Accessibility in the provinces of Finland

Relative, mean and integral accessibility in the existing provinces of Finland and in the proposed new provinces was studied applying graph theory, through evaluating the shapes of the provinces by reference to polygonal graphs, and, in a more detailed analysis, through using flow graphs to represent the accessibility between locations. The sensitivity of the ac­cessibility structure was tested by means of two simulation experiments. The poorest accessibility levels existed in the more northerly provinces, although some provinces weak in this respect could also be found in Southern and Central Finland, especially when accessibility was studied in relation to the size of the province. This correlates with a certain backwardness in the development of the administrative regions in relation to population development. The proposed province revisions have not corrected this situation entirely. The locations of the provincial capitals are close to the (pareto‑)optimum in general, the non‑optimal cases being ones in which the most significant centres of population growth have been located elsewhere than in the provincial capital or its immediate sur­roundings. Integral accessibility as a measure of optimal location is not sensitive to changes in spatial structure, and extremely large movements of population would be required to cause any substantial alteration in the location of the optimal centre.

THE WRITHE OF ORIENTED POLYGONAL GRAPHS

Given an edge-oriented polygonal graph in ℝ3, we describe a method for computing the writhe as the average of weighted directional writhe numbers of the graph in a few directions. These directions are determined by the graph and the weights are determined by areas of path-connected open regions on the unit sphere. Within each open region, the directional writhe is constant. We obtain a closed formula which extends the formula for the writhe of a polygon in ℝ3, including the important special case of writhe of embedded open arcs.