# Automatic Detection of Multilevel Communities: Scalable, Selective and Resolution-Limit-Free +
## 2 Method
### Applications to Real-World Networks
Figure 7: _Cont._  
The last network we study in this section is the American college football network (for short, we will call it the \"football network\"); it was constructed from the schedule of the Division I games of the 2000 season of United States college football [2]. This network consists of 115 nodes representing 115 college football teams, distinguished by their college names. Among all teams, 107 were affiliated with 11 different conferences each containing 6 to 13 teams, and the rest 8 teams were independent of any conference. Edges of the network represent scheduled games between the connected teams during the 2000 season, which turned out to be much more frequent between teams of the same conference than between those of different conferences. Since [PERSON] and [PERSON] firstly recreated the conference assignments correctly for most teams with their algorithm in 2002 [2], the football network has been cited and investigated repeatedly in community detection literature. However, in 2010, [PERSON] pointed out there was a serious error in [PERSON]'s and [PERSON]'s metadata recorded in Figure 5 of [2]: the conference assignments for those teams seemed to be collected during the 2001 season rather than the 2000 season [55; 66]. In Figure 8a, we exhibit the conference assignments corrected by [PERSON] in Appendix C2 of [66] with nodes of different colors; especially, independent teams are denoted by red hexagons. We also annotate the corresponding name of the conference beside each group of nodes. For comparison, we exhibit in Supplementary Figure S7 the metadata of [PERSON]'s and [PERSON]'s [2]; validity of the metadata has been demonstrated in [66]. With our method, we also detect multilevel communities in the football network, see Figure 8b,c for the plateaus. Among them, the strongest plateau suggests a 12-community division, which is naturally displayed in Figure 8a with edges inside communities being shorter than those between different communities. Obviously, our division perfectly recovers the members for all 11 conferences: teams of the same conference are all classified into the same community. As for the 8 independent teams, 5 of them have been put into an individual community (\"Independents\" in Figure 8a), and the other 3 are assigned to two conferences that they played most of their games with. [PERSON]'s and [PERSON]'s division agrees with ours, except only one node (node 37, representing team \"Central Florida\") is assigned to conference \"Mid America\" [2], which, to our viewpoint, is only a minor difference. Figure 7: Communities in the dolphins’ network. (**a**) [PERSON] and [PERSON]’s divisions. The whole population is firstly divided into two major groups (rectangles and ellipses, separated by the dashed line), then ellipses can be further divided into four small communities shown in different colors (cyan, purple, red and turquoise). (**b**) Our divisions. The whole population can be divided into either two communities (rectangles and ellipses, on opposite sides of the dashed line), or seven small communities shown in different colors (blue, orange, cyan, red, turquoise, green and purple). For better visibility, in both (**a,b**) we enclose the small communities shown in different colors in dashed boxes. (**c,d**) Plateaus drawn in the same way as Figure 6c,d. Apparently, detection \"errors\" observed in Supplementary Figure S7, as well as those reported by [PERSON] and [PERSON] in [2], are both due to the errors in the metadata [66], rather than the failure of the community detection algorithms [55]. Figure 8: Communities in the American college football network. (**a**) Structure of the network: 115 nodes represent 115 American college football teams, and edges between them denote scheduled games between these teams. Except 8 independent teams (denoted by the red hexagons), other teams are all affiliated with 11 different conferences. We show teams of different conferences by nodes of different colors, and display our 12-community division by naturally separated clusters.