Small-World Network Model
Watts-Strogatz Model Visualization
Network Metrics
Total Edges
0
Average Degree
0
Clustering Coefficient
0
Average Path Length
0
Small-World Index
0
Understanding the Small-World Model
The Watts-Strogatz small-world model demonstrates how real-world networks combine high clustering with short path lengths. The model starts with a regular ring lattice where each node connects to its k nearest neighbors. Through random rewiring with probability p, the network transitions from regular to small-world to random.
Key Parameters:
- k (Initial Connections): Each node initially connects to k/2 neighbors on each side
- p (Rewiring Probability): The chance each edge gets rewired to a random node
Network Regimes:
- p = 0: Regular lattice with high clustering but long paths
- p ≈ 0.01-0.1: Small-world regime with high clustering and short paths
- p = 1: Random network with low clustering but short paths
Metrics Explained:
- Clustering Coefficient: Measures how connected a node's neighbors are to each other (0-1)
- Average Path Length: Mean shortest path between all node pairs
- Small-World Index: Ratio of clustering to path length compared to a random network
