Problem with implementing squared terms in the objective function

I’m trying to implement either one of these objective functions, but I’m having a hard time with the squared terms. I’m attaching both so you can take a look at the structure and see if you can give me any tips. Is there any way to implement either one of them?

1- Matrix notation:

$x$: decision variable

$1$: column of ones

$k$: squared matrix

2- Summation notation:

$x$: decision variable
$m$: degree of the node i
$rho$: parameter that takes into account the influence of the neighbors that surround node i
$a$: terms of the adjacency matrix. Shows if nodes i and j are connected

Thank you in advance!