For a set S⊆ V (G) in a network G, the Steiner distance d G (S) of S is the minimum size among all connected subnetworks whose vertex sets contain S. The Steiner k-eccentricity ɛ k (v) of a vertex v of G is the maximum Steiner distance among all k-vertex set S which contains the vertex v, ie, ε k (v)= max {d (S)| S⊆ V (G),| S|= k, v∈ S}. Based on Steiner k-eccentricity, the connective Steiner k-eccentricity index is introduced. As a newly structural invariant, some properties of the connective Steiner 3-eccentricity index are investigated. Firstly we present an O (n 2)-polynomial time algorithm to calculate the connective Steiner 3-eccentricity index of trees. Secondly some optimal problems among some network classes are discussed. As its application, finally we consider the network similarity measure based on the connective Steiner 3-eccentricity index. By two different methods, we study its advantages. Numerical results show that the measure based on the connective Steiner 3-eccentricity index has more advantages than the ones based on other topological indices (graph energy, Randić index, the largest adjacent eigenvalue, the largest Laplacian eigenvalue).