helps in discovering properties and behaviors that influence development, management and success of an OSS project.
• #4: Developers collaborate mostly with the same fixed subset of other important colleagues, instead of spreading the cooperation to each component of the team.
• #5: Formally, it cab be measured by the so called rich-club coefficient ϕ(k). Intuitively, ϕ(k) measures how far the set of nodes with degree k is from being a complete subgraph. The value of ϕ(k) ranges from 0 (all nodes are disconnected) to 1 (a clique), with higher values showing a stronger rich-club behavior in the network. It is monotonically increasing even for random networks, so a normalized coefficient has been introduced in literature: ϕ(k) is divided by the coefficient calculated for a random network with same degree distribution of the original one.
• #6: Presence or absence of a rich-clubs in open source projects has not been studied in a systematic way and has not been applied to a large dataset as the one that GitHub can now provide.
• #9: Clashing: same name of different users Duplicity: different names for the same users Solution: use SHA value to associate git commits to GitHub users (if still present)
• #11: Two users are connected in the PR graph if they commented/interacted on the same PR…
• #13: Calculaton of rich-club coefficient is run for each project’s supergraph to have a global view of the effect. Maximum value for each project is shown: each of the 60 graphs presents a rich club behavior, even if most of them have values only slightly higher than 1. For this reason, we want to better understand the correspondence between the coefficient and the actual graphs.
• #14: The first example that we take is the materialize repositorty: rich-club coefficient with respect to node degree is presented. It is possible to notice a rich-club behavior for a range of degrees, with a peak on k=49, which should correspond to groups of nodes with degree at least 49 connected to each other.
• #15: This seems to go against the open source paradigma: project “owned” by few users. Established in 2014 by a team of 4 developers, with 3,853 commits and 252 contributors. Nevertheless, the project only has two top contributors (more than 1,000 commits), which belong to the original team, and no frequent contributors
• #16: Mixed behavior presence: slightly over than 1, then dramatically lower. The overall intuition is that the graph does not present rich-clubs
• #17: It was publicly announced by Apple in 2014 and was later open sourced in December 2015. Currently, the project has more than 84k commits and 674 contributors, with 14 top contributors (more than 1.000 commits) and 44 frequent contributors (between 100 and 1.000 commits). Remarkably, 4 of the top contributors and 21 of the frequent contributors do not belong to Apple according to their GitHub profile. This is a sign that the project has successfully attracted and retained external talent.
• #18: In this table, the 10 projects with highest coefficient for the supergraph are presented. Along with them, the coefficient for the other kind of graphs is calculated when possible. Infact,also these other graphs can «hide» other clubs structures.
• #19: Maximum coefficient distribution for each kind of graph as a further insight. Blue line is the one already discussed.Green and orange line show commits and issues maximum coefficient distribution: density has a peak on 1 meaning that most of the graphs do not present strong rich-clubs. Red line has its peak around 1.4: most of the projects present evident rich-club structures. This behavior could be related to the fact that PR is the most critical level in open-source software development and few trusthworty developers are in charge of most of the tasks.
• #20: We focused also the attention on the users: almost 50% of the projects, have users tha belongs to multiple clubs. The distribution presents the number of users shared across all the projects’ clubs: this means that, on average, 7 developers are in the PR club, as well as in the commits and issues club. These developers form a sub-community inside the project that has strong influence in all the project’s levels.
• #22: As rich-club phenomenon is quite complex and also its application on OSS communities relatively new, plenty of further works can be done. First of all, we want to apply weighted coefficient version to check if other patterns arise. We want to extend the analysis at the module and the ecosystem level. And third, we want to introduce time variable: in this work the graphs are built using the entire data as a 1-year snapshot, but it is possible to build monthly graphs and check if temporal clubs show up.
• #23: With this, I have concluded the presentation. Thank you for the attention.