This paper by Erzsébet Ravasz and Albert-László Barabási explores the hierarchical organization in complex networks. It shows that many real networks, such as the World Wide Web, actor network, and semantic web, exhibit two key properties: scale-free topology and high clustering. These properties are attributed to a hierarchical structure, where small groups of nodes organize into larger groups while maintaining a scale-free topology. The clustering coefficient of different groups follows a strict scaling law, which can be used to identify hierarchical organization in real networks. The paper discusses the differences between scale-free networks and random networks, noting that scale-free networks have a power-law degree distribution, while random networks have an exponential distribution. It also highlights that many real networks, including metabolic networks and protein interaction networks, exhibit both scale-free and high clustering properties. The authors propose a hierarchical network model that combines scale-free topology with high clustering. This model is constructed by iteratively replicating and connecting smaller modules, resulting in a network with a hierarchical structure. The model shows that the clustering coefficient follows a scaling law, C(k) ~ k^{-1}, which is not observed in traditional scale-free or random network models. The paper also examines real networks to test the presence of hierarchical organization. It finds that several real networks, including the actor network, language network, and Internet at the domain level, exhibit the scaling law C(k) ~ k^{-1}, indicating a hierarchical structure. In contrast, networks such as the power grid and router-level Internet do not follow this scaling law, suggesting a lack of hierarchical organization. The authors also discuss a stochastic model that can generate different scaling exponents for the clustering coefficient, depending on the parameters of the model. This model shows that the scaling of the clustering coefficient is not unique to the hierarchical network model but can be observed in other growing network models. The paper concludes that hierarchical organization is a fundamental characteristic of many complex networks. It provides a new perspective on the topology of complex networks, showing that the presence of a hierarchical structure can explain both the scale-free topology and high clustering coefficient observed in real networks. The hierarchical structure also has implications for the role of hubs in complex networks, as hubs play a key role in connecting different communities within the network.This paper by Erzsébet Ravasz and Albert-László Barabási explores the hierarchical organization in complex networks. It shows that many real networks, such as the World Wide Web, actor network, and semantic web, exhibit two key properties: scale-free topology and high clustering. These properties are attributed to a hierarchical structure, where small groups of nodes organize into larger groups while maintaining a scale-free topology. The clustering coefficient of different groups follows a strict scaling law, which can be used to identify hierarchical organization in real networks. The paper discusses the differences between scale-free networks and random networks, noting that scale-free networks have a power-law degree distribution, while random networks have an exponential distribution. It also highlights that many real networks, including metabolic networks and protein interaction networks, exhibit both scale-free and high clustering properties. The authors propose a hierarchical network model that combines scale-free topology with high clustering. This model is constructed by iteratively replicating and connecting smaller modules, resulting in a network with a hierarchical structure. The model shows that the clustering coefficient follows a scaling law, C(k) ~ k^{-1}, which is not observed in traditional scale-free or random network models. The paper also examines real networks to test the presence of hierarchical organization. It finds that several real networks, including the actor network, language network, and Internet at the domain level, exhibit the scaling law C(k) ~ k^{-1}, indicating a hierarchical structure. In contrast, networks such as the power grid and router-level Internet do not follow this scaling law, suggesting a lack of hierarchical organization. The authors also discuss a stochastic model that can generate different scaling exponents for the clustering coefficient, depending on the parameters of the model. This model shows that the scaling of the clustering coefficient is not unique to the hierarchical network model but can be observed in other growing network models. The paper concludes that hierarchical organization is a fundamental characteristic of many complex networks. It provides a new perspective on the topology of complex networks, showing that the presence of a hierarchical structure can explain both the scale-free topology and high clustering coefficient observed in real networks. The hierarchical structure also has implications for the role of hubs in complex networks, as hubs play a key role in connecting different communities within the network.