Hierarchical data: efficiently build a list of every descendant for each node

Question

I have a two column data set depicting multiple child-parent relationships that form a large tree. I would like to use this to build an updated list of every descendant for

Answer 1

A solution using networkx, there may be a more efficient method in the documentation, but this nested loop does the trick.

import pandas as pd
from timeit import timeit

df = pd.DataFrame(
    {
        'child':     [3102, 2010, 3011, 3000, 3033, 2110, 3111, 2100],
        'parent':    [2010, 1000, 2010, 2110, 2100, 1000, 2110, 1000]
    },  columns=['child', 'parent']
)

In networkx 2.0, use from_pandas_edgelist to create a directed graph:

import networkx as nx
DiG = nx.from_pandas_edgelist(df, 'parent', 'child', create_using=nx.DiGraph())

Simply iterate over the nodes and the ancestors of each node.

for n1 in DiG.nodes():
    for n2 in nx.ancestors(DiG, n1):
        print(n1,n2)

3000 1000
3000 2110
3011 1000
3011 2010
2100 1000
2110 1000
3111 1000
3111 2110
3033 1000
3033 2100
2010 1000
3102 1000
3102 2010

Wrapped into a function:

def all_descendants_nx():
    DiG = nx.from_pandas_edgelist(df,'parent','child',create_using=nx.DiGraph())
    return pd.DataFrame.from_records([(n1,n2) for n1 in DiG.nodes() for n2 in nx.ancestors(DiG, n1)], columns=['descendant','ancestor'])

print(timeit(all_descendants_nx, number=50)) #to compare to Stephen's nice answer
0.05033063516020775

all_descendants_nx()
    descendant  ancestor
0   3000    1000
1   3000    2110
2   3011    1000
3   3011    2010
4   2100    1000
5   2110    1000
6   3111    1000
7   3111    2110
8   3033    1000
9   3033    2100
10  2010    1000
11  3102    1000
12  3102    2010

Answer 2

This is a method using numpy to iterate down the tree a generation at a time.

Code:

import numpy as np
import pandas as pd  # only used to return a dataframe


def list_ancestors(edges):
    """
    Take edge list of a rooted tree as a numpy array with shape (E, 2),
    child nodes in edges[:, 0], parent nodes in edges[:, 1]
    Return pandas dataframe of all descendant/ancestor node pairs

    Ex:
        df = pd.DataFrame({'child': [200, 201, 300, 301, 302, 400],
                           'parent': [100, 100, 200, 200, 201, 300]})

        df
           child  parent
        0    200     100
        1    201     100
        2    300     200
        3    301     200
        4    302     201
        5    400     300

        list_ancestors(df.values)

        returns

            descendant  ancestor
        0          200       100
        1          201       100
        2          300       200
        3          300       100
        4          301       200
        5          301       100
        6          302       201
        7          302       100
        8          400       300
        9          400       200
        10         400       100
    """
    ancestors = []
    for ar in trace_nodes(edges):
        ancestors.append(np.c_[np.repeat(ar[:, 0], ar.shape[1]-1),
                               ar[:, 1:].flatten()])
    return pd.DataFrame(np.concatenate(ancestors),
                        columns=['descendant', 'ancestor'])


def trace_nodes(edges):
    """
    Take edge list of a rooted tree as a numpy array with shape (E, 2),
    child nodes in edges[:, 0], parent nodes in edges[:, 1]
    Yield numpy array with cross-section of tree and associated
    ancestor nodes

    Ex:
        df = pd.DataFrame({'child': [200, 201, 300, 301, 302, 400],
                           'parent': [100, 100, 200, 200, 201, 300]})

        df
           child  parent
        0    200     100
        1    201     100
        2    300     200
        3    301     200
        4    302     201
        5    400     300

        trace_nodes(df.values)

        yields

        array([[200, 100],
               [201, 100]])

        array([[300, 200, 100],
               [301, 200, 100],
               [302, 201, 100]])

        array([[400, 300, 200, 100]])
    """
    mask = np.in1d(edges[:, 1], edges[:, 0])
    gen_branches = edges[~mask]
    edges = edges[mask]
    yield gen_branches
    while edges.size != 0:
        mask = np.in1d(edges[:, 1], edges[:, 0])
        next_gen = edges[~mask]
        gen_branches = numpy_col_inner_many_to_one_join(next_gen, gen_branches)
        edges = edges[mask]
        yield gen_branches


def numpy_col_inner_many_to_one_join(ar1, ar2):
    """
    Take two 2-d numpy arrays ar1 and ar2,
    with no duplicate values in first column of ar2
    Return inner join of ar1 and ar2 on
    last column of ar1, first column of ar2

