Fig. 3: Different ways of constructing isolators in real-world power grids.
From: Network isolators inhibit failure spreading in complex networks
a–c Alternative methods of creating an isolator in a given network. We show the network structure before (top left) and after (top right) the addition of a network isolator, as well as corresponding adjacency matrices (bottom) with the different shades of blue representing the weight Aij of the respective edge. A lower prior connectivity simplifies the creation of isolators as measured by the vertex cut (a) or edge cut (b, c) which is visible in the adjacency matrix (entries colored red). The creation of network isolators results in characteristic patterns in the adjacency matrix in terms of the capacities of the isolator edges (shades of blue). d–f Realisation of network isolators in real-world power grids. We construct network isolators in the British power grid (d), the Scandinavian power grid (e) and the Central European power grid (f) using the recipes illustrated in (a–c). For each power grid, we colour code the flow changes after the failure of a single link carrying a unit flow (red). In each case, the network isolator inhibits flow changes, i.e. ΔF = 0, (light grey) in the part of the network that is shielded by the isolator.
