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):

diameter = g.diameter()

Available Metrics¶

Basic Properties¶

import pygraphina as pg

g = pg.core.erdos_renyi(n=30, p=0.2, seed=42)

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)