Graph Metrics¶

Graph metrics characterize properties of the entire graph.

API Location

All graph metrics are available as instance methods on graph objects (PyGraph and PyDiGraph).

Some commonly used metrics are also available as top-level convenience functions:

# Instance method (recommended)
diameter = g.diameter()

# Top-level function (also works)
diameter = pg.diameter(g)

Available Metrics¶

Basic Properties¶

g.node_count()  # Number of nodes
g.edge_count()  # Number of edges
g.density()  # Edge density (0 to 1)
g.is_directed()  # Whether graph is directed
g.is_empty()  # Whether graph has no nodes

Connectivity¶

g.is_connected()  # Is graph fully connected
g.count_components()  # Number of connected components

Path-Based¶

g.diameter()  # Maximum shortest path
g.radius()  # Minimum eccentricity
g.average_path_length()  # Mean shortest path

Clustering¶

g.average_clustering()  # Mean clustering coefficient
g.transitivity()  # Fraction of triangles

Structural¶

g.assortativity()  # Degree correlation
g.has_negative_weights()  # Contains negative edges
g.has_self_loops()  # Contains self-loops
g.is_bipartite()  # Can be 2-colored

Examples¶

import pygraphina as pg

# Create a test graph
g = pg.core.barabasi_albert(100, 3, seed=42)

# Basic metrics
print(f"Nodes: {g.node_count()}")
print(f"Edges: {g.edge_count()}")
print(f"Density: {g.density():.4f}")

# Connectivity
print(f"Connected: {g.is_connected()}")
print(f"Components: {g.count_components()}")

# Path metrics
print(f"Diameter: {g.diameter()}")
print(f"Radius: {g.radius()}")

# Clustering
print(f"Avg Clustering: {g.average_clustering():.4f}")
print(f"Transitivity: {g.transitivity():.4f}")

# Structural
print(f"Assortativity: {g.assortativity():.4f}")

Interpretation¶

Density: How many edges vs maximum possible
Diameter: Maximum communication distance
Clustering: Local transitivity (friend of friend is friend)
Assortativity: High-degree nodes connect to high-degree (positive) or low-degree (negative) nodes

Time Complexity¶

Metric	Complexity
Basic	O(1) to O(V)
Diameter	O(V·E)
Clustering	O(V·d²)
Path Length	O(V·E)
Assortativity	O(E)