Assign Group Number to Dataframe - Matching across two columns

In a df such as the one below, I would like to assign a group number based on shared values across two columns - regardless of order

data = [[1, 10], [1, 15], [0, 15], [4, 0], [2, 3]]
df = pd.DataFrame(data, columns=['Value_1', 'Value_2'])

Desired output would assign a new column with a group number as such:

Group number is such that values shared in either the Value_1 or Value_2 column signal the same group value. i.e. since both 2 and 3 are not found elsewhere in the table in the Value_1 or Value_2 column, they are assigned to a new group. Whereas 1 and 15 are found multiple times. Regardless of the other number in the adjacent row, it is assigned to the same group number. Likewise 0 is found in a Value_1 and a Value_2 column and is linked to Group 1 via the 15

I have the following working as desired

def consolidate(sets):
    setlist = 
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    for i, s1 in enumerate(setlist):
        if s1:
            for s2 in setlist[i+1:]:
                intersection = s1.intersection(s2)
                if intersection:
                    s2.update(s1)
                    s1.clear()
                    s1 = s2
    return 
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def group_ids(pairs):
    groups = consolidate(map(set, pairs))
    d = {}
    for i, group in enumerate(sorted(groups)):
        for elem in group:
            d[elem] = i
    return d

df["C"] = df["Value_1"].replace(group_ids(zip(df.Value_1, df.Value_2)))

You can use networkx to automate the connected component search:

import networkx as nx

G = nx.from_pandas_edgelist(df, source='Value_1', target='Value_2')

mapper = {node: i for i, sub in enumerate(nx.connected_components(G), start=1)
          for node in sub}

df['Group'] = df['Value_1'].map(mapper)

Output:

   Value_1  Value_2  Group
0        1       10      1
1        1       15      1
2        0       15      1
3        4        0      1
4        2        3      2

Graph:

generalization

You can generalize to any number of columns, using melt:

df = pd.DataFrame({'Value_1': [9, 1, 0, 4, 2],
                   'Value_2': [10, 15, 15, 0, 3],
                   'Value_3': [20, 21, 22, 23, 23]
                  })
cols = ['Value_1', 'Value_2', 'Value_3']

G = nx.from_pandas_edgelist(df.melt(cols[0], cols[1:]),
                            source=cols[0], target='value')

mapper = {node: i for i, sub in enumerate(nx.connected_components(G), start=1)
          for node in sub}

df['Group'] = df[cols[0]].map(mapper)

Output:

   Value_1  Value_2  Value_3  Group
0        9       10       20      1
1        1       15       21      2
2        0       15       22      2
3        4        0       23      2
4        2        3       23      2

Graph: