  The local structure entropy is a new method which is proposed to identify the
influential nodes in the complex networks. In this paper a new form of the
local structure entropy of the complex networks is proposed based on the
Tsallis entropy. The value of the entropic index $q$ will influence the
property of the local structure entropy. When the value of $q$ is equal to 0,
the nonextensive local structure entropy is degenerated to a new form of the
degree centrality. When the value of $q$ is equal to 1, the nonextensive local
structure entropy is degenerated to the existing form of the local structure
entropy. We also have find a nonextensive threshold value in the nonextensive
local structure entropy. When the value of $q$ is bigger than the nonextensive
threshold value, change the value of $q$ will has no influence on the property
of the local structure entropy, and different complex networks have different
nonextensive threshold value.
  The results in this paper show that the new nonextensive local structure
entropy is a generalised of the local structure entropy. It is more reasonable
and useful than the existing one.
