Abstract: The edge neighbor toughness is generalized to the weighted graphs, and the concept of weighted edge neighbor toughness of a graph is proposed. After presenting the weighted edge neighbor toughness of some basic graphs, this paper focuses on the extreme problem of the weighted edge neighbor toughness of certain types of graphs, and designs an algorithm to compute the maximum weighted edge neighbor toughness of the complementary graph of cycles. The results show that the weighted edge neighbor toughness can accurately characterize the invulnerability of some networks.

Key words: network invulnerability, weighted graph, toughness, weighted edge neighbor toughness