The paper "Modularity from Fluctuations in Random Graphs and Complex Networks" by Roger Guimerà, Marta Sales-Pardo, and Luís A. Nunes Amaral explores the mechanisms by which modularity emerges in complex networks. The authors show that finding the modularity of a network is analogous to finding the ground-state energy of a spin system, and demonstrate that stochastic network models, such as random graphs and scale-free networks, can give rise to modular structures due to fluctuations in the establishment of links. They provide both numerical and analytical evidence that these networks have high modularity, which is magnified by the large number of ways a network can be partitioned into modules. The paper also discusses the implications of these findings for defining statistically significant modularity in complex networks, emphasizing the need to compare modularity to the null case of a random graph. The results highlight the role of fluctuations in the emergence of modularity and provide a framework for understanding and quantifying it in various network models.The paper "Modularity from Fluctuations in Random Graphs and Complex Networks" by Roger Guimerà, Marta Sales-Pardo, and Luís A. Nunes Amaral explores the mechanisms by which modularity emerges in complex networks. The authors show that finding the modularity of a network is analogous to finding the ground-state energy of a spin system, and demonstrate that stochastic network models, such as random graphs and scale-free networks, can give rise to modular structures due to fluctuations in the establishment of links. They provide both numerical and analytical evidence that these networks have high modularity, which is magnified by the large number of ways a network can be partitioned into modules. The paper also discusses the implications of these findings for defining statistically significant modularity in complex networks, emphasizing the need to compare modularity to the null case of a random graph. The results highlight the role of fluctuations in the emergence of modularity and provide a framework for understanding and quantifying it in various network models.