Find crossing edges in a graph from adjacency matrix

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Is there any way to find the crossing edges from the adjacency matrix of a given undirected graph $G=(V,E)$? For example in the following graph ( actually a tree in this specific example) $e_{3, 13}$ and $e_{1, 14}$ are crossing, how can I extract this information from the adjacency matrix of the graph? Coordinates of all vertices are given and fix.

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