We present a Langevin molecular dynamics study of an equimolar mixture of monodispersed oppositely charged di-block four-armed polyelectrolyte stars. We used an implicit solvent coarse-grained representation of the polyelectrolyte stars, and varied the length of the terminal charged blocks that reside on each arm. By varying the polymer concentration, we computed PV diagrams and determined the free-swelling equilibrium concentration with respect to a pure water reservoir as a function of the charged block length. We investigated various structural properties of the resulting equilibrium structures, like the number of ionic bonds, dangling arms, isolated stars, and cluster sizes. The ionic bonds featured a broad distribution of the number of arms involved and also displayed a distribution of net charges peaked around the neutral ionic bond. Our main result is that for charged block length equal to 4 and 5 ionized beads the resulting macro-aggregate spans the box and forms a network phase. Furthermore, we investigated the restructuring dynamics of ionic bonds; the results suggested both short bond lifetimes and a high frequency of ballistic association/dissociation events. Bonds result strong enough to yield a stable gel phase, but they are still weak enough to allow network restructuring under thermal fluctuations.