1. Multilayer network researchers use graphs to simulate single-layer networks and obtain a symmetric adjacency matrix A. Then they use multilayer graphs to model multilayer networks, which are adjacency matrices of a set of weighted single-layer graphs, including intra-layer relationships and inter-layer interactions.
2. Similarity-based networks can use various connections and metrics to define the weights between edges in a multi-layer network. Without the concept of application-driven edges, edges are usually constructed based on the similarity ω between nodes, thus forming a so-called similarity-based network.
3. Node embedding needs a lot of computing and storage space to extract meaningful information from complex networks.
4. Clustering based on persistent graph. The researchers proposed a multi-layer network clustering method. The goal of researchers is to cluster multi-layer networks in an unsupervised environment from the perspective of shape similarity of data recorded at different resolutions.
Multilayer network is widely used in many research fields because of its high practicability in modeling interdependent systems.
However, the clustering of multi-layer networks, especially the clustering using high-order interactive information, is still in its infancy. On the contrary, high-level connection is usually the key to multi-layer network applications.
In a recent paper published by PNAS, researchers introduced the concept of topological data analysis into the study of complex multi-layer networks, and proposed a topological method of network clustering, which they called multi-layer network clustering (CPD).
CPD systematically considers the different high-order characteristics of node interaction within the network layer and between layers, and integrates the information from neighboring nodes.
By applying CPD to a new problem of social importance, the researchers illustrate the effectiveness of CPD: in the context of family insurance claims, houses are zoned to show the risks caused by weather and climate.
1 1, think about it from another angle.
Two Christians, A and B, are addicted to cigarettes while praying. A Christian asked the priest, "Can I smoke when I pray?" The