The line of authority within a business establishes who is in charge of giving who orders, and it contributes to the efficient attainment of the company's objectives when properly used. From: http://www.businessdictionary.com/definition/line-of-authority.html

It's the "Confucian" line. Actually, it is more of a "ladder". You go up the line and down the line. You get the picture. 系

I assume the reference is to delineation of authority as depicted in the formal hierarchy of an organization chart, solid lines showing reporting relationships within an organization.