code: def test_edge_paths(self):
      # Difficult edge cases
  
      # Edge test1
      edge_test1 = self.build_operands("eb,cb,fb->cef")
      path, path_str = np.einsum_path(*edge_test1, optimize="greedy")
      self.assert_path_equal(path, ["einsum_path", (0, 2), (0, 1)])
  
      path, path_str = np.einsum_path(*edge_test1, optimize="optimal")
      self.assert_path_equal(path, ["einsum_path", (0, 2), (0, 1)])
  
      # Edge test2
      edge_test2 = self.build_operands("dd,fb,be,cdb->cef")
      path, path_str = np.einsum_path(*edge_test2, optimize="greedy")
      self.assert_path_equal(
          path, ["einsum_path", (0, 3), (0, 1), (0, 1)]
      )
  
      path, path_str = np.einsum_path(*edge_test2, optimize="optimal")
      self.assert_path_equal(
          path, ["einsum_path", (0, 3), (0, 1), (0, 1)]
      )
  
      # Edge test3
      edge_test3 = self.build_operands("bca,cdb,dbf,afc->")
      path, path_str = np.einsum_path(*edge_test3, optimize="greedy")
      self.assert_path_equal(
          path, ["einsum_path", (1, 2), (0, 2), (0, 1)]
      )
  
      path, path_str = np.einsum_path(*edge_test3, optimize="optimal")
      self.assert_path_equal(
          path, ["einsum_path", (1, 2), (0, 2), (0, 1)]
      )
  
      # Edge test4
      edge_test4 = self.build_operands("dcc,fce,ea,dbf->ab")
      path, path_str = np.einsum_path(*edge_test4, optimize="greedy")
      self.assert_path_equal(
          path, ["einsum_path", (1, 2), (0, 1), (0, 1)]
      )
  
      path, path_str = np.einsum_path(*edge_test4, optimize="optimal")
      self.assert_path_equal(
          path, ["einsum_path", (1, 2), (0, 2), (0, 1)]
      )
  
      # Edge test5
      edge_test4 = self.build_operands(
          "a,ac,ab,ad,cd,bd,bc->",
          size_dict={"a": 20, "b": 20, "c": 20, "d": 20},
      )
      path, path_str = np.einsum_path(*edge_test4, optimize="greedy")
      self.assert_path_equal(
          path, ["einsum_path", (0, 1), (0, 1, 2, 3, 4, 5)]
      )
  
      path, path_str = np.einsum_path(*edge_test4, optimize="optimal")
      self.assert_path_equal(
          path, ["einsum_path", (0, 1), (0, 1, 2, 3, 4, 5)]
      )
  
imports: import itertools
  import sys
  import platform
  import pytest
  import numpy
  from numpy.testing import assert_, assert_equal, assert_array_equal, assert_almost_equal, assert_raises, suppress_warnings, assert_raises_regex, assert_allclose
label_desc: Use image node_id 5 for calling the TestEinsumPath obj's underlying member method code with example usage: obj.test_edge_paths() without return types