    Ex:

        ar1 = np.array([[1,  2,  3],
                        [4,  5,  3],
                        [6,  7,  8],
                        [9, 10, 11]])

        ar2 = np.array([[ 1,  2],
                        [ 3,  4],
                        [ 5,  6],
                        [ 7,  8],
                        [ 9, 10],
                        [11, 12]])

        numpy_col_inner_many_to_one_join(ar1, ar2)

        returns

        array([[ 1,  2,  3,  4],
               [ 4,  5,  3,  4],
               [ 9, 10, 11, 12]])
    """
    ar1 = ar1[np.in1d(ar1[:, -1], ar2[:, 0])]
    ar2 = ar2[np.in1d(ar2[:, 0], ar1[:, -1])]
    if 'int' in ar1.dtype.name and ar1[:, -1].min() >= 0:
        bins = np.bincount(ar1[:, -1])
        counts = bins[bins.nonzero()[0]]
    else:
        counts = np.unique(ar1[:, -1], False, False, True)[1]
    left = ar1[ar1[:, -1].argsort()]
    right = ar2[ar2[:, 0].argsort()]
    return np.concatenate([left[:, :-1],
                           right[np.repeat(np.arange(right.shape[0]),
                                           counts)]], 1)

Timing Comparison:

Test cases 1 & 2 provided by @taky2, test cases 3 & 4 comparing performance on tall and wide tree structures respectively – most use cases are likely somewhere in the middle.

df = pd.DataFrame(
    {
        'child': [3102, 2010, 3011, 3000, 3033, 2110, 3111, 2100],
        'parent': [2010, 1000, 2010, 2110, 2100, 1000, 2110, 1000]
    }
)

df2 = pd.DataFrame(
    {
        'child': [4321, 3102, 4023, 2010, 5321, 4200, 4113, 6525, 4010, 4001,
                  3011, 5010, 3000, 3033, 2110, 6100, 3111, 2100, 6016, 4311],
        'parent': [3111, 2010, 3000, 1000, 4023, 3011, 3033, 5010, 3011, 3102,
                   2010, 4023, 2110, 2100, 1000, 5010, 2110, 1000, 5010, 3033]
    }
)

df3 = pd.DataFrame(np.r_[np.c_[np.arange(1, 501), np.arange(500)],
                         np.c_[np.arange(501, 1001), np.arange(500)]],
                   columns=['child', 'parent'])

df4 = pd.DataFrame(np.r_[np.c_[np.arange(1, 101), np.repeat(0, 100)],
                         np.c_[np.arange(1001, 11001),
                               np.repeat(np.arange(1, 101), 100)]],
                   columns=['child', 'parent'])

%timeit get_ancestry_dataframe_flat(df)
10 loops, best of 3: 53.4 ms per loop

%timeit add_children_of_children(df)
1000 loops, best of 3: 1.13 ms per loop

%timeit all_descendants_nx(df)
1000 loops, best of 3: 675 µs per loop

%timeit list_ancestors(df.values)
1000 loops, best of 3: 391 µs per loop

%timeit get_ancestry_dataframe_flat(df2)
10 loops, best of 3: 168 ms per loop

%timeit add_children_of_children(df2)
1000 loops, best of 3: 1.8 ms per loop

%timeit all_descendants_nx(df2)
1000 loops, best of 3: 1.06 ms per loop

%timeit list_ancestors(df2.values)
1000 loops, best of 3: 933 µs per loop

%timeit add_children_of_children(df3)
10 loops, best of 3: 156 ms per loop

%timeit all_descendants_nx(df3)
1 loop, best of 3: 952 ms per loop

%timeit list_ancestors(df3.values)
10 loops, best of 3: 104 ms per loop

%timeit add_children_of_children(df4)
1 loop, best of 3: 503 ms per loop

%timeit all_descendants_nx(df4)
1 loop, best of 3: 238 ms per loop

%timeit list_ancestors(df4.values)
100 loops, best of 3: 2.96 ms per loop

Notes:

get_ancestry_dataframe_flat not timed on cases 3 & 4 due to time and memory concerns.

add_children_of_children modified to identify root node internally, but allowed to assume a unique root. First line root_node = (set(dataframe.parent) - set(dataframe.child)).pop() added.

all_descendants_nx modified to accept a dataframe as an argument, instead of pulling from an external namespace.

Example demonstrating proper behavior:

np.all(get_ancestry_dataframe_flat(df2).sort_values(['descendant', 'ancestor'])\
                                       .reset_index(drop=True) ==\
       list_ancestors(df2.values).sort_values(['descendant', 'ancestor'])\
                                 .reset_index(drop=True))
Out[20]: True

Answer 3

Here is a method which builds a dict to allow easier navigation of the tree. Then runs the tree once and adds the children to their grand parents and above. And finally adds the new data to the dataframe.

