Hello!

I am trying to do an analysis where I compare two directed acyclic graphs to see if the topologies are similar or different. The tip vertices have the same names, but the internal vertices have different names (a product of how these graphs were created by a different program, `admixtools2`

). I have tried `identical_graphs()`

, `intersection()`

, and `difference()`

. However, it seems that vertices must have the same names across graphs if similarities are to be called. Is there any way to compare graph topology if the graphs don’t share internal vertex names?

Thank you in advance!

For an example, here are two graphs which have the same exact topologies. The tip vertices have the names `diploperennis_`

, `mexicana_`

, `parviglumis_`

, `Nold_`

, and `maize_`

. The graph objects are named `g0`

and `g2`

.

```
> g0
IGRAPH 39726c3 DNW- 11 11 --
+ attr: name (v/c), type (e/c), weight (e/n), low (e/n), high (e/n)
+ edges from 39726c3 (vertex names):
[1] R ->diploperennis_ R ->Rr Rr ->Rrl Rr ->admix
[5] Rrl ->mexicana_ admix ->Nold_ admix ->admixw admixw->parviglumis_
[9] Rrl ->admixy admixy->maize_ admixw->admixy
> g2
IGRAPH 270d00c DNW- 11 11 --
+ attr: name (v/c), type (e/c), weight (e/n), low (e/n), high (e/n)
+ edges from 270d00c (vertex names):
[1] R ->diploperennis_ R ->Rr Rr ->Rrr Rrr ->mexicana_
[5] Rrrr ->parviglumis_ Rrrp ->Rrrr admix->maize_ Rrr ->admix
[9] Rr ->Rrrp Rrrr ->admix Rrrp ->Nold_
```

and here’s the output if using `identical_graphs()`

or `intersection()`

on these two graphs:

```
> igraph::identical_graphs(g0,g2) #should be true
[1] FALSE
> igraph::intersection(g0,g2) #shows which edges are shared between graphs
IGRAPH 4d6dff6 DN-- 14 2 --
+ attr: name (v/c), type_1 (e/c), type_2 (e/c), weight_1 (e/n), weight_2 (e/n), low_1
| (e/n), low_2 (e/n), high_1 (e/n), high_2 (e/n)
+ edges from 4d6dff6 (vertex names):
[1] R->diploperennis_ R->Rr
```