<image>Below (a)(b)(c)(d) are four plane graphs:

(1) Count the number of vertices, edges, and regions (excluding the infinite region outside the graph) for each plane graph, and fill in the corresponding results in the table: \frac{}_
(2) Observe the table. If we denote the number of vertices, edges, and regions of a plane graph as E, F, and G respectively, try to deduce the relationship between E, F, and G;
(3) It is known that a certain plane graph has 2009 vertices and forms 2009 regions. Based on the above relationship, determine the number of edges of this plane graph.