This is a simple blender python script adds a button inside the UI of the ShadingEditor. The functionality of the button will add a simple node group defined by create_test_group.

CustomNodeGroup.py

import bpy



class NODE_PT_MAINPANEL(bpy.types.Panel):
    """Creates a Panel in the Object properties window"""
    bl_label       = "Custom Node Group"
    bl_idname      = "NODE_PT_MAINPANEL"
    bl_space_type  = 'NODE_EDITOR'
    bl_region_type = 'UI'
    bl_category    = "New Tab"
    
    
    def draw(self, context):
        layout = self.layout

        row = layout.row()
        row.operator("node.test_operator")



def create_test_group(operator, context, group_name):
    context.object.active_material.use_nodes = True
    
    # create a new group
    test_group = bpy.data.node_groups.new(group_name, "ShaderNodeTree")
    

    # setup nodes inside the group
    group_in = test_group.nodes.new("NodeGroupInput")
    group_in.location = (-200,0)
    test_group.inputs.new("NodeSocketFloatFactor", "Factor WaveMix")
    test_group.inputs.new("NodeSocketFloatFactor", "Factor Noise")
    test_group.inputs[0].min_value     = 0.0
    test_group.inputs[0].max_value     = 1.0
    test_group.inputs[0].default_value = 0.5

    group_out = test_group.nodes.new("NodeGroupOutput")
    group_out.location = (400,0)
    test_group.outputs.new("NodeSocketColor", "Output")

    texNoise_node = test_group.nodes.new(type="ShaderNodeTexNoise")
    texNoise_node.location = (0,0)
    texNoise_node.inputs[2].default_value = 10
    
    texWave_node = test_group.nodes.new(type="ShaderNodeTexWave")
    texWave_node.location = (0,-250)
    
    mix_node = test_group.nodes.new(type="ShaderNodeMixRGB")
    mix_node.location = (200,0)
    mix_node.use_clamp = True
    mix_node.blend_type = 'MIX'
    
    
    # setup connections between the nodes
    connect = test_group.links.new
    connect(group_in.outputs[0], mix_node.inputs[0])
    connect(group_in.outputs[1], texNoise_node.inputs[2])
    connect(texNoise_node.outputs[0], mix_node.inputs[1])
    connect(texWave_node.outputs[0], mix_node.inputs[2])
    connect(mix_node.outputs[0], group_out.inputs[0])

    return test_group



class NODE_OT_TEST(bpy.types.Operator):
    bl_idname = "node.test_operator"
    bl_label  = "Add Custom Node Group"


    @classmethod
    def poll(cls, context):
        space = context.space_data
        return space.type == "NODE_EDITOR"
    

    def execute(self, context):
        custom_node_name = "Test Node"
        my_group = create_test_group(self, context, custom_node_name)
        node_tree = context.object.active_material.node_tree
        new_node = node_tree.nodes.new("ShaderNodeGroup")
        new_node.node_tree = bpy.data.node_groups[my_group.name]
        new_node.use_custom_color = True
        new_node.color = (0.5, 0.4, 0.3)
        return {"FINISHED"}
        


def register():
    bpy.utils.register_class(NODE_OT_TEST)
    bpy.utils.register_class(NODE_PT_MAINPANEL)



def unregister():
    bpy.utils.unregister_class(NODE_OT_TEST)
    bpy.utils.unregister_class(NODE_PT_MAINPANEL)



if __name__ == "__main__":
    register()