This paper introduces two new concepts for analyzing weighted complex networks: subgraph intensity and coherence. Subgraph intensity is defined as the geometric mean of the weights of a subgraph, while coherence is the ratio of the geometric mean to the arithmetic mean of the weights. These measures allow for the generalization of motif scores and the clustering coefficient to weighted networks. The authors apply these concepts to financial and metabolic networks, demonstrating that incorporating weights can significantly alter conclusions drawn from unweighted network analysis. The paper discusses the importance of considering interaction strengths in network analysis, as weights can represent various types of interactions, such as transportation fluxes, reaction fluxes, or measurement noise. The authors propose a method for calculating the intensity and coherence of subgraphs, which can be used to identify motifs with statistically significant deviations from a reference system. The paper also introduces a weighted clustering coefficient, which is derived from the unweighted clustering coefficient by replacing the number of triangles with the sum of triangle intensities. This coefficient is shown to be more sensitive to changes in network structure than the unweighted version, as demonstrated in the analysis of a financial network. The weighted clustering coefficient is able to detect the effects of a market crash, which is not clearly visible in the unweighted version. In the analysis of a directed metabolic network, the authors show that incorporating weights into network motifs can significantly change the conclusions drawn from their statistics. The results indicate that the weighted clustering coefficient is more effective in capturing the dynamics of complex systems compared to unweighted measures. The paper concludes that the introduction of intensity and coherence measures provides a more comprehensive understanding of weighted complex networks, allowing for a more accurate analysis of network structure and dynamics. The authors emphasize the importance of considering weights in network analysis, as they can significantly influence the interpretation of network characteristics.This paper introduces two new concepts for analyzing weighted complex networks: subgraph intensity and coherence. Subgraph intensity is defined as the geometric mean of the weights of a subgraph, while coherence is the ratio of the geometric mean to the arithmetic mean of the weights. These measures allow for the generalization of motif scores and the clustering coefficient to weighted networks. The authors apply these concepts to financial and metabolic networks, demonstrating that incorporating weights can significantly alter conclusions drawn from unweighted network analysis. The paper discusses the importance of considering interaction strengths in network analysis, as weights can represent various types of interactions, such as transportation fluxes, reaction fluxes, or measurement noise. The authors propose a method for calculating the intensity and coherence of subgraphs, which can be used to identify motifs with statistically significant deviations from a reference system. The paper also introduces a weighted clustering coefficient, which is derived from the unweighted clustering coefficient by replacing the number of triangles with the sum of triangle intensities. This coefficient is shown to be more sensitive to changes in network structure than the unweighted version, as demonstrated in the analysis of a financial network. The weighted clustering coefficient is able to detect the effects of a market crash, which is not clearly visible in the unweighted version. In the analysis of a directed metabolic network, the authors show that incorporating weights into network motifs can significantly change the conclusions drawn from their statistics. The results indicate that the weighted clustering coefficient is more effective in capturing the dynamics of complex systems compared to unweighted measures. The paper concludes that the introduction of intensity and coherence measures provides a more comprehensive understanding of weighted complex networks, allowing for a more accurate analysis of network structure and dynamics. The authors emphasize the importance of considering weights in network analysis, as they can significantly influence the interpretation of network characteristics.