Hmark14. They measured the accuracy of algorithms and studied the properties of the LFR benchmark graphs. Later, Peel applied two algorithms on both weighted and unweighted networks with 100 nodes and examined the performance of algorithms developed for weighted networks against those for unweighted ones for different parts of the problem space17. Recently, Hric et al. compared the accuracy of eleven different algorithms on both the LFR benchmark and a collection of real world graphs with sizes vary from 34 to 5189809 nodes18. Overall, as an extension of the GN benchmark, the LFR has drawn a lot of attention: Early, researchers employed small artificial and/or real world networks as benchmarks (e.g. the GN benchmark and the Zachary’s karate club network); while nowadays people shifted towards the use of large stylised large artificial or real world networks with some kind of ground truth obtained from metadata information (e.g. the LFR benchmark and the DBLP collaboration network19). However, as of today, a detailed study of the dependency with the network size is missing as most of the PD-148515 chemical information existing. Here k iextand k itotScientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/studies include a few, selected, set of values of the number of nodes and the mixing parameter, and do not consider the real computing time needed to perform the analysis. In this paper, we evaluate eight different state-of-the-art community detection algorithms available in the “igraph” package20, which is a widely used collection of network analysis tools in R, Python, C and C++, on the LFR benchmark for undirected, unweighted graphs with non-overlapping communities. Details of the algorithms can be found in the methods section. Our contribution is threefold: First and foremost, we provide actual techniques to GW 4064 web determine which is the most suited algorithm in most circumstances based on observable properties of the network under consideration. Secondly, we use the mixing parameter as an easily measurable indicator of finding the ranges of reliability of the different algorithms. Finally, we systematically study the dependency with network size focusing on both the algorithm’s predicting power and the effective computing time. In this section, we compare the results of community detection algorithms in terms of accuracy and computing time. The former is defined as a measure of similarity between the modular structure generated by the LFR benchmark (see Methods Section) and the partition identified by the respective community detection algorithms . The latter is the real computing time needed to perform the community detection. This section is organised as follows: First, by employing the LFR generative model, we unveil the relationship between the mixing parameter and the accuracy of the community detection algorithms. Accuracy is measured in two different, complementary ways: The normalised mutual information8, and the ratio between the number of detected communities and the number of communities given by the LFR generating model. Then, we measure the computing time of community detection algorithms and show the relationship between the mixing parameter and the computing time. We then present the mixing parameter as computed from the communities detected by the different algorithms as a function of the input mixing parameter. Last, we present the comparisons of community detection algorithms in terms of accuracy and computing time as a functi.Hmark14. They measured the accuracy of algorithms and studied the properties of the LFR benchmark graphs. Later, Peel applied two algorithms on both weighted and unweighted networks with 100 nodes and examined the performance of algorithms developed for weighted networks against those for unweighted ones for different parts of the problem space17. Recently, Hric et al. compared the accuracy of eleven different algorithms on both the LFR benchmark and a collection of real world graphs with sizes vary from 34 to 5189809 nodes18. Overall, as an extension of the GN benchmark, the LFR has drawn a lot of attention: Early, researchers employed small artificial and/or real world networks as benchmarks (e.g. the GN benchmark and the Zachary’s karate club network); while nowadays people shifted towards the use of large stylised large artificial or real world networks with some kind of ground truth obtained from metadata information (e.g. the LFR benchmark and the DBLP collaboration network19). However, as of today, a detailed study of the dependency with the network size is missing as most of the existing. Here k iextand k itotScientific RepoRts | 6:30750 | DOI: 10.1038/srepwww.nature.com/scientificreports/studies include a few, selected, set of values of the number of nodes and the mixing parameter, and do not consider the real computing time needed to perform the analysis. In this paper, we evaluate eight different state-of-the-art community detection algorithms available in the “igraph” package20, which is a widely used collection of network analysis tools in R, Python, C and C++, on the LFR benchmark for undirected, unweighted graphs with non-overlapping communities. Details of the algorithms can be found in the methods section. Our contribution is threefold: First and foremost, we provide actual techniques to determine which is the most suited algorithm in most circumstances based on observable properties of the network under consideration. Secondly, we use the mixing parameter as an easily measurable indicator of finding the ranges of reliability of the different algorithms. Finally, we systematically study the dependency with network size focusing on both the algorithm’s predicting power and the effective computing time. In this section, we compare the results of community detection algorithms in terms of accuracy and computing time. The former is defined as a measure of similarity between the modular structure generated by the LFR benchmark (see Methods Section) and the partition identified by the respective community detection algorithms . The latter is the real computing time needed to perform the community detection. This section is organised as follows: First, by employing the LFR generative model, we unveil the relationship between the mixing parameter and the accuracy of the community detection algorithms. Accuracy is measured in two different, complementary ways: The normalised mutual information8, and the ratio between the number of detected communities and the number of communities given by the LFR generating model. Then, we measure the computing time of community detection algorithms and show the relationship between the mixing parameter and the computing time. We then present the mixing parameter as computed from the communities detected by the different algorithms as a function of the input mixing parameter. Last, we present the comparisons of community detection algorithms in terms of accuracy and computing time as a functi.

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