By events of fusion and fission mitochondria generate a partially interconnected, irregular network of poorly specified architecture. Here, its organization is examined theoretically by taking into account the physical association of mitochondria with microtubules. Parameters of the cytoskeleton mesh are derived from the mechanics of single fibers. The model of the mitochondrial reticulum is formulated in terms of a dynamic spatial graph. The graph dynamics is modulated by the density of microtubules and their crossings. The model reproduces the full spectrum of experimentally found mitochondrial configurations. In centrosome-organized cells, the chondriome is predicted to develop strong structural inhomogeneity between the cell center and the periphery. An integrated analysis of the cytoskeletal and the mitochondrial components reveals that the structure of the reticulum depends on the balance between anterograde and retrograde motility of mitochondria on microtubules, in addition to fission and fusion. We propose that it is the combination of the two processes that defines synergistically the mitochondrial structure, providing the cell with ample capabilities for its regulative adaptation.