# Totally homogeneous networks

@article{Shi2019TotallyHN, title={Totally homogeneous networks}, author={Dinghua Shi and Linyuan Lu and Guanrong Chen}, journal={National Science Review}, year={2019}, volume={6}, pages={962 - 969} }

In network science, the non-homogeneity of node degrees has been a concerned issue for study. [] Key Method These two vector spaces are related through a boundary operator, e.g., mapping the boundary of a triangle in one space to the sun of three links in the other space. Under the new framework, some important concepts and methodologies from algebraic topology, such as characteristic number, homology group and Betti number, will have a play in network science leading to foreseeable new research directions…

## 29 Citations

### Towards the cycle structures in complex network: A new perspective

- Computer Science
- 2019

This paper defines two cycle-based node characteristics, namely cycle number and cycle ratio, which can be used to measure a node's importance, and finds that an ordinary network can be converted into a hypernetwork by considering its basic cycles as hyperedges.

### Characterizing cycle structure in complex networks

- Computer ScienceCommunications Physics
- 2021

The authors investigate the cycle organization of synthetic and real systems, and use such information to define a centrality measure that is more informative than traditional indexes to the end of understanding network dismantling, synchronization, and spreading processes.

### Representing complex networks without connectivity via spectrum series

- Computer ScienceInf. Sci.
- 2021

### The characteristics of cycle-nodes-ratio and its application to network classification

- Computer ScienceCommun. Nonlinear Sci. Numer. Simul.
- 2021

### Computing cliques and cavities in networks

- Computer Science, MathematicsCommunications Physics
- 2021

The authors introduce the concept of computability for searching maximum clique in large networks and an optimized algorithm for finding cavities with different orders and applies the algorithm to the neuronal network of C. elegans to find all of its cliques and some cavities of different orders.

### Optimizing higher-order network topology for synchronization of coupled phase oscillators

- PhysicsCommunications Physics
- 2022

This work defines the directed hyperlink, and rigorously demonstrates that for the directed interaction, the structural symmetry can be preserved in the optimally synchronizable network with 2-hyperlink interactions, in contrast to the conclusion for 1- hyperlink interactions.

### Optimizing higher-order network topology for synchronization of coupled phase oscillators

- PhysicsCommunications Physics
- 2022

Networks in nature have complex interactions among agents. One significant phenomenon induced by interactions is synchronization of coupled agents, and the interactive network topology can be tuned…

### Reorderability of node-filtered order complexes.

- Computer SciencePhysical review. E
- 2020

This work harnesses applied topological methods to determine which of six growing graph models exhibit topology that is robust to randomizing node order, termed global re orderability, and robust to temporally local node swaps, termed local reorderability.

### Determinable and interpretable network representation for link prediction

- Computer ScienceScientific Reports
- 2022

Experimental results showed that the AIProbS can reach state-of-the-art precision beyond baseline models on some small data whose distribution of training and test sets is usually not unified enough for machine learning methods to perform well.

### Correlation analysis of combined layers in multiplex networks based on entropy

- Computer SciencePloS one
- 2022

A new structure entropy is proposed by combining the overlapping links between the combined layers of a multiplex network and the correlation between layers is evaluated by structure entropy, and the results are consistent with the behaviors exhibited by the network.

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