Evolutionary　games　and　population　dynamics　are　finding　increasing　applications　in　design　learning　and　control　protocols　for　a　variety　of　resource　allocation　problems.　The　implicit　requirement　for　full　communication　has　been　the　main　limitation　of　the　evolutionary　game　dynamic　approach　in　engineering　tasks　with　various　information　constraints.　This　article　intends　to　build　population　games　and　dynamics　with　both　static　and　dynamical　graphical　communication　structures.　To　this　end,　we　formulate　a　population　game　model　with　graphical　strategy　interactions　and　derive　its　corresponding　population　dynamics.　In　particular,　we　first　introduce　the　concept　of　generalized　Nash　equilibria　for　population　games　with　graphical　strategy　interactions,　and　establish　the　equivalence　between　the　set　of　generalized　Nash　equilibria　and　the　set　of　rest　points　of　its　distributed　population　dynamics.　Furthermore,　the　conditions　for　convergence　to　generalized　Nash　equilibrium　and　particularly　to　Nash　equilibrium　are　obtained　for　the　distributed　population　dynamics　with　both　static　and　dynamical　graphical　structures.　These　results　provide　a　new　approach　to　design　distributed　Nash　equilibrium　seeking　algorithms　for　population　games　with　both　static　and　dynamical　communication　networks,　and　hence,　expand　the　applicability　of　the　population　game　dynamics　in　the　design　of　learning　and　control　protocols　under　distributed　circumstances.