Abstract
Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. While interactions can occur between two nodes as pairwise interactions, i.e., edges, they can also occur between three or more nodes, which are described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions in complex networks. We propose two new Laplacians to generalize standard graph centrality measures for higher-order interactions. We then compare the performances of the generalized centrality measures using the size of giant component and the Susceptible-Infected-Recovered (SIR) simulation model to show the effectiveness of using higher-order interactions. We further compare them with the first-order interactions (i.e., edges). Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions.
Highlights
Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids
There is a need for more broad and general hypergraph Laplacians to model diffusion to detect the critical higher-order interactions. To address these limitations, we propose two new hypergraph Laplacians based on the diffusion framework that allow us to find the influential higher-order interactions in a hypergraph of any size and with any desired classical centrality measure; one is based on diffusion between fixed size hyperedges, and the other is based on diffusion between all hyperedges
We explain the size of giant component measure and how we model SIR on hypergraphs using the proposed Laplacians for evaluation
Summary
Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. This report presents a novel method to identify critical higher-order interactions in complex networks. Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions. Identifying critical (influential) nodes and edges has practical importance in network science. In12–14, the authors use the betweenness centrality of edges to detect critical edges In other words, they assume that edges connecting two connected components are important. There are a few studies that explore other critical structures in graphs, such as critical groups of nodes and edges These studies do not consider higher-order interactions in hypergraphs. In21, the authors study the Scientific Reports | (2021) 11:21288
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