Interdependent Infrastructure Cascade

Network Topology

Nodes per layer 26

Average degree (edge density) 5.4

Attack Setup

Coupling fraction q 60%

Initial removal (power layer) 18%

Attack strategy

Ready — press Step or Auto-run

Live State

Cascade round

Coupled nodes

—

Power grid alive

100%

Water/comms alive

100%

Largest surviving component (both layers)

100%

How it works

Real cities run two coupled networks: a power grid and the water/communications systems that depend on it for pumps, valves and relays (and which the power grid's own controllers depend on in turn). This is the Buldyrev interdependent-network percolation model — the mechanism behind real cascading blackouts, not a single isolated grid.

Each round applies mutual percolation:

1. Remove failed nodes from layer A.
2. A's giant connected component (GCC) forms; any A-node
   outside it becomes non-functional.
3. Every coupled node depends on its partner in the other
   layer — if partner failed, this node fails too.
4. Recompute layer B's GCC; propagate failures back to A.
5. Repeat until no node changes state (convergence).

Unlike percolation on a single isolated network — which degrades gracefully as nodes are removed — two coupled networks can collapse abruptly: a small initial attack removes nodes from A, which strands a few B-nodes, which strands a few more A-nodes, and so on until the whole system fragments well before either layer alone would have failed.

Nodes per layer / average degree — network size and how densely each ring backbone is wired with random shortcuts. A denser network survives a larger attack before its own giant component fragments.
Coupling fraction q — the share of nodes with a real cross-layer dependency link. q = 0 makes the two layers fail independently; higher q makes collapse sharper and more sudden.
Initial removal — the fraction of power-layer nodes knocked out at round 0 (storm damage, an attack, an overload trip). Before you press Step, the nodes that would be hit are previewed with a dashed orange ring.
Attack strategy — random failure spreads risk evenly; targeting the highest-degree hubs first is far more destructive for the same removal fraction — compare the two degree-distribution panels below to see why.
Step / Auto-run — advance the cascade one round at a time, or let it run to convergence. The history panel tracks every round's survival fractions live.
Drag to pan, scroll/pinch to zoom the network view; use "Reset view" to snap back.

Power grid (top) ↔ Water / comms (bottom)

Functioning node Failed node Coupling link Previewed attack target

Hover a node for details

Cascade history (% alive per round)

Degree distribution