diff --git a/README.md b/README.md
index 92a3cd8..37d356e 100644
--- a/README.md
+++ b/README.md
@@ -87,6 +87,7 @@ python -m graphviz2drawio test/directed/hello.gv.txt
 - [ ] Text on edge alignment #59 
 - [ ] Text alignment inside of shape
 - [ ] Support for node with `path` shape #47
+- [ ] Ensure undirected graphs are not drawn with arrows
 - [ ] Run ruff in CI
 - [ ] Publish api docs to GH pages
 - [ ] Restore codecov to test GHA
diff --git a/graphviz2drawio/graphviz2drawio.py b/graphviz2drawio/graphviz2drawio.py
index 48daa50..592bf85 100755
--- a/graphviz2drawio/graphviz2drawio.py
+++ b/graphviz2drawio/graphviz2drawio.py
@@ -2,7 +2,7 @@
 
 from pygraphviz import AGraph
 
-from .models import parse_nodes_edges_clusters
+from .models.SvgParser import parse_nodes_edges_clusters
 from .mx.MxGraph import MxGraph
 
 
diff --git a/graphviz2drawio/models/__init__.py b/graphviz2drawio/models/__init__.py
index d3fe148..b43295e 100644
--- a/graphviz2drawio/models/__init__.py
+++ b/graphviz2drawio/models/__init__.py
@@ -1,4 +1,3 @@
 # flake8: noqa: F401
 from .Arguments import Arguments
 from .Rect import Rect
-from .SvgParser import parse_nodes_edges_clusters
diff --git a/graphviz2drawio/mx/Curve.py b/graphviz2drawio/mx/Curve.py
index e62fa87..9d5e043 100644
--- a/graphviz2drawio/mx/Curve.py
+++ b/graphviz2drawio/mx/Curve.py
@@ -1,8 +1,9 @@
 import math
+from typing import Callable, Any
 
 from svg.path import CubicBezier
 
-from graphviz2drawio.models.Errors import InvalidCbError
+from ..models.Errors import InvalidCbError
 
 linear_min_r2 = 0.9
 
@@ -24,15 +25,22 @@ def __str__(self) -> str:
         return f"{self.start} , {control}, {self.end}"
 
     @staticmethod
-    def is_linear(cb: CubicBezier) -> bool:
-        m, b = Curve._linear_regression(cb.start, cb.end)
-        control1_prediction = m * cb.control1.real + b
-        control2_prediction = m * cb.control2.real + b
+    def is_linear(cb: CubicBezier, is_rotated: bool = False) -> bool:
+        line = _line(cb.start, cb.end)
+
+        if line is None:
+            if is_rotated:  # Prevent infinite recursion
+                return False
+            return Curve.is_linear(_rotate_bezier(cb), True)
 
         return math.isclose(
-            control1_prediction, cb.control1.imag, abs_tol=threshold
+            line(cb.control1.real),
+            cb.control1.imag,
+            rel_tol=0.1,
         ) and math.isclose(
-            control2_prediction, cb.control2.imag, abs_tol=threshold
+            line(cb.control2.real),
+            cb.control2.imag,
+            rel_tol=0.1,
         )
 
     def cubic_bezier_coordinates(self, t: float) -> complex:
@@ -88,3 +96,30 @@ def _derivative_of_cubic_bezier(p: list, t: float):
             + (6.0 * t * (1.0 - t) * (p[2] - p[1]))
             + (3.0 * (t**2) * (p[3] - p[2]))
         )
+
+
+def _line(start: complex, end: complex) -> Callable[[float], float] | None:
+    """Calculate the slope and y-intercept of a line."""
+    denom = end.real - start.real
+    if denom == 0:
+        return None
+    # Linearity is used to determine if a cubic Bézier is actually a line
+    # BUT we need to check for vertical lines or vertically oriented Beziers
+    # Maybe caller should flip x/y and call again?
+    m = (end.imag - start.imag) / denom
+    b = start.imag - (m * start.real)
+
+    def y(x: float) -> float:
+        return (m * x) + b
+
+    return y
+
+
+def _rotate_bezier(cb):
+    """Reverse imaginary and real parts for all components."""
+    return CubicBezier(
+        complex(cb.start.imag, cb.start.real),
+        complex(cb.control1.imag, cb.control1.real),
+        complex(cb.control2.imag, cb.control2.real),
+        complex(cb.end.imag, cb.end.real),
+    )
diff --git a/test/test_curve.py b/test/test_curve.py
index e69de29..ef6475a 100644
--- a/test/test_curve.py
+++ b/test/test_curve.py
@@ -0,0 +1,13 @@
+from graphviz2drawio.mx.Curve import _line
+
+
+def test_line():
+    line = _line(complex(-5, 10), complex(-3, 4))
+    assert line(0) == -5
+    assert line(1) == -8
+    assert line(2) == -11
+
+
+def test_line_vertical():
+    line = _line(complex(1, 10), complex(1, 4))
+    assert line is None
diff --git a/test/test_graphs.py b/test/test_graphs.py
index 568deea..ed7001c 100644
--- a/test/test_graphs.py
+++ b/test/test_graphs.py
@@ -92,6 +92,16 @@ def test_polylines() -> None:
 
     root = ElementTree.fromstring(xml)
     check_xml_top(root)
+    assert False
+
+
+def test_polylines_curved() -> None:
+    file = "test/undirected/polylines_curved.gv.txt"
+    xml = graphviz2drawio.convert(file)
+
+    root = ElementTree.fromstring(xml)
+    check_xml_top(root)
+    # assert False
 
 
 def test_cluster() -> None: