def generateGraph(z):
    '''
        Generates a dictionary {vertex: set(links)} from the matrix
    '''
    graph = {}
    for key,value in enumerate(range(0,len(z))):
        z[value] = list(z[value])
        graph[value] = set()
        for k,v in enumerate(z[value]):
            if int(z[value][k]) == 1:
                graph[value].add(k)
    return graph

def countClusters(graph):
    '''
        Counts the number of independent sub-graphs
    '''
    clusters = 0
    while graph != {}:
        clusters += 1
        for edge in graph[next(iter(graph))]:
            if edge in graph:
                for vertex in depthFirstSearch(graph,edge):
                    del graph[vertex]
    return clusters

def depthFirstSearch(graph, vertex, visited=None):
    '''
        Searches a graph by vising recursively all vertices
    '''
    if visited is None:
        visited = set()
    visited.add(vertex)
    for nextVertex in graph[vertex] - visited:
        dfs(graph, nextVertex, visited)
    return visited



m = ['11000',
     '11000',
     '00110',
     '00110',
     '00001']
graph = generateGraph(m)
clusters = countClusters(graph)
print clusters