How to Read Equations for Matrix Operations

Depending on your background in math, you may or may not already know how to interpret Equation (???)(eq:degcenteq). Essentially, the number at the bottom of the sigma is where to start. The number at the top of the Sigma symbol (\(\Sigma\)) is where to end. The equation to the left is the operation to be performed. Thus, one reads the Equation (???)(eq:degcenteq) as, starting at column \(j=1\), and ending at the last possible column \(J\) (remember that \(J\) is simply the total number of columns in the matrix), add up all possible values of the cells designated by the row \(i\) and column \(j\) combination in matrix A. Thus, to calculate the degree centrality of each \(i = a, b, c\) in the below matrix, each of the following calculations would be performed.

	a	b	c
a	-	1	0
b	1	-	1
c	0	1	-

\(C_D(a)=aa+ab+ac=1\)
\(C_D(b)=ba+bb+bc=2\)
\(C_D(c)=ca+cb+cb=1\)

In the same way if we had the formula:

\[\begin{align*} C_D(i) = \sum_{i = 1}^{I}A_{ij} \end{align*}\]

Then it would be telling us to sum values of each column \(j\) down each row \(i\):

\(C_D(a)=aa+ba+ca=1\)
\(C_D(b)=ab+bb+cb=2\)
\(C_D(c)=ac+bc+cc=1\)

The sigma notation is useful for summarizing this repetitive process in a simple, condensed form.