## JSON code of the network

{"nodes":["r","a","b","c","d","e","f","g","h","i","1","2","3","4","5"],"edges": [["r","a"],["a","b"],["b","1"],["b","c"],["c","d"],["d","2"],["a","e"],["e","c"],["e","3"],["r","f"],["f","g"],["g","4"],["g","h"],["h","d"],["f","i"],["i","h"],["i","5"]]}

## Visualization of the network

*r* is the root and the leaves are labeled from 1 to 5.
Arcs are oriented from the parent to the child.

## Classes containing this network or not

### Classes which contain this network (with direct proof)

### Classes which do not contain this network (with direct proof)

- binary tree-based: Suppose
*N* is tree-based, and consider the tree *T* it is based on. If reticulation arc (*c*,*d*) is chosen in *T*, there would remain no leaf below *h* in *T*. A symmetric argument works for arc (*h*,*d*) and *c*, which leads to a contradiction. - binary spread-1: Suppose there exists an order of the leaves which corresponds to spread 1. Vertices
*b*, *e*, *g*, *i* are all above leaf 2 as well as above another leaf which is not below the other ones. So whatever two leaves, say 1 and 3, we choose to be around leaf 2 in the order, 4 and 5 will not be, so the leaves below *g* and *h* will not be an interval in this order. - binary level-2:
*c*, *d* and *h* are three reticulation vertices in the same blob.

### All classes

In the inclusion diagram below, the names of classes containing this network are colored green and the name of the classes not containing it are colored red.

## About this website

This website was programmed and is maintained by Philippe Gambette.
It was started during the internship of Maxime Morgado at LIGM, in June-July 2015,
and also contains contributions made from Narges Tavassoli from November 2016 to January 2017.

Please contact Philippe Gambette if you have any suggestions about this website, especially about problems, properties, results or subclasses to add.

### How to cite

P. Gambette, M. Morgado, N. Tavassoli & M. Weller (2018)

*ISIPhyNC, an Information System on Inclusions of Phylogenetic Network Classes*, manuscript in preparation.

### Database content

73 classes of phylogenetic networks including 35 classes of binary phylogenetic networks (defined in a total of 20 bibliographic references), 51 inclusion relationships proved directly between classes (including some found in a total of 9 bibliographic references), 24 networks (68 memberships to a class, 56 non-memberships to a class), 3 problems considered, 3 properties considered, 37 theorems proved directly (including some found in a total of 17 bibliographic references) including 26 positive results (which can be extended to subclasses) and 11 negative results (which can be extended to superclasses).