<｜begin▁of▁sentence｜>### Instruction:
As a Software Architect who designs the high-level structure of software systems and applications, you have been tasked with analyzing the network structure of a complex system. You can retrieve the system's graph data from a file named graph_data.gml. Utilizing the path_length_hist function from the igraph API, you are required to compute and display the histogram of path lengths within the network graph. Additionally, it is essential to determine the count of unconnected vertex pairs within the system for further analysis and optimization.
### Response:
import igraph as ig

# Read a graph from a file
g = ig.Graph.Read_GML('graph_data.gml')

# Calculate the path length histogram of the graph
directed = False # Set to True if you want to consider directed paths
path_length_histogram, unconnected_pairs = g.path_length_hist(directed)

# Print the results
print('Path lengths:', path_length_histogram)
print('Unconnected pairs:', unconnected_pairs)
<|EOT|>
