## 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","c"],["c","1"],["c","g"],["g","2"],["b","d"],["d","g"],["d","h"],["h","3"],["a","e"],["e","h"],["e","i"],["i","4"],["r","f"],["f","i"],["f","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)

- binary level-3: Easy to check.
- binary galled network: All common arcs between reticulation cycles, (
*b*,*d*) and (*a*,*e*), are tree arcs. - binary regular: If we contract each reticulation vertex of this network with its child, we obtain the Hasse diagram of {{1},{2},{3},{4},{5},{1,2},{2,3},{1,2,3},{3,4},{1,2,3,4},{4,5},{1,2,3,4,5}}.
- binary leaf outerplanar: Easy to check.
- binary nearly stable: The unique parents of the only vertices which are not stable,
*d* and *e*, respectively *b* and *a*, are stable. - binary time-consistent: Here is a time-consistent labeling
*t*:
*t*(*r*)=0
*t*(*a*)=1
*t*(*b*)=2
*t*(*c*)=*t*(*d*)=*t*(*e*)=*t*(*f*)=*t*(*g*)=*t*(*h*)=*t*(*i*)=3
*t*(1)=*t*(2)=*t*(3)=*t*(4)=*t*(5)=4

- binary 1-reticulated: Each tree vertex can reach at most one reticulation vertex by 2 internally vertex-disjoint paths:
*r* can reach *i*, *a* can reach *h* and *b* can reach *g*.

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

### 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).