The paper introduces the rich-club phenomenon in complex networks, where high-degree nodes (hubs) are more interconnected than low-degree nodes. It provides an analytical expression for the rich-club coefficient, ϕ(k), which quantifies the fraction of edges among high-degree nodes relative to the maximum possible. The coefficient is used to detect structural ordering in networks, distinguishing between random and structured networks. The paper also discusses the difference between rich-club ordering and assortative mixing, showing that they are not necessarily related. The analysis is applied to real-world networks, including biological, social, and technological systems. The results show that the rich-club coefficient increases with degree in many networks, indicating the presence of rich-club ordering. However, this increase is not always indicative of the phenomenon, as random networks also exhibit similar behavior. To address this, the paper introduces normalization ratios, ρ_unc(k) and ρ_ran(k), which compare the observed rich-club coefficient to those of uncorrelated and maximally random networks, respectively. These ratios help distinguish between true rich-club ordering and random effects. The study finds strong rich-club ordering in the Scientific Collaboration Network, where highly connected scientists form tightly interconnected groups. In contrast, the Protein Interaction Network shows no rich-club ordering, suggesting that highly connected proteins are not tightly interconnected. The Internet at the Autonomous System level also lacks rich-club ordering, indicating that hubs are not densely interconnected. The paper also discusses the extension of the rich-club concept to weighted networks, where the strength of connections is considered instead of degree. The analysis provides a framework for quantitatively assessing the rich-club phenomenon in complex networks, enabling the evaluation of network structure and function in various domains. The results highlight the importance of considering both structural and functional properties in understanding network behavior.The paper introduces the rich-club phenomenon in complex networks, where high-degree nodes (hubs) are more interconnected than low-degree nodes. It provides an analytical expression for the rich-club coefficient, ϕ(k), which quantifies the fraction of edges among high-degree nodes relative to the maximum possible. The coefficient is used to detect structural ordering in networks, distinguishing between random and structured networks. The paper also discusses the difference between rich-club ordering and assortative mixing, showing that they are not necessarily related. The analysis is applied to real-world networks, including biological, social, and technological systems. The results show that the rich-club coefficient increases with degree in many networks, indicating the presence of rich-club ordering. However, this increase is not always indicative of the phenomenon, as random networks also exhibit similar behavior. To address this, the paper introduces normalization ratios, ρ_unc(k) and ρ_ran(k), which compare the observed rich-club coefficient to those of uncorrelated and maximally random networks, respectively. These ratios help distinguish between true rich-club ordering and random effects. The study finds strong rich-club ordering in the Scientific Collaboration Network, where highly connected scientists form tightly interconnected groups. In contrast, the Protein Interaction Network shows no rich-club ordering, suggesting that highly connected proteins are not tightly interconnected. The Internet at the Autonomous System level also lacks rich-club ordering, indicating that hubs are not densely interconnected. The paper also discusses the extension of the rich-club concept to weighted networks, where the strength of connections is considered instead of degree. The analysis provides a framework for quantitatively assessing the rich-club phenomenon in complex networks, enabling the evaluation of network structure and function in various domains. The results highlight the importance of considering both structural and functional properties in understanding network behavior.