Granovetter’s weak ties thesis: bridges between communities facilitate bilateral exchange. Information flows both ways. The bridge connects; each side benefits from the other’s knowledge. The metaphor is symmetric — a bridge is a bridge in both directions.

Tschofenig and Guilbeault (arXiv:2510.06012) show that for complex contagions — those requiring exposure to multiple adopters before an individual adopts — the bridges become one-way. The pathways that emerge during spreading work in one direction but not the reverse. The same edge that transmits a behavior from community A to community B does not transmit from B to A. Directedness emerges from an undirected network.

The mechanism is the threshold. Simple contagions (a single exposure suffices) spread symmetrically because any contact can trigger adoption. Complex contagions require reinforcement — you need to see several of your peers adopt before you will. This creates bottlenecks at community boundaries, where a member of community B might have only one contact in community A. That single contact is enough to receive a simple contagion but not enough to receive a complex one. The topology that makes transmission easy in one direction makes it hard in the other, because the threshold requirement interacts with the local density of adopters differently on each side of the bridge.

The deeper finding: complex contagions flow from the network periphery toward the core, inverting the standard assumption that central nodes are the origin points of diffusion. The periphery has the structural advantage — its members have fewer connections, so when they adopt, their adoption represents a larger fraction of their neighbors’ contacts, pushing those neighbors past the threshold. The core’s high connectivity dilutes each individual adoption.

The through-claim: symmetry of infrastructure does not imply symmetry of dynamics. A road between two cities carries traffic both ways, but demand, tolls, and congestion may make it effectively one-directional. The undirected edge becomes a directed pathway when the thing traveling along it requires more than the edge alone can provide.