Rewrite python doc

1 files changed, 7 insertions, 5 deletions

diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx
index b9c2a42f..3d7c28b6 100644
--- a/src/python/gudhi/simplex_tree.pyx
+++ b/src/python/gudhi/simplex_tree.pyx
@@ -621,12 +621,14 @@ cdef class SimplexTree:
         return (normal0, normals, infinite0, infinites)
 
     def collapse_edges(self, nb_iterations = 1):
-        """Assuming the simplex tree is a 1-skeleton graph, this method collapse edges (simplices of higher dimension
-        are ignored) and resets the simplex tree from the remaining edges.
-        A good candidate is to build a simplex tree on top of a :class:`~gudhi.RipsComplex` of dimension 1 before
-        collapsing edges
+        """Assuming the complex is a graph (simplices of higher dimension are ignored), this method implicitly
+        interprets it as the 1-skeleton of a flag complex, and replaces it with another (smaller) graph whose
+        expansion has the same persistent homology, using a technique known as edge collapses
+        (see :cite:`edgecollapsearxiv`).
+
+        A natural application is to get a simplex tree of dimension 1 from :class:`~gudhi.RipsComplex`,
+        then collapse edges, perform :meth:`expansion()` and finally compute persistence
         (cf. :download:`rips_complex_edge_collapse_example.py <../example/rips_complex_edge_collapse_example.py>`).
-        For implementation details, please refer to :cite:`edgecollapsesocg2020`.
 
         :param nb_iterations: The number of edge collapse iterations to perform. Default is 1.
         :type nb_iterations: int