Networks are the invisible architecture of reality.

In networks, weak ties often provide the most valuable bridges between clusters.

The strength of a network lies not in its nodes, but in its connections.

Small world networks explain why we're all just six handshakes apart.

Scale-free networks follow power laws - a few hubs hold most of the connections.

Network effects create winner-take-most markets and exponential growth.

The most robust networks are both clustered and well-connected.

In complex networks, simple local rules can create sophisticated global behavior.

Network topology determines information flow and resilience to failure.

Cascades in networks explain how small triggers can cause massive effects.

The value of a network grows exponentially with its size.

Centrality measures reveal who holds the real power in any network.

Networks self-organize toward efficiency and robustness through simple rules.

Homophily - the tendency to connect with similar others - shapes social networks.

Network science reveals the universal patterns underlying diverse complex systems.

From neural networks to social networks, connectivity creates complexity.