tells us nothing more than this.

Identity grade matrix {#identity-grade-matrix .unnumbered}
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Suppose the grade matrix $A$ is the identity matrix. That is, each agent gives themselves the maximum grade 1, and every other agent the minimum grade 0. Now an eigenvector of $A$, and the PeerRank solution assigns each agent with the average grade $\frac{1}{m}$. Again, this is what we might expect. The grade matrix tells us nothing more than all agents are symmetric, and so dividing the mark between them might seem reasonable.

Bivalent grade matrices {#bivalent-grade-matrices .unnumbered}
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Suppose that agents partition into two types: good and bad. The good agents give a grade of 1 to other good agents, and 0 to bad agents. The bad agents gives a grade of 1 to every agent. In each iteration of the PeerRank method, the grades of the good agents remain unchanged at 1. On the other hand, the grades of the bad agents monotonically decrease towards their fixed point at 0. We also get the same fixed point if the bad agents give a grade of 0 to every agent besides themselves (irrespective of the grade that they give themselves). Again, this is what we might expect. 