This paper compares recent approaches to community structure identification in complex networks, focusing on their sensitivity and computational cost. The authors revisit the modularity measure and evaluate the performance of various methods on ad hoc networks with known community structures. They find that more accurate methods tend to be more computationally expensive, and both aspects are important when choosing a method for practical applications. The study proposes a standard benchmark test for community detection methods. The paper discusses the challenges of community detection in large networks, where the number of communities is often unknown and may be hierarchical. It reviews the graph bipartitioning problem and its relation to community detection. The authors compare different methods based on their sensitivity and computational cost, using ad hoc networks with known community structures. They propose a more accurate measure of algorithm sensitivity based on information theory, the normalized mutual information measure. The study evaluates the performance of various methods on networks with different levels of community diffusion, measured by the ratio of external links to total links. It shows that most methods perform well for low levels of community diffusion, but some methods struggle as the diffusion increases. The computational cost of different methods is also analyzed, showing that faster methods are often less accurate, while slower methods are more accurate. The authors suggest that the choice of algorithm depends on the specific application, balancing accuracy and computational cost. For small networks, more accurate methods are preferred, while for larger networks, faster methods are more suitable. The paper concludes that finding a method that is both accurate and fast is challenging, and further research is needed to develop such methods.This paper compares recent approaches to community structure identification in complex networks, focusing on their sensitivity and computational cost. The authors revisit the modularity measure and evaluate the performance of various methods on ad hoc networks with known community structures. They find that more accurate methods tend to be more computationally expensive, and both aspects are important when choosing a method for practical applications. The study proposes a standard benchmark test for community detection methods. The paper discusses the challenges of community detection in large networks, where the number of communities is often unknown and may be hierarchical. It reviews the graph bipartitioning problem and its relation to community detection. The authors compare different methods based on their sensitivity and computational cost, using ad hoc networks with known community structures. They propose a more accurate measure of algorithm sensitivity based on information theory, the normalized mutual information measure. The study evaluates the performance of various methods on networks with different levels of community diffusion, measured by the ratio of external links to total links. It shows that most methods perform well for low levels of community diffusion, but some methods struggle as the diffusion increases. The computational cost of different methods is also analyzed, showing that faster methods are often less accurate, while slower methods are more accurate. The authors suggest that the choice of algorithm depends on the specific application, balancing accuracy and computational cost. For small networks, more accurate methods are preferred, while for larger networks, faster methods are more suitable. The paper concludes that finding a method that is both accurate and fast is challenging, and further research is needed to develop such methods.