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Influence graph for company board

Short answer

Vertices: P, RD, M, O, CFO. Directed edges: P→RD, P→M, P→O; RD→O; M→O. CFO is isolated. The graph has 5 edges, P has out-degree 3, O has in-degree 3.

Construct an influence graph for the board members of a company if the President can influence the Director of Research and Development, the Director of Marketing, and the Director of Operations; the Director of Research and Development can influence the Director of Operations; the Director of Marketing can influence the Director of Operations; and no one can influence, or be influenced by, the Chief Financial Officer.

An influence graph is a directed graph in which each person is a vertex and there is a directed edge from A to B if A can influence B.

Vertices: P (President), RD (Director of Research and Development), M (Director of Marketing), O (Director of Operations), CFO (Chief Financial Officer).

Edges (influencer → influenced):

  • P → RD, P → M, P → O
  • RD → O
  • M → O
  • CFO has no edges (isolated vertex).
            P
         /  |  \
        v   |   v
       RD   |    M
         \  |   /
          v v  v
            O                CFO  (isolated)

(P has edges to RD, M and O; RD and M each have an edge to O.)

Adjacency matrix (row influences column):

PRDMOCFO
P01110
RD00010
M00010
O00000
CFO00000

Reading it: the graph has 5 edges. P has out-degree 3 and in-degree 0, O has in-degree 3 (influenced by P, RD and M) and out-degree 0, and the CFO has in-degree and out-degree 0.

✓ Answer checked by Claude Opus 5.5 (high effort)

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