Eradicating catastrophic collapse in interdependent networks via reinforced nodes

Significance Percolation theory assumes that only the largest connected component is functional. However, in reality, some components that are not connected to the largest component can also function. Here, we generalize the percolation theory by assuming a fraction of reinforced nodes that can function and support their components, although they are disconnected from the largest connected component. We find that the reinforced nodes reduce significantly the cascading failures in interdependent networks system. Moreover, including a small critical fraction of reinforced nodes can avoid abrupt catastrophic failures in such systems.