Fig. 9

Example of an instance where the Louvain method performs better due to more balanced partitions. The (least resolved) tree \((T,\sigma )\) explains the BMG \((\vec {G}_\text {orig},\sigma )\) with vertex set V. The graph \(H_\text {orig}=[{\mathcal {R}}(\vec {G}_\text {orig},\sigma ), V]\) is the Aho graph corresponding to the informative triple set \({\mathcal {R}}(\vec {G}_\text {orig},\sigma )\). The perturbed digraph \((\vec {G},\sigma )\) is obtained from \((\vec {G}_\text {orig},\sigma )\) by inserting the arcs \((b_3,a_1)\), \((c_2,a_1)\), and \((c_2, b_1)\) and deletion of \((a_1,b_2)\). The corresponding Aho graph \(H=[{\mathcal {R}}(\vec {G},\sigma ), V]\) is connected because the perturbation introduced the additional informative triple \(c_2b_1|b_2\). The green and pink frames correspond to the partitions \({\mathcal {V}}_1\) and \({\mathcal {V}}_2\) of V constructed by the methods Louvain (c) and MinCut, respectively