diff --git a/Project.toml b/Project.toml
index ad7b6c5..56663d9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,7 +6,6 @@ version = "0.1.1"
 [deps]
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/src/GromovWitten.jl b/src/GromovWitten.jl
index fe28fb5..bde750c 100644
--- a/src/GromovWitten.jl
+++ b/src/GromovWitten.jl
@@ -9,8 +9,6 @@ import Combinatorics: permutations, with_replacement_combinations
 
 import StatsBase: countmap
 
-import Graphs: nv, ne, Edge, dst, src, DiGraph
-
 export cache_integral_result
 export coefterm
 export constterm
diff --git a/src/coefterm.jl b/src/coefterm.jl
index 2f54425..befe5fc 100644
--- a/src/coefterm.jl
+++ b/src/coefterm.jl
@@ -8,8 +8,8 @@
 #Where I(q) is the Feynman Integral and P(x,q) the Propagator.
 #=function coefterm(x::Vector,q::Vector,G::FeynmanGraph ,p::QQMPolyRingElem,d::Integer;l=zeros(Int,nv(G)))
    #here l is leak vector of the graph G.
-    ee=Edge.(G.edge) 
-    G=DiGraph(Edge.(G.edge)) # convert from graph to Graph (so we can use nv(G))
+    ee=edges(G) 
+    G=DiGraph(edges(G)) # convert from graph to Graph (so we can use nv(G))
     L=zeros(Int,nv(G)) #  define zeros Vector of length nv(G)
     for ev in ee
         if src(ev) == dst(ev) #checking for loop term. 
@@ -94,7 +94,7 @@ Let   Ω=[x1,...,xn] be  a given Order and $a$  a branche type,flip_signature  r
 It will return -2 in case the Graph G has a loop. 
 """
 function flip_signature(G::FeynmanGraph ,p::Vector{Int64},a::Vector{Int64}) #graph G, list p, branch type a
-    ee=Edge.(G.edge)
+    ee=edges(G)
     b=zeros(Int,length(a))
     for (i, (ai, ev)) in enumerate(zip(a, ee))
         if ai == 0 && src(ev) != dst(ev)
@@ -137,7 +137,7 @@ julia> signature_and_multiplicities(G,a)
 ```
 """
 function signature_and_multiplicities(G::FeynmanGraph, a::Vector{Int64})
-    ee = Edge.(G.edge)
+    ee = edges(G)
     p = Vector{Int64}()
     b = Vector{Tuple{Int64, Vector{Int64}}}()
     l = zeros(Int, nv(G))
@@ -208,8 +208,8 @@ function signature_and_multiplicities(G::FeynmanGraph, a::Vector{Int64})
 end
 
 
-function find_equal_pairs(ve::Vector{Tuple{Int64, Int64}})
-    equal_pairs = Dict{Tuple{Int, Int}, Vector{Int}}()
+function find_equal_pairs(ve::Vector{Edge})
+    equal_pairs = Dict{Edge, Vector{Int}}()
     for (i, pair) in enumerate(ve)
         if haskey(equal_pairs, pair)
             push!(equal_pairs[pair], i)
diff --git a/src/coeftermV.jl b/src/coeftermV.jl
index a998e65..7ad8d40 100644
--- a/src/coeftermV.jl
+++ b/src/coeftermV.jl
@@ -106,8 +106,8 @@ end
     return hp
 end
 function coeftermX( x::Vector, q::Vector,z::Vector,G::graph ,p::QQMPolyRingElem,d::Integer;l=zeros(Int,nv(G)))
-    ee=Edge.(G.edge)
-    G=DiGraph(Edge.(G.edge))
+    ee=edges(G)
+    G=DiGraph(edges(G))
     L=zeros(Int,nv(G))
     for ev in ee
         if src(ev) == dst(ev)
@@ -122,8 +122,8 @@ function coeftermX( x::Vector, q::Vector,z::Vector,G::graph ,p::QQMPolyRingElem,
     return p
 end =#
 function lis(G::FeynmanGraph,d::Int64,l::Vector{Int64})
-    ee = Edge.(G.edge)
-    #G=DiGraph(Edge.(G.edge))
+    ee = edges(G)
+    #G=DiGraph(edges(G))
     L=zeros(Int,nv(G))
      @inbounds for ev in ee
         if src(ev) != dst(ev)
diff --git a/src/feynmanIntegral.jl b/src/feynmanIntegral.jl
