Python/graphs/connected_components.py
Christian Clauss cd3e8f95a0
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2020-07-06 08:48:18 +05:30

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Python

"""
https://en.wikipedia.org/wiki/Component_(graph_theory)
Finding connected components in graph
"""
test_graph_1 = {0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}
test_graph_2 = {0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}
def dfs(graph: dict, vert: int, visited: list) -> list:
"""
Use depth first search to find all vertices
being in the same component as initial vertex
>>> dfs(test_graph_1, 0, 5 * [False])
[0, 1, 3, 2]
>>> dfs(test_graph_2, 0, 6 * [False])
[0, 1, 3, 2]
"""
visited[vert] = True
connected_verts = []
for neighbour in graph[vert]:
if not visited[neighbour]:
connected_verts += dfs(graph, neighbour, visited)
return [vert] + connected_verts
def connected_components(graph: dict) -> list:
"""
This function takes graph as a parameter
and then returns the list of connected components
>>> connected_components(test_graph_1)
[[0, 1, 3, 2], [4, 5, 6]]
>>> connected_components(test_graph_2)
[[0, 1, 3, 2], [4], [5]]
"""
graph_size = len(graph)
visited = graph_size * [False]
components_list = []
for i in range(graph_size):
if not visited[i]:
i_connected = dfs(graph, i, visited)
components_list.append(i_connected)
return components_list
if __name__ == "__main__":
import doctest
doctest.testmod()