Identifying the influence of nodes is one of the major research topics in the structural analysis of social networks.The current measures of researching the node influence can be divided into two categories:centrality measure and node removal measure.The former mainly identifies the influence of the node by degree or shortest path

without considering the connectivity of social networks; while the latter by the damage of the structure of a social network when some nodes are removed.The node removal measure is incapable to be applied in large-scale since the computational complexity.We propose a new parameter

connectedness centrality

to identify the influence of nodes in networks by combining the local connectivity and shortest paths.We give a method to compute the connectedness centrality of the node and obtain the precise values in some specific networks.Finally

an experiment using a real-word network shows that our method can well identify the influence of the node in social networks.