index 4f215d7..8da5f69 100644
--- a/src/feynmanIntegral.jl
+++ b/src/feynmanIntegral.jl
@@ -35,7 +35,7 @@ julia> feynman_integral_branch_type(F,a,g)
 ```
 """
 function feynman_integral_branch_type(F::FeynmanIntegral, a::Vector{Int64}; l=zeros(Int, nv(F.G)))
-    ee = Edge.(F.G.edge)
+    ee = edges(F.G)
     N = sum(a)
     f = signature_and_multiplicities(F.G, a)
     p = 0
@@ -62,7 +62,7 @@ function feynman_integral_branch_type(F::FeynmanIntegral, a::Vector{Int64}; l=ze
     return p
 end
 function feynman_integral_branch_type(F::FeynmanIntegral, a::Vector{Int64},g::Vector{Int64}; aa=1,l=zeros(Int,nv(F.G)))
-    ee = Edge.(F.G.edge)
+    ee = edges(F.G)
     N = sum(a)
     f = signature_and_multiplicities(F.G, a)
     p = 0
@@ -142,7 +142,7 @@ julia> feynman_integral_branch_type_order(F,a,Ω,g)
 ```
 """
 function feynman_integral_branch_type_order(F::FeynmanIntegral, a::Vector{Int64}, o::Vector{Int64}; l=zeros(Int, nv(F.G)))
-    ee = Edge.(F.G.edge)
+    ee = edges(F.G)
     N = sum(a)
     f = signature_and_multiplicities_order(F.G, a,o)
     p = 0
@@ -172,7 +172,7 @@ function feynman_integral_branch_type_order(F::FeynmanIntegral, a::Vector{Int64}
     return p
 end
 function feynman_integral_branch_type_order(F::FeynmanIntegral, a::Vector{Int64}, o::Vector{Int64}, g::Vector{Int64}; aa=1,l=zeros(Int,nv(F.G)))
-    ee = Edge.(F.G.edge)
+    ee = edges(F.G)
     N = sum(a)
     f = signature_and_multiplicities_order(F.G, a,o)
     p = 0
@@ -253,12 +253,11 @@ julia> feynman_integral_degree_order(F,Ω,3,g)
 ```
 """
 function feynman_integral_degree_order( F::FeynmanIntegral,o::Vector{Int64},d::Integer,;l=zeros(Int,nv(F.G)) )
-    # ve==F.G.edge
-     indices = find_equal_pairs(F.G.edge)
+     indices = find_equal_pairs(edges(F.G))
      if isempty(indices)
          return feynman_integral_deg_order(F,o,d;l)
      else
-         ee=Edge.(F.G.edge)
+         ee=edges(F.G)
  
          re = Vector{Vector{Any}}()
          res = []
@@ -301,12 +300,11 @@ function feynman_integral_degree_order( F::FeynmanIntegral,o::Vector{Int64},d::I
      end
  end
 function feynman_integral_degree_order( F::FeynmanIntegral,o::Vector{Int64},d::Integer,g::Vector{Int} ;aa=1,l=zeros(Int,nv(F.G)) )
-    # ve==F.G.edge
-     indices = find_equal_pairs(F.G.edge)
+     indices = find_equal_pairs(edges(F.G))
      if isempty(indices)
          return feynman_integral_deg_order(F,o,d,g;aa,l)
      else
-         ee=Edge.(F.G.edge)
+         ee=edges(F.G)
  
          re = Vector{Vector{Any}}()
          res = []
@@ -349,7 +347,7 @@ function feynman_integral_degree_order( F::FeynmanIntegral,o::Vector{Int64},d::I
      end
  end
 function feynman_integral_deg_order(F::FeynmanIntegral,o::Vector{Int64},d::Integer;l=zeros(Int,nv(F.G)))
-    ee=Edge.(F.G.edge)
+    ee=edges(F.G)
     a=partition(length(ee),d) 
     sum=0
     for ai in a
@@ -358,7 +356,7 @@ function feynman_integral_deg_order(F::FeynmanIntegral,o::Vector{Int64},d::Integ
     return sum
 end 
 function feynman_integral_deg_order(F::FeynmanIntegral,o::Vector{Int64},d::Integer,g;aa=1,l=zeros(Int,nv(F.G)))
-    ee=Edge.(F.G.edge)
+    ee=edges(F.G)
     a=partition(length(ee),d) 
     sum=0
     for ai in a
@@ -403,12 +401,11 @@ julia> feynman_integral_degree(F,3,g)
 ```
  """
