<｜begin▁of▁sentence｜>### Instruction:
In the course of constructing a model for studying the epidemiological pathways of a contagious disease, we aim to employ a particular network structure inspired by the Dorogovtsev-Goltsev-Mendes (DGM) graph as a framework to simulate interactions within a population. To facilitate this aspect of the model, could you synthesize a DGM graph at the second generation and evaluate its structural properties? Specifically, we are interested in ascertaining the total count of vertices representing individuals and connections akin to potential transmission lines (edges), as well as determining the network's planarity - a characteristic that might significantly influence the simulation's outcomes and interpretations. This analysis is a foundational step in furthering our understanding of the disease's spread through complex human contacts.
### Response:
import networkx as nx

# Generate a Dorogovtsev-Goltsev-Mendes graph for generation number 2
G = nx.dorogovtsev_goltsev_mendes_graph(2)

# Print the number of nodes and edges in the graph
print('Number of nodes:', G.number_of_nodes())
print('Number of edges:', G.number_of_edges())

# Check if the graph is planar
is_planar = nx.check_planarity(G)[0]
print('Is the graph planar?', is_planar)
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