ABSTRACT
The payoff from modelling a social network with typed edges is that one can determine the structure of the complete ecosystem of individuals with all of their multiple relationship types. This new, enhanced graph will then be embedded, using a standard spectral embedding since it is just a conventional graph with cn nodes. It is possible that a node might have versions with no connections in a particular subgraph — they have no relationships of a particular kind. However, the addition of the vertical edges ensures that they are connected in the larger graph. The vertical edges model a kind of resistance associated with the differences between roles. Edge prediction uses proximity of two unconnected nodes as the basis for suggesting that the two individuals "should" or "might" have a relationship. To illustrate the power of the typed-edge representation, one can build the combined social network of Florentine families.
