A method and associated systems for rewarding online users as a function of network topology. An online-reward system receives a network topology and an unweighted base reward schedule that specifies amounts of incentive rewards to be awarded to performing users who perform a solicited desired action and to intermediary users who forward such a solicitation to another user. The system computes a position value for each node as a function of the node's position in the topology and uses those values to weight the base rewards. Each time the network topology changes, this process is repeated to immediately update weightings of nodes affected by the change. When a network user performs a solicited activity, the processor physically transfers rewards to the accounts of the performing and intermediary users, using the weighted values to determine the amount of each reward.