How to store distances of nodes from root in breadth-first tree?

Question

Let G(V,E) be an undirected graph. I want create a breadth-first tree from G storing nodes with corresponding distances from root. please help.

import networkx as nx

g=nx.erdos_renyi_graph(12,.1)
visited = [] 
queue = []     
tree={}
def bfs(visited, g, node):
  visited.append(node)
  queue.append(node)

  while queue:
    s = queue.pop(0)
    tree[s]=[]
    for neighbour in list(g.adj[s]):
      if neighbour not in visited:
        visited.append(neighbour)
        tree[s].append(neighbour)
        queue.append(neighbour)

bfs(visited, g, 1)
print(tree)

Answer 1

You could keep every item as (node, distance) and append (neighbour, distance+1)

import matplotlib.pyplot as plt
import networkx as nx

# --- functions ---

def bfs(g, node):
    distance = 0
    visited = [node]
    queue = [(node, distance)]

    tree = {}

    while queue:
        s, distance = queue.pop(0)
        tree[s] = []
        for neighbour in list(g.adj[s]):
            if neighbour not in visited:
                visited.append(neighbour)
                tree[s].append((neighbour, distance+1))
                queue.append((neighbour, distance+1))

    return tree
  
# --- main ---

#G = nx.erdos_renyi_graph(12, .1)
G = nx.Graph()
G.add_edges_from(([1,2],[2,3], [2,4], [3, 5], [4,5]))

tree = bfs(G, 1)
print(tree)

nx.draw(G, with_labels=True)
plt.show()

Result (manually reformated):

{
  1: [(2, 1)], 
  2: [(3, 2), (4, 2)], 
  3: [(5, 3)], 
  4: [], 
  5: []
}

For graph

---

Evenutally you can even use tree[(s, distance)]

def bfs(g, node):
    distance = 0
    visited = [node]
    queue = [(node, distance)]

    tree = {}

    while queue:
        s, distance = queue.pop(0)
        tree[(s, distance)] = []
        for neighbour in list(g.adj[s]):
            if neighbour not in visited:
                visited.append(neighbour)
                tree[(s, distance)].append((neighbour, distance+1))
                queue.append((neighbour, distance+1))

    return tree

Result (manually reformated):

{
  (1, 0): [(2, 1)], 
  (2, 1): [(3, 2), (4, 2)], 
  (3, 2): [(5, 3)], 
  (4, 2): [], 
  (5, 3): []
}

---

BTW:

I was thinking to use json.dumps(tree, indent=2) to reformat result automatically but it can't convert node to json.

But pretty printer can format it in similar way

import pprint
pprint.pprint(tree, indent=2)

Result:

{ (1, 0): [(2, 1)],
  (2, 1): [(3, 2), (4, 2)],
  (3, 2): [(5, 3)],
  (4, 2): [],
  (5, 3): []}