Social　networks　are　becoming　important　dissemination　platforms,　and　a　large　body　of　works　have　been　performed　on　viral　marketing,　but　most　are　to　maximize　the　benefits　associated　with　the　number　of　active　nodes.　In　this　paper,　we　study　the　benefits　related　to　interactions　among　activated　nodes.　Furthermore,　due　to　the　uncertainty　in　edge　probability　estimates　in　social　networks,　we　propose　the　robust　profit　maximization　problem　to　have　the　best　solution　in　the　worst　case　of　probability　settings.　We　design　a　double　sandwich　algorithm　to　this　problem　and　further　improve　the　algorithm　with　sampling　method　such　that　it　increases　robustness　of　the　output.　Through　real　data　sets,　we　verify　the　effectiveness　of　our　proposed　algorithm.