  We explore the intriguing effects of underlying star topological structure in
the framework of Schelling's segregation model with blocks. The significant
consequences exerted by the star topology are both theoretically analysed and
numerically simulated with and without introducing a fraction of altruistic
agents, respectively. The collective utility of the model with pure egoists
alone can be optimized and the optimum stationary state is achieved with the
underlying star topology of blocks. More surprisingly, once a proportion of
altruists are introduced, the average utility gradually decreases as altruists'
fraction increases. This presents a sharp contrast to the results in
Schelling's model with lattice topology of blocks. Furthermore, an adding-link
mechanism is introduced to bridge the gap between the lattice and the star
topologies, and extend our analysis to more general scenarios. A novel scaling
law of the average utility function are found for star topology of blocks.
