I'm an undergraduate student doing my best to learn about tensor networks, but I'm stuck on Equation (2) of this paper "A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States" (https://arxiv.org/abs/1306.2164), which is
$$ F_{\gamma\omega\rho\sigma} = \sum^D_{\alpha,\beta,\delta,\nu,\mu=1} A_{\alpha\beta\delta\sigma} B_{\beta\gamma\mu} C_{\delta\nu\mu\omega}E_{\nu\rho\alpha} $$
Are the variables that the author chose to contract over arbitrary? Or are they a result of coinciding dimensions, like how $\beta$ is the second dimension of A and first dimension of B, or how the same relationship is present for $\nu$ in C and E?
It may be that I'm focusing way too hard on the details, but I want to know how the indices of C and E collapse/contract to be compatible with B and so on (IF it is the case that this contraction happens because indices coincide).
Thank you!