## JSON code of the network

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

## Visualization of the network

*r* is the root and the leaves are labeled from 1 to 4.
Arcs are oriented from the parent to the child.

## Classes containing this network or not

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

- binary normal: The network contains no redundant arc, and all parents of reticulations have a tree child:
*a* and *e*, parents of *b*, have respectively *c* and *f* as tree child; *e* and *f*, parents of *d*, have respectively *2* and *4* as tree child. - binary time-consistent: Here is a time-consistent labeling
*t*:
*t*(*r*)=0
*t*(*a*)=*t*(*b*)=*t*(*e*)=1
*t*(*c*)=*t*(*d*)=*t*(*f*)=*t*(1)=2
*t*(2)=*t*(3)=*t*(4)=3

- binary level-2: Easy to check.
- binary spread-2: Any set on any order on 4 vertices is composed of at most 2 intervals.
- binary galled network: The common arcs between the two reticulation cycles are (
*r*,*a*) and (*r*,*e*), which are tree arcs.

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

- binary galled tree: Easy to check.
- binary nested: Easy to check.
- binary spread-1: Suppose by contradiction that there exists an order where there is exactly one interval for each cluster. Clusters {2,3} of vertex
*c* and {3,4} of vertex *f* force 3 to be between 2 and 4 in this order. So 1 cannot be between 2 and 3 nor between 4 and 3. Therefore, either cluster {1,2,3} of vertex *a* and {1,3,4} of vertex *e* have to appear as 2 intervals in this order (split respectively by 4 or by 2). - binary 2-reticulated: There are two reticulation vertices,
*b* and *d*, which can be reached using two directed internally vertex disjoint paths from tree vertex *r*.

### 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).