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.