Fig 1.
Stage A), Method evaluation. Here, to verify the performance of the proposed algorithm, three datasets were used: 1- a multilayer network constructed from a generated artificial modular single-network (created through a modular single-network generation algorithm, see S1 Appendix), 2- a multilayer network simulated from a synthetic modular single-network provided by the Graph Challenge data repository, and 3- a real social multilayer network published by Rossi et al. [57], based on five social interconnections (Facebook, lunch, coauthor, leisure, and work). The multilayer simulation algorithm in cases 1 and 2 was described in S1 Appendix. In all these three multilayer datasets, gold-standard communities were specified previously. For every dataset, the original multilayer and the aggregated single-layer network is used by methods PLCDM and ML-LCD (multilayer-specific), and Seed-Set-Expansion (single-layer-specific) to explore communities. Stage B), Application of the PLCDM on a reconstructed two-layer network of the colon adenocarcinoma (COAD).
Fig 2.
Demo of community detection procedure.
(A) Extraction of a community using the information share (z-score) extent of vertices. (B) Random walk with random restart process from a seed node in a typical multilayer network.
Table 1.
Applied evaluation measures.
Table 2.
Topological properties of multilayer networks employed in the study.
Fig 3.
PLCDM performance in comparison with other methods ML-LCD and seed-set-expansion.
Using Multilayer3 dataset (real data for social connections), in the predefined ground-truth communities, every node was selected as the seed node, and using three local community detection methods (PLCDM, ML-LCD, and Seed-Set-Expansion) result community was predicted for that selected seed. Then, the predicted community of each method was compared to the original ground-truth community and evaluated using eight metrics. As demonstrated, except Recall, in all measures PLCDM has better results. Notably, the false discovery rate of PLCDM is smaller than the other two methods. Every boxplot demonstrates the values gained by a method in this iterative process. Therefore their inter-quartile range and their average are comparable.
Table 3.
Evaluating PLCDM the Multilayer1 data.
Table 4.
Assessing PLCDM using the Multilayer2 data.
Table 5.
Comparison of PLCDM with other methods based on the Multilayer3 data.
Fig 4.
Global vs. Here, a synthetic multilayer network of containing 25 nodes in three layers and two modules of size five ({0,1,2,3,4} and {5,6,7,8,9}), as gold-standard modules, were used to compare global versus local community detection methods. A) The original single-layer modular graph and its ground-truth communities. B) The aggregated network of multilayer in which communities were unfolded by the main Lovain algorithm. C) The PLCDM method were applied on seed nodes {1, 7} in two separate executions. For every seed node, the detected module is matched with the ground-truth one. D) The global method, generalized Louvain (gLouvain), applied to the network, and six modules of different sizes were extracted. E) The multilayer Infomap, applied to the network and global communities were disclosed.
Table 6.
Biased random walk on a typical multilayer network versus its aggregated network.
Fig 5.
Pathway enrichment result of explored module around the seed gene HMMR.
Fig 6.
Pathway enrichment result of explored module around the seed gene ECT2.