Imagine a network in which nodes are connected by links representing different kinds of connections.
Example: Alice and Bob transact financially with each other, so they are connected by a "transaction link". Bob and Carol both belong to the same sports club, so they are connected by a "club link".
From a graph theoretic perspective with Alice, Bob, and Carol as nodes, edge colouring would seem to be one way of thinking about this, yet my very shallow research seems to indicate that edge colouring is primarily concerned with edge colouring theorems and algorithms. I am more interested in using these different kinds of edges to analyse the graph in the sense of network science.
What is the correct framework or body of literature for thinking about the single network which includes Alice, Bob, and Carol, while preserving the different types of connections that they have?