-linear scale. Different colours refer to different number of nodes: red (N = 233), green (N = 482), blue (N = 1000), black (N = 3583), cyan (N = 8916), and TAPI-2 cost purple (N = 22186). Please notice that the vertical axis might have different scale ranges. The vertical red line corresponds to the strong definition of community where = 0.5. The other parameters are described in Table 1.them presents the accuracy of a given community detection algorithms and is subdivided in two plots: one for the computed value of NMI and the upped sub-panel contains the standard deviation of the measures when repeated over 100 different network realisations. Most of the algorithms can well uncover the communities when ?0.2.Scientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/Figure 4. (Lower row) The mean value of the mixing parameter estimated by the community detection algorithms ?dependent on the mixing parameter . (upper row) The standard deviation of ?dependent on . Different colours refer to different number of nodes: red (N = 233), green (N = 482), blue (N = 1000), black (N = 3583), cyan (N = 8916), and purple (N = 22186). Please notice that the vertical axis on the subfigures might have different scale ranges. The vertical red line corresponds to the strong definition of community where = 0.5. The green line y = x corresponds to the case which ?= ? The other parameters are described in Table 1. In this case, the detecting abilities of Fastgreedy, Infomap, Label propagation, Multilevel, Walktrap, Spinglass and Edge betweenness algorithms are independent of network size (Panel (a,b,d ), Fig. 5). For Leading eigenvector, the accuracies decrease smoothly with network size (Panel (c), Fig. 5). For very large ?0.75, most of the algo-Scientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/Figure 5. (Lower row) The mean value of normalised mutual information dependent on the number of nodes N in the benchmark graphs on a linear-log scale. (upper row) The standard deviation of the normalised mutual information dependent on N on a linear-log scale. Different colours refer to different values of the mixing parameter: red ( = 0.03), green ( = 0.18), blue ( = 0.33), black ( = 0.48), cyan ( = 0.63), and purple ( = 0.75). Please notice that the vertical axis on the subfigures might have different scale ranges. The horizontal black dotted line corresponds to I = 1. Due to the computing speed, Spinglass and Edge betweenness algorithms have been tested only on CEP-37440 site networks with N 1000, and Infomap algorithm has been tested on networks with N 22186. The other parameters are described in Table 1.Scientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/rithms fail to detect the community structure except for the Walktrap and Edge betweenness algorithms and the accuracy barely depends on network size. In the intermediate region of , NMI is usually decreasing with network size and . Finally, we present the computing time as a function of the network size. The results are represented in Fig. 6 on a log-log scale. Each panel presents the computing time of a given community detection algorithms and is subdivided in two plots: one for the measured value of computing time in second and the upped sub-panel contains the standard deviation of the measures when repeated over different network realisations. In the log-log scale, there is a significant linear correlation between the computing time and the netwo.-linear scale. Different colours refer to different number of nodes: red (N = 233), green (N = 482), blue (N = 1000), black (N = 3583), cyan (N = 8916), and purple (N = 22186). Please notice that the vertical axis might have different scale ranges. The vertical red line corresponds to the strong definition of community where = 0.5. The other parameters are described in Table 1.them presents the accuracy of a given community detection algorithms and is subdivided in two plots: one for the computed value of NMI and the upped sub-panel contains the standard deviation of the measures when repeated over 100 different network realisations. Most of the algorithms can well uncover the communities when ?0.2.Scientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/Figure 4. (Lower row) The mean value of the mixing parameter estimated by the community detection algorithms ?dependent on the mixing parameter . (upper row) The standard deviation of ?dependent on . Different colours refer to different number of nodes: red (N = 233), green (N = 482), blue (N = 1000), black (N = 3583), cyan (N = 8916), and purple (N = 22186). Please notice that the vertical axis on the subfigures might have different scale ranges. The vertical red line corresponds to the strong definition of community where = 0.5. The green line y = x corresponds to the case which ?= ? The other parameters are described in Table 1. In this case, the detecting abilities of Fastgreedy, Infomap, Label propagation, Multilevel, Walktrap, Spinglass and Edge betweenness algorithms are independent of network size (Panel (a,b,d ), Fig. 5). For Leading eigenvector, the accuracies decrease smoothly with network size (Panel (c), Fig. 5). For very large ?0.75, most of the algo-Scientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/Figure 5. (Lower row) The mean value of normalised mutual information dependent on the number of nodes N in the benchmark graphs on a linear-log scale. (upper row) The standard deviation of the normalised mutual information dependent on N on a linear-log scale. Different colours refer to different values of the mixing parameter: red ( = 0.03), green ( = 0.18), blue ( = 0.33), black ( = 0.48), cyan ( = 0.63), and purple ( = 0.75). Please notice that the vertical axis on the subfigures might have different scale ranges. The horizontal black dotted line corresponds to I = 1. Due to the computing speed, Spinglass and Edge betweenness algorithms have been tested only on networks with N 1000, and Infomap algorithm has been tested on networks with N 22186. The other parameters are described in Table 1.Scientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/rithms fail to detect the community structure except for the Walktrap and Edge betweenness algorithms and the accuracy barely depends on network size. In the intermediate region of , NMI is usually decreasing with network size and . Finally, we present the computing time as a function of the network size. The results are represented in Fig. 6 on a log-log scale. Each panel presents the computing time of a given community detection algorithms and is subdivided in two plots: one for the measured value of computing time in second and the upped sub-panel contains the standard deviation of the measures when repeated over different network realisations. In the log-log scale, there is a significant linear correlation between the computing time and the netwo.