Code:

def add_children_of_children(dataframe, root_node):
    # build a dict of lists to allow easy tree descent
    tree = {}
    for idx, (child, parent) in dataframe.iterrows():
        tree.setdefault(parent, []).append(child)

    data = []

    def descend_tree(parent):
        # get list of children of this parent
        children = tree[parent]

        # reverse order so that we can modify the list while looping
        for child in reversed(children):
            if child in tree:

                # descend tree and find children which need to be added
                lower_children = descend_tree(child)

                # add children from below to parent at this level
                data.extend([(c, parent) for c in lower_children])

                # return lower children to parents above
                children.extend(lower_children)

        return children

    descend_tree(root_node)

    return dataframe.append(
        pd.DataFrame(data, columns=dataframe.columns))

Timings:

There are three test methods in the test code, seconds from a timeit run:

• 0.073 - add_children_of_children() from above.
• 0.153 - add_children_of_children() with the output sorted.
• 3.385 - original get_ancestry_dataframe_flat() pandas implementation.

So a native data structure approach is considerably faster than the original implementation.

Test Code:

import pandas as pd

df = pd.DataFrame(
    {
        'child': [3102, 2010, 3011, 3000, 3033, 2110, 3111, 2100],
        'parent': [2010, 1000, 2010, 2110, 2100, 1000, 2110, 1000]
    }, columns=['child', 'parent']
)

def method1():
    # the root node is the node which is not a child
    root = set(df.parent) - set(df.child)
    assert len(root) == 1, "Number of roots != 1 '{}'".format(root)
    return add_children_of_children(df, root.pop())

def method2():
    dataframe = method1()
    names = ['ancestor', 'descendant']
    rename = {o: n for o, n in zip(dataframe.columns, reversed(names))}
    return dataframe.rename(columns=rename) \
        .sort_values(names).reset_index(drop=True)

def method3():
    return get_ancestry_dataframe_flat(df)

def get_ancestry_dataframe_flat(df):

    def get_child_list(parent_id):

        list_of_children = list()
        list_of_children.append(
            df[df['parent'] == parent_id]['child'].values)

        for i, r in df[df['parent'] == parent_id].iterrows():
            if r['child'] != parent_id:
                list_of_children.append(get_child_list(r['child']))

        # flatten list
        list_of_children = [
            item for sublist in list_of_children for item in sublist]
        return list_of_children

    new_df = pd.DataFrame(columns=['descendant', 'ancestor']).astype(int)
    for index, row in df.iterrows():
        temp_df = pd.DataFrame(columns=['descendant', 'ancestor'])
        temp_df['descendant'] = pd.Series(get_child_list(row['parent']))
        temp_df['ancestor'] = row['parent']
        new_df = new_df.append(temp_df)

    new_df = new_df\
        .drop_duplicates()\
        .sort_values(['ancestor', 'descendant'])\
        .reset_index(drop=True)

    return new_df

print(method2())
print(method3())

from timeit import timeit
print(timeit(method1, number=50))
print(timeit(method2, number=50))
print(timeit(method3, number=50))

Test Results:

    descendant  ancestor
0         2010      1000
1         2100      1000
2         2110      1000
3         3000      1000
4         3011      1000
5         3033      1000
6         3102      1000
7         3111      1000
8         3011      2010
9         3102      2010
10        3033      2100
11        3000      2110
12        3111      2110

    descendant  ancestor
0         2010      1000
1         2100      1000
2         2110      1000
3         3000      1000
4         3011      1000
5         3033      1000
6         3102      1000
7         3111      1000
8         3011      2010
9         3102      2010
10        3033      2100
11        3000      2110
12        3111      2110

0.0737142168563
0.153700592966
3.38558308083

Answer 4

Here is one way using isin() and map

df_new = df.append(df[df['parent'].isin(df['child'].values.tolist())])\
.reset_index(drop = True)

df_new.loc[df_new.duplicated(), 'parent'] = df_new.loc[df_new.duplicated(), 'parent']\
.map(df.set_index('child')['parent'])

df_new = df_new.sort_values('parent').reset_index(drop=True)
df_new.columns = [' descendant' , 'ancestor']

You get

    descendant  ancestor
0   2010    1000
1   2100    1000
2   2110    1000
3   3000    1000
4   3011    1000
5   3033    1000
6   3102    1000
7   3111    1000
8   3011    2010
9   3102    2010
10  3033    2100
11  3000    2110
12  3111    2110