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**Exchangeable random networks.**
*(English)*
Zbl 1206.68028

Summary: We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that characterize the degree distribution of the ensemble graphs, together with some features that are important for applications, such as subgraph distributions and kernel of the adjacency matrix. A particular case of directed networks with power-law out-degree is studied in more detail, as an example of the flexibility of the model in applications.

### MSC:

68M10 | Network design and communication in computer systems |

05C80 | Random graphs (graph-theoretic aspects) |

68R10 | Graph theory (including graph drawing) in computer science |