# Exploring Data Model Relations in OpenStreetMap
## 4 Experimental Analysis
### Relation Analysis
#### 4.2.3 Membership Size of Relations  
The previous subsection concentrated on the composition of super-relations. However, in reality, these super-relations and relations with a large number of members are for the most part in the minority. Upon a deeper inspection of the membership size of relations in all of our four cities, we found that the actual distribution of membership size for relations is very heavily skewed towards relations with 10 or fewer members. Considering relations with 10 or less members we find that there are 1377 (74.35%) in Zurich, 5445 (85.03%) in Madrid, 7655 (83.40%) in Vienna and 11,902 (89.81%) in Rome. When we extend this to relations with 20 members or fewer we observe only a small increase in the relative percentages. These are 1462 (78.92%) in Zurich, 5582 (87.17%) in Madrid, 7911 (86.20%) in Vienna and 12,133 (91.73%) in Rome. This is an important result, as it reinforces the advice from the OSM Wiki which advocates keeping the number of members within any relation to a managable number. In Figure 2, we provide charts for the distribution of membership size of relations where the number of relations are 10 or less. The distributions are remarkably similar with all of the four cities displaying very dense clustering around membership size of two and three members. However, no strong patterns emerge. We speculate anecdotally the clustering around membership size of two or three members maybe related in some way to the experience levels of the contributors or the advice from the OSM Wiki on maintaining relations with a manageable number of members. This issue will need to be investigated further.  
In each of the four cities, we found a small number of relations containing only a single member. While this is a valid relation in OSM and by our definition in Section 3, it may not be correct in reality and may be the result of an erroneous interpretation of what relations actually represent. There are  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**CITY** & **N** & **W** & **R** & **N + W** & **W + R** & **N + R** & **N + W + R** \\ \hline Madrid \# & 290 & 3519 & 288 & 2256 & 26 & 3 & 21 \\ Madrid \% & 4.53 & **54.96** & 4.5 & **35.23** & 0.41 & 0.05 & 0.33 \\ Rome \# & 76 & 8146 & 411 & 4576 & 10 & 3 & 4 \\ Rome \% & 0.57 & **61.59** & 3.11 & **34.60** & 0.08 & 0.02 & 0.03 \\ Vienna \# & 217 & 6073 & 251 & 2588 & 16 & 1 & 31 \\ Vienna \% & 2.36 & **66.18** & 2.74 & **28.2** & 0.17 & 0.01 & 0.34 \\ Zurich \# & 89 & 600 & 115 & 1015 & 5 & 1 & 30 \\ Zurich \% & 4.8 & **32.35** & 6.2 & **54.72** & 0.27 & 0.05 & 1.62 \\ \hline \end{tabular}
\end{table}
Table 2: Composition of relations in the four cities based on the data objects of their members.  
48 of these single member relations in Vienna, 61 in Madrid, 69 in Zurich and 199 in Rome. It might be useful that contributors to OSM in these cities inspect these single member relations in order to ascertain if there is corrective action needed. In the case of Zurich, the majority of these relations have type=public_transport, while, in the case of three other cities, the dominant type of relation has the tag type=multipolygon.