As Japan enters an era of declining population, public transportation networks that maintain a high level of service at low cost are urgently needed. This paper proposes a normative methodology for studying nodes, which are a fundamental element in public transportation network design. Transportation nodes are identified by means of a network design problem to efficiently transport passengers. Specifically, public transportation lines are aggregated into a shape called a graph spanner, and the points where many demands intersect are considered heuristically. We considered that the solution space of the constructed problem is too large to derive an exact solution, so we constructed an algorithm to derive a solution heuristically using the cross-entropy method, which is one of the meta-heuristics. We confirmed the behavior of the proposed method on a test network and discussed some of the solutions obtained.