We were briefly brainstormed how IOU debt network can be represented on the blockchain and how it can be embedded into a mining process in the previous two blogs: debt graph and mining. We can extend the model with trust lines as well, meaning that the IOU network can be optimized and a new IOU can be issued only if there is an existing trust line between two participants. Trust line can be represented again with a matrix T, where
T[i,j] = 1 if participant i trusts participant j
It is an open question what further properties shall a trust matrix have. As an example, it might be reflexive and or transitive:
reflexive: if T[i,j] = 1 then T[j,i] =1 as well
transitive: if T[i,j] = 1 and T[j,k] = 1 then T[i,k] = 1
Having a trust matrix means that there is the possibility to issue a credit or to optimize a relationship between i an j if and only if T[i,j] = 1. Certainly, it is pretty much an open question what should happen if a trust line can be deleted as well.
