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O2 MO diagram From the MO diagram, we can see that it has 2 electrons in a $\sigma$ orbital, 4 in $\pi$ orbitals, and 2 in $\pi$* orbitals. Taking this together gives a bond order 2, with 1 coming from the sigma electrons and another 1 being the net value for the $\pi$ and $\pi$* electrons.
To answer this question it is advantageous to treat a molecule as a graph and use the well known adjacency matrix from graph theory. Here is the wikipedia definition: For a simple graph with vertex set $V$, the adjacency matrix is a square $|V| × |V|$ matrix $\mathbb{A}$ such that its element $\mathbb{A}_{ij}$ is one when there is an edge from vertex $i$ ...