### Next, of the W-CPM method and four popular

Next, we compare the quality of found communities of the six overlapping community detection algorithms in terms of NMI. To this end, another three sets of LFR networks are generated by tuning the mixing parameter ?, the fraction of overlapping nodes on, and the number of communities each node belongs to om, respectively. These three sets of LFR networks are used to test the in?uence of community structure, overlapping density, and overlapping diversity on the performance of the W-CPM. For the mixing parameter ?, the larger the value of ?, the more unclear the community structure of LFR networks. An LFR network is considered to hold a clear community structure when ? ? 0.5, and an unclear community structure in case ?>0.5. We need toFig. 5. Runtime(s) of the W-CPM method and four popular overlapping community detection algorithms that are not based on clique percolation theory. (a) Runtime(s) on large-scale synthetic networks with different sizes. (b) Runtime(s) on large-scale synthetic networks with different average degrees. These synthetic networks have the same setting as those in Fig. 4.stress that the unclear community structure does not mean that the community structure can not be de?ned for LFR networks. For given network size and maximum community size, we can generate LFR networks with well-de?ned communitystructure for all values of mixing parameter with ?<0.9 63. To further verify the performance of W-CPM on different community sizes and network sizes, each set of LFR networks consists of four groups of networks, i.e., smaller network size and smaller community size (n = 10000, cmin = 10, cmax = 50), smaller network size and larger community size (n = 10000, cmin = 20, cmax = 100), larger network size and smaller community size (n = 50000, cmin = 10, cmax = 50), and larger network size and larger community size (n = 50000, cmin = 20, cmax = 100). The remaining parameters are ?xed and set as follows. The average degree d = 10, the maximum degree dmax = 50, the average clustering coef?cient c=0.7, and the exponents of the power- law distribution of node degrees ?1 and community sizes ?2 are 2 and 1, respectively. The parameters adopted in the above three sets of LFR networks are set according to those recommended in 19. Note that we only present the quality of communities found by SCP in the following experiments, since for a given network SCP and Reid's algorithm always detect an identical result and the only difference between them is their computational ef?ciency