The set of all relations $\alpha\subset X\times Y$ is a semiheap with respect to the ternary operation $[\alpha_1,\alpha_2,\alpha_3]=\alpha_1\alpha_2^{-1}\alpha_3$ ($\alpha^{-1}$ is $\alpha^{*}$in notation of Tom Ellis). Your relation yields $[\rho,\rho,\rho]=\rho$ and is called an idempotent (http://en.wikipedia.org/wiki/Semiheap).

The set of all relations $\alpha\subset X\times Y$ is a semiheap with respect to the ternary operation $[\alpha_1,\alpha_2,\alpha_3]=\alpha_1\alpha_2^{-1}\alpha_3$ ($\alpha^{-1}$ is $\alpha^{*}$in notation of Tom Ellis and $\alpha^{op}$ by Todd Trimble). Your relation yields $[\rho,\rho,\rho]=\rho$ and is called an idempotent (http://en.wikipedia.org/wiki/Semiheap).