Social network analysis is a popular tool to understand the relationships between interacting agents by studying the structural properties of their connections. However, this kind of analysis can miss some of the domain-specific knowledge available in the original information domain and its propagation through the associated network. In this work, we develop an extension of classical social network analysis to incorporate external information from the original source of the network. With this extension we propose a new centrality measure, the semantic value, and a new affinity function, the semantic affinity, that establishes fuzzy-like relationships between the different actors in the network. We also propose a new heuristic algorithm based on the shortest capacity problem to compute this new function. As an illustrative case study, we use the novel proposals to analyze and compare the gods and heroes from three different classical mythologies: 1) Greek; 2) Celtic; and 3) Nordic. We study the relationships of each individual mythology and those of the common structure that is formed when we fuse the three of them. We also compare our results with those obtained using other existing centrality measures and embedding approaches. In addition, we test the proposed measures on a classical social network, the Reuters terror news network, as well as in a Twitter network related to the COVID-19 pandemic. We found that the novel method obtains more meaningful comparisons and results than previous existing approaches in every case.