On-line social networks have gradually become an indispensable tool for people. Identifying nodes with high influence in the network as an initial source of communication is of great significance in social perception and rumor control. According to the independent cascade model, in this paper we present an index describing the finite step propagation range expectation as the degree of propagation, and design an efficient recursive algorithm. Based on the local topology information, the index combines the propagation probability to characterize the influence, which can better reflect the propagation influence of a single node. For a single propagation source influence ordering problem, the node degree of propagation and propagation capability are better consistent with each other. And the propagation degree can well describe the propagation influence of nodes under different networks and propagation probabilities. For maximizing the multi-propagation source influence, in this paper we propose a propagation-based heuristic algorithm which is called propagation discount algorithm. This algorithm makes the joint influence of multiple propagation sources maximized. Finally, in this paper we apply the above method to three real networks, showing better effects than the classic indicators and methods. The algorithm has three advantages. First, the expected value of the final propagation range of each node in the small network can be accurately calculated. Second, the degree of propagation fully considers the local topology of the node and belongs to a locality indicator. Third, the indicator combines the effect of propagation probability and yields good outcomes under different networks and propagation probabilities.