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A branched geometry (top) and the structure of the corresponding tree matrix (bottom). Nonzero matrix entries are colored either green or blue depending on the color of the node corresponding to the row. The green nodes at the ends of each segment are algebraic conservation nodes and so the corresponding green rows each sum to 0. The matrix need not be symmetric; aij is not in general equal to aji because the entries depend on the volume of compartments i and j, respectively.
