Chapter 3.1, Problem 47E

Management Management is attempting to identify the most active person in labor’s efforts to unionize. The following diagram shows how influence flow from one employees to another among the four most active employees.

Construct matrix $A$ with elements

$a_{ij}=\{\begin{array}{c}1\\ 0\end{array}\begin{array}{c}Ifi\inf luences\text{}jdirectly\\ Otherwise\end{array}$

Construct matrix $B$ with elements

$b_{ij}=\{\begin{array}{c}1\\ 0\end{array}\begin{array}{c}ifi\inf luencesjthroughatmostoneperson,withi\ne j.\\ Otherwise\end{array}$

The person $i$ is most active in influencing others if the sum of the elements in row $i$ of the matrix $A+B$ is the largest. Who is the most active person $?$