5a. The figure shows the superiority of GANC in extracting clusters **of nodes from the same** categories. When sub-categories are employed for the assessment, the superiority of GANC becomes more pronounced.

![0_image_1.png](0_image_1.png)

![0_image_0.png](0_image_0.png)

Figure 5a alone does not provide a fair comparison as any singleton would have homogeneity proportion of 1. In Figure 5b, the homogeneity proportion **is plotted versus the size**
of the extracted clusters for the three algorithms.

The Blondel et al. algorithm produces clusters as small as 14 to as large as 250,000 nodes. However the largest homogeneous cluster that is extracted has 38 nodes. The quality of clusters degrade as the size of the clusters increase. This trend is very likely to be due to the resolution limit of modularity.

Both GANC and Dhillon-Guan-Kulis produce a very large cluster (the core cluster [60]).

Excluding the core, Dhillon-Guan-Kulis produces clusters of an average size of n/k **which is**
around 37,000 nodes in this example (See Figure 5b). This behavior of **the Dhillon-GuanKulis algorithm is due to the underlying region-growing procedure it adopts from Metis**
[17].

The clusters extracted by GANC are much smaller than the other two algorithms. Excluding the core, the cluster sizes are between 7 and 225. Similar to previous observations of Leskovec et al. [60], the strongly-connected clusters of the large graphs listed in Table 4 diminish in number as we move towards the center of the graph. Having a small homogeneity proportion is then expected for the core as it includes several clusters that are not very well-connected and are lumped together. If we study a clustering that is in a lower level in the hierarchy, further clusters would be extracted from the core and the core shrinks. The resulting clusters are not as well-connected in terms of NAssoc though. In other words, the most isolated and well-connected clusters are extracted at the higher levels of the hierarchy.