Reporting Link A: Defining the Organization and Its Small World
Type A links represent reporting structure
A1 Direct Report
Embedded hierarchy link that connects every organization node to its parent node (see whole/part node-link and core hierarchy pages for more on this fundamental link type)
A2 Matrix Report

Matrix links represent co-managers, a second boss typically at the same level as the direct report boss (or higher). In nature and social networks these cross-links are the “weak ties,” the shortcuts that create the “small world” effects demonstrated by the new network science (e.g., Watts). In organizations, this translates into alternative decision-making pathways and, hopefully, faster, better decisions.

Each shortcut adds an element of stress. Nature finds a few shortcuts have a big shortening impact, but quickly reaches a point where more shortcuts don’t increase overall shortness. Too many matrix reports don’t add value and do accumulate high organizational design stress
Two nodes cannot have both a direct and matrix relationship
Matrix Size. How big Is big? Counting positions in matrix hierarchies shows impact of matrix links at management level
Direct “absolute” span and size  (‘the temperature’), the count by direct reporting links (A1) only, each position counted once, the org view of headcount Matrix “relative” span and size (‘the heat index’), the count by both direct and matrix reporting links (A1 + A2), the manager view of responsibilities.