# Graph-Driven Exploration of Issue Handling Schemes in Software Projects
## 5 Experimental Results and Analysis
### Profiles of Issue Handling Paths
#### 5.2.2 Path Classification and Aggregation
A sample of the paths with loops is presented in Table 8.  
Having analyzed some open source projects, we identified that 0.1-6% of issues were handled by paths with loops. In the open source project MongoDB, we detected 174 paths (20.1%) with loops, covering 350 bug issues (4.9%). Most of these paths (142) covered single issues. For the issues _Improvement_, _New Feature_, we found that 17.5% of paths had loops, covering 4.3% of issues. Most loops involved sequences of three states initiated by developers. However, some single-state loops comprised the repetition of the _Closed_ state (12 loops) separated by short delays, probably resulting from faults in Jira API usage. Beyond regular loops, we can also trace repeating states in paths. In MongoDB, we observed repetitions of the _Open_ state in 44.5% of paths, which covered 7.9% of all bug issues. However, the 10 paths with the highest issue coverage (66%) were free of state repetition anomalies. Among the 100 paths with the highest issue coverage, _Open_ state repetition occurred in 22% of paths, covering 3.4% of issues. In the case of single-issue paths (70% paths, 6.9% of all issues), this anomaly was observed for 50% of paths. Most repetitions of the _Open_ state followed the _Closed_ state (as well as _Needs scheduling_ and _Backlog_), indicating reporting and resolution deficiencies. In Apache Lucene, 2.46% of bug issues and 2.70% of new functionality issues were handled in loops. Most (about 80%) of these loops involved the repetition of one state (e.g., _Open_ state) resulting from some deficiencies. In the Arrow project, only a single regular loop was detected within bug handling paths: O,IPrs,**C,Reo,C,Reo,C** (covering one issue). Anomalous paths were mostly related to diverse patterns comprising the _Reopen_ state or \begin{table}
\begin{tabular}{c c c c c c} \hline \hline N & **Path** & **AVG** & **MAX** & **Q2** & **Q3** \\ \hline
9 & N,**IN,**REV,**TbT,**REO,**IN,**REV,TbT,** & & & & \\
**REO,**IN,**REV,**TbT,V/C & & & & & \\
4 & N,**IN,**NIF,**IN,**NIF,**IN,**REV,TbT,V/C & & & & \\
2 & N,**IN,**REV,**TbT,**REO,**IN,**REV,**TbT,**REO,**IN,**REV,**TbT,**V/C & & & & \\
2 & **TbT,**REO,**IN,**REV,**TbT,**REO,**IN,**REV,**TbT,V/C & & & & \\
2 & **N,**IN,**N,**IN,**N,**IN,**REV,TbT,V/C & & & & \\
2 & **N,**IN,**REV,**IN,**REV,**IN,**IN,**IN,**REV,TbT,V/C & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Anomalous paths in the commercial project P1 (bug issues). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**N** & **Path** & **AVG** & **MAX** & **Q2** & **Q3** \\ \hline
44 & NED,NES,OPE,IPR,ICR,**CLO** & 43.1 & 366.2 & 11.0 & 37.3 \\
37 & NED,**INV,**WFU,**INV,**WFU,**INV,**CLO,CLO & 43.0 & 240.9 & 32.3 & 49.1 \\
12 & NED,**INV,**WFU,**INV,**WFU,**INV,**WFU,**INV,**CLO & 113.5 & 545.1 & 59.4 & 133.3 \\
11 & NES,OPE,**NES,**NES,OPE,IPR,ICR,CLO & 13.7 & 35.2 & 11.0 & 15.5 \\
9 & NED,**INV,**WFU,**INV,**WFU,**INV,**WFU,**INV,**WFU,**CLO & 112.0 & 281.4 & 91.2 & 117.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Anomalous paths in the MongoDB project (bug issues). some randomly repeated states. Among the 10 paths with the highest issue coverage (in total 95.5%), only 2 comprised the _Reopen_ state, and they covered less than 1% of all bugs. On the other hand, among the 33 single-issue paths, 85% comprised the _Reopen_ state. The repetition of the _Open_ state appeared in 7 paths (covering 0.9% issues) among all 78 paths (covering 6047 issues). Other anomalies were related to the repetition of _Resolved_x_ states with the same or diverse specification of \(\mathsf{x}\) (in most cases, _Resolved_fix_, and sometimes the suffix _fix_ was replaced by _duplicate, not a problem_, or _rejected_). They appeared mostly in low-coverage paths (20.5% paths), thus handling of 1.1% issues.