| the organization of interactions in complex systems can be described by networks connecting different units . these graphs are useful representations of the local and global complexity of the underlying systems . the origin of their topological structure can be diverse , resulting from different mechanisms including multiplicative processes and optimization . in spatial networks or in graphs where cost constraints are at work , as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain , optimization plays an important part in shaping their organization . in this paper we study network designs resulting from a pareto optimization process , where different simultaneous constraints are the targets of selection . we analyze three variations on a problem finding phase transitions of different kinds . distinct phases are associated to different arrangements of the connections ; but the need of drastic topological changes does not determine the presence , nor the nature of the phase transitions encountered . instead , the functions under optimization do play a determinant role . this reinforces the view that phase transitions do not arise from intrinsic properties of a system alone , but from the interplay of that system with its external constraints . |