Rinse cranberries, discarding any bruised or under-ripe berries. Bring water and sugar to a boil in a medium saucepan on high heat. Stir to dissolve the sugar. Add the cranberries to the pot and return to a boil. Lower heat and simmer for 10 minutes or until most of the cranberries have burst. Remove from heat and let cool completely at room temperature. Add walnuts and transfer to a bowl to chill in the refrigerator. Cranberry sauce will continue to thicken as it cools.