This paper presents a study of complex weighted networks, focusing on the scientific collaboration network and the worldwide air-transportation network. These networks are characterized by their complex topological structures and heterogeneous connection strengths. The authors introduce new metrics that combine topological and weighted properties to better characterize the statistical properties and heterogeneity of the network. These metrics allow for the investigation of correlations between weighted quantities and the underlying topological structure of the network. The scientific collaboration network is analyzed using the number of co-authored papers between scientists, while the air-transportation network is analyzed using the number of available seats on flights between airports. The authors define metrics such as vertex strength, which measures the total weight of connections for each node, and weighted clustering coefficients, which measure the local cohesiveness of a node based on the weights of its connections. The study reveals that the strength of nodes in both networks is highly skewed, with a heavy-tailed distribution. The strength of a node is found to be proportional to its degree in the absence of correlations between the weights of edges and the degrees of nodes. However, in the air-transportation network, the strength of nodes grows faster than their degree, indicating a strong correlation between the weight and the topological properties of the network. The authors also analyze the average weight of connections between nodes and find that in the air-transportation network, the average weight is proportional to the product of the degrees of the connected nodes. This indicates an assortative mixing behavior, where high-degree nodes are more likely to be connected to other high-degree nodes. The study also examines the structural organization of weighted networks, finding that different degree classes exhibit different properties in the local connectivity structure. The authors introduce new metrics that combine topological information with the weight distribution of the network, providing a more comprehensive understanding of the network's architecture. The results show that the weighted clustering coefficient is larger than the topological clustering coefficient in the air-transportation network, indicating that interconnected triples are more likely to be formed by edges with larger weights. In the scientific collaboration network, the weighted clustering coefficient is close to the topological one, indicating that group collaborations tend to be stable and determine the average intensity of interactions in the network. Overall, the study highlights the importance of considering both topological and weighted properties in the analysis of complex networks, providing a more accurate characterization of their structure and organization.This paper presents a study of complex weighted networks, focusing on the scientific collaboration network and the worldwide air-transportation network. These networks are characterized by their complex topological structures and heterogeneous connection strengths. The authors introduce new metrics that combine topological and weighted properties to better characterize the statistical properties and heterogeneity of the network. These metrics allow for the investigation of correlations between weighted quantities and the underlying topological structure of the network. The scientific collaboration network is analyzed using the number of co-authored papers between scientists, while the air-transportation network is analyzed using the number of available seats on flights between airports. The authors define metrics such as vertex strength, which measures the total weight of connections for each node, and weighted clustering coefficients, which measure the local cohesiveness of a node based on the weights of its connections. The study reveals that the strength of nodes in both networks is highly skewed, with a heavy-tailed distribution. The strength of a node is found to be proportional to its degree in the absence of correlations between the weights of edges and the degrees of nodes. However, in the air-transportation network, the strength of nodes grows faster than their degree, indicating a strong correlation between the weight and the topological properties of the network. The authors also analyze the average weight of connections between nodes and find that in the air-transportation network, the average weight is proportional to the product of the degrees of the connected nodes. This indicates an assortative mixing behavior, where high-degree nodes are more likely to be connected to other high-degree nodes. The study also examines the structural organization of weighted networks, finding that different degree classes exhibit different properties in the local connectivity structure. The authors introduce new metrics that combine topological information with the weight distribution of the network, providing a more comprehensive understanding of the network's architecture. The results show that the weighted clustering coefficient is larger than the topological clustering coefficient in the air-transportation network, indicating that interconnected triples are more likely to be formed by edges with larger weights. In the scientific collaboration network, the weighted clustering coefficient is close to the topological one, indicating that group collaborations tend to be stable and determine the average intensity of interactions in the network. Overall, the study highlights the importance of considering both topological and weighted properties in the analysis of complex networks, providing a more accurate characterization of their structure and organization.