Let $n \geq 3$ be an integer. Two players play a game on an empty graph with $n + 1$ vertices, consisting of the vertices of a regular n-gon and its center. They alternately select a vertex of the n-gon and draw an edge (that has not been drawn) to an adjacent vertex on the n-gon or to the center of the n-gon. The player who first makes the graph connected wins. Between the player who goes first and the player who goes second, who has a winning strategy? Note: an empty graph is a graph with no edges.