Probing the robustness of nested multi-layer networks

TL;DR

This paper investigates the robustness of multi-layer networks with scale-free and core-periphery structures, analyzing how different node removal strategies affect the network's connectivity, with implications for bipartite network resilience.

Contribution

It introduces a novel analysis of multi-layer network robustness considering intra- and inter-layer links, supported by empirical data from ecology and economics.

Findings

Certain attack strategies drastically reduce network robustness.

Intra-layer links can enhance the network's resilience.

Robustness varies significantly with attack type and intra-layer coupling.

Abstract

We consider a multi-layer network with two layers, $\mathcal{L}_{1}$, $\mathcal{L}_{2}$. Their intra-layer topology shows a scale-free degree distribution and a core-periphery structure. A nested structure describes the inter-layer topology, i.e., some nodes from $\mathcal{L}_{1}$, the generalists, have many links to nodes in $\mathcal{L}_{2}$, specialists only have a few. This structure is verified by analyzing two empirical networks from ecology and economics. To probe the robustness of the multi-layer network, we remove nodes from $\mathcal{L}_{1}$ with their inter- and intra-layer links and measure the impact on the size of the largest connected component, $F_{2}$, in $\mathcal{L}_{2}$, which we take as a robustness measure. We test different attack scenarios by preferably removing peripheral or core nodes. We also vary the intra-layer coupling between generalists and specialists, to study their impact on the robustness of the multi-layer network. We find that some combinations of attack scenario and intra-layer coupling lead to very low robustness values, whereas others demonstrate high robustness of the multi-layer network because of the intra-layer links. Our results shed new light on the robustness of bipartite networks, which consider only inter-layer, but no intra-layer links.