Consider the following two vertex-weighted graphs, and denote them as having vertex sets V=\{v_{1}, v_{2}, \ldots, v_{6}\} and W=\{w_{1}, w_{2}, \ldots, w_{6}\}, respectively (numbered in the same direction and way). The weights in the second graph are such that for all 1 \leq i \leq 6, the weight of w_{i} is the sum of the weights of the neighbors of v_{i}. Determine the sum of the weights of the original graph.