  function feynman_integral_degree(F::FeynmanIntegral, d::Int64 ; l=zeros(Int, nv(F.G)) )
-    # ve==F.G.edge
-     indices = find_equal_pairs(F.G.edge)
+     indices = find_equal_pairs(edges(F.G))
      if isempty(indices)
          return feynman_integral_deg(F,d;l)
      else
-         ee=Edge.(F.G.edge)
+         ee=edges(F.G)
  
          re = Vector{Vector{Any}}()
          res = []
@@ -448,12 +445,11 @@ julia> feynman_integral_degree(F,3,g)
      end
  end
  function feynman_integral_degree( F::FeynmanIntegral,d::Integer,g::Vector{Int} ;aa=1,l=zeros(Int,nv(F.G)) )
-    # ve==F.G.edge
-     indices = find_equal_pairs(F.G.edge)
+     indices = find_equal_pairs(edges(F.G))
      if isempty(indices)
          return feynman_integral_deg(F,d,g;aa,l)
      else
-         ee=Edge.(F.G.edge)
+         ee=edges(F.G)
  
          re = Vector{Vector{Any}}()
          res = []
@@ -493,7 +489,7 @@ julia> feynman_integral_degree(F,3,g)
      end
  end
  function feynman_integral_deg( F::FeynmanIntegral,d::Integer ;l=zeros(Int,nv(F.G)))
-    ee=Edge.(F.G.edge)
+    ee=edges(F.G)
     a=partition(length(ee),d) 
     sum=0
     for ai in a
@@ -502,7 +498,7 @@ julia> feynman_integral_degree(F,3,g)
     return sum
 end 
 function feynman_integral_deg( F::FeynmanIntegral,d::Integer,g ;aa=1,l=zeros(Int,nv(F.G)))
-    ee=Edge.(F.G.edge)
+    ee=edges(F.G)
     a=partition(length(ee),d) 
     sum=0
     for ai in a
diff --git a/src/graph.jl b/src/graph.jl
index 254a06c..a981148 100644
--- a/src/graph.jl
+++ b/src/graph.jl
@@ -3,18 +3,32 @@
 #            graph.jl : define graph and Polynomial Ring.                     #
 #                                                                             #
 ###############################################################################
+struct Edge
+    src::Int
+    dst::Int
+end
+Edge(e::Tuple{Int, Int}) = Edge(e[1], e[2])
+src(e::Edge) = e.src
+dst(e::Edge) = e.dst
+
+Base.show(io::IO, e::Edge) = show(io, (src(e), dst(e)))
+
 struct FeynmanGraph
-    edge::Vector
+    _edges::Vector{Edge}
 end
- # edge(G::FeynmanGraph) = Edge.(G.edge)
-    nv(G::FeynmanGraph) = nv(DiGraph(Edge.(G.edge)))
-    ne(G::FeynmanGraph) = length(Edge.(G.edge))
+FeynmanGraph(edges::Vector{Tuple{Int, Int}}) = FeynmanGraph(Edge.(edges))
+
+edges(G::FeynmanGraph) = G._edges
+nv(G::FeynmanGraph) = length(union([e.src for e in G._edges], [e.dst for e in G._edges]))
+ne(G::FeynmanGraph) = length(G._edges)
+
+Base.show(io::IO, G::FeynmanGraph) = print(io, "FeynmanGraph(", [ (src(e), dst(e)) for e in edges(G) ], ")")
 
 function feynman_graph(edges::Vector{Tuple{Int, Int}})
     return FeynmanGraph(edges)
 end
 #=function polynomial_ring(G::FeynmanGraph, x::String, q::String, z::String)
-    ee=Edge.(G.edge)
+    ee=edges(G)
     if length(ee)==0
         throw(DomainError(G,"G must be non empty graph"))
     else
@@ -22,7 +36,7 @@ end
     end
 end
 function polynomial_ring(G::FeynmanGraph, x::String, q::String)
-    ee=Edge.(G.edge)
+    ee=edges(G)
     if length(ee)==0
         throw(DomainError(G,"G must be non empty graph"))
     else
@@ -55,4 +69,3 @@ end
 function feynman_integral(G::FeynmanGraph)
     return FeynmanIntegral(G)
 end
- edge(F::FeynmanIntegral) = Edge.(F.G.edge)
\ No newline at end of file