With the gradual entry into the era of "Internet of Things" , large-scale parallel and distributed systems play a crucial role, which motivates us to explore qualitative and quantitative metric to characterize the fault tolerance and reliability of these systems. A more accurate assessment about the fault tolerance and reliability of large-scale parallel and distributed systems can be achieved by h-extra edge-connectivity. It can dynamically measure the size of the separated component under large-scale faulty links. The use of cartesian product operations to assemble large-scale interconnection networks has received extensive attention due to easy operation and scalability. Given a recursively assembled interconnection network G, the distribution of its values of h-extra edge-connectivity is non-uniform. The h-extra edge-connectivity of G, if any, is well-defined for each positive integer 1 < h< L1V(G)1=2]. This paper focuses on the concentration phenomenon about h-extra edge-connectivity of the n-th cartesian product of interconnection network K4 (denoted by kh(K4n )): as n-> oo , for about 64.5% of positive integers h< 2 x 4n-1 , the h-extra edge-connectivities of the n-th cartesian product of interconnection network K4 are concentrated on 3n numbers. That is, at least [3ng 3gt g(g 1)]4t links must be deleted to disconnect network K4n , provided that the deletion of these links does not isolate any subnetwork with at most h 1 processors for about 64.5% of positive integers h < 2 x 4n-1 , 0 < t<n<1 and g? {1;2;3} . It is exactly equal to the minimum cardinality of links, such that whose removal will disconnect the networkKn4with all its resulting components having at least g X 4t processors. Our results provide a more precise way to evaluate the reliability of interconnection networks
