# Generalised popularity-similarity optimisation model for growing hyperbolic networks beyond two dimensions

@article{Kovcs2022GeneralisedPO, title={Generalised popularity-similarity optimisation model for growing hyperbolic networks beyond two dimensions}, author={Bianka Kov{\'a}cs and S{\'a}muel G. Balogh and Gergely Palla}, journal={Scientific Reports}, year={2022}, volume={12}, pages={1-15} }

Hyperbolic network models have gained considerable attention in recent years, mainly due to their capability of explaining many peculiar features of real-world networks. One of the most widely known models of this type is the popularity-similarity optimisation (PSO) model, working in the native disk representation of the two-dimensional hyperbolic space and generating networks with small-world property, scale-free degree distribution, high clustering and strong community structure at the same…

## 5 Citations

### Model-independent methods for embedding directed networks into Euclidean and hyperbolic spaces

- Computer Science
- 2022

A framework based on the dimension reduction of proximity matrices reflecting the network topology, coupled with a general conversion method transforming Euclidean node coordinates into hyperbolic ones even for directed networks is proposed.

### Maximally modular structure of growing hyperbolic networks

- Computer Science
- 2022

This work shows that for the popularity-similarity optimization model from this family, the generated networks become also extremely modular in the thermodynamic limit, in spite of lacking any explicit community formation mechanism in the model deﬁnition.

### Random hyperbolic graphs in $d+1$ dimensions

- Mathematics, Computer Science
- 2020

The rescaling of network parameters is found that allows to reduce random hyperbolic graphs of arbitrary dimensionality to a single mathematical framework and indicates that RHGs exhibit similar topological properties, regardless of the dimensionality of their latenthyperbolic spaces.

### Model-independent embedding of directed networks into Euclidean and hyperbolic spaces

- Computer ScienceCommunications Physics
- 2023

A framework based on the dimension reduction of proximity matrices reflecting the network topology coupled with a general conversion method transforming Euclidean node coordinates into hyperbolic ones even for directed networks is introduced.

### Dimension matters when modeling network communities in hyperbolic spaces

- Computer Science
- 2022

It is shown that there is an important qualitativeerence between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities, and considering only one more dimension allows for more realistic and diverse community structures.

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