On the almost borderenergetic digraph

The energy of a digraph is defined as the sum of absolute values of the real parts of the eigenvalues for the adjacency matrix of a digraph. As an extension of graph energy, there are many applications such as chemistry, physics and communication networks and so on. For an [Formula: see text]-order digraph [Formula: see text], if its energy [Formula: see text] satisfies [Formula: see text], then [Formula: see text] is a borderenergetic digraph. Here, we define the almost borderenergetic digraph. That is, a digraph [Formula: see text] of [Formula: see text] vertices is almost borderenergetic if its energy satisfies [Formula: see text]. In this research, a series of almost borderenergetic digraphs can be constructed by removing arcs from a complete digraph and discussing the structures of the deleted arcs.