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The filamentary structure in 13CO radio maps of the Orion A, Orion B and Monoceros R2 molecular clouds was analyzed using the Minimal Spanning Tree. This represents the first time the MST has been applied to an extended region such as maps of molecular clouds. The method of preparing and analyzing the data is presented. Integrated maps over a range of velocities were examined as well as a velocity cube constructed from individual 0.5 km s-1 wide channel maps. The results show that there is overwhelming objective and statistical evidence that the filamentary structure does exist in all three of these regions. Previous techniques to identify filaments were generally visual, and therefore subjective. The major filaments in Orion A show linear features extending throughout the entire length. The structure in the velocity cube clearly shows the continuous velocity gradient. Orion B cloud shows distinct regions with north to south orientations. The velocity cube contains a number of filaments at greatly differing velocities, with little evidence of large scale velocity gradients. Mon R2 cloud exhibits two main filamentary components, one of which is associated with both bright condensed regions. The velocity structure reveals an overall velocity gradient.
