Nodal Analysis - Deriving equations at each node
What I would do is completely ignore any of the voltage arrows for your analysis. You should be labeling the nodes and have a reference node anyways, which isn't present in that diagram.

For example, here I've removed those arrows, renamed nodes with lowercase letters, and designated a ground node at the bottom. Do all your analysis using Va, Vb, Vc, Vc, Vd, and Ve. Branch currents are assumed to follow the direction of the arrow on the branch (I1, I2, I3, I4, and I5).



edit:

Apparently, arrows denote the assumed positive potential as being from arrowhead minus arrowtail, so we can find that:

\begin{align}
V_1 = V_b\\
V_2 = V_c
\end{align}