<｜begin▁of▁sentence｜>### Instruction:
Given a graph with edges connecting vertices in a cycle (0-1-2-3-0), can you use the write_dot function in igraph to output the graph structure in DOT format to a file named 'simple_graph.dot'? Additionally, demonstrate how a similar task can be accomplished using networkx's integration with pydot by saving the graph in DOT format to a file named 'simple_graph_nx.dot'. Note that this requires the graph data to be defined with edges connecting vertices in a cycle.
### Response:
import igraph as ig
import networkx as nx
# Create a simple igraph graph
g = ig.Graph([(0, 1), (1, 2), (2, 3), (3, 0)])
# Write the graph to a DOT file
g.write_dot('simple_graph.dot')

# To perform a similar task using networkx
# Create a simple networkx graph
G = nx.cycle_graph(4)
# Write the graph to a DOT file using pydot (need to install pydot)
nx.nx_pydot.write_dot(G, 'simple_graph_nx.dot')
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