How to know max number of connected nodes in a graph-without going back to previous node

Question

Suppose we need to draw a graph with many points. For example INPUT : {1#2,2#3,3#11,1#11,4#11,4#5,5#6,4#12} OUTPUT : 7

One node can be connected to many other nodes directly. We need to find the max connected nodes in this graph but not allowed to go back.

I have tried a lot to get any algorithm to solve this problem but not able to find. Can someone please help me for this?

Thanks in Advance, Krishan

What do you mean by 'max' number? You need to clarify what exactly the input and output is. Are you given an edge list? A node count? — VoidStar, Apr 09 '15 at 05:11
We need to find out the max possible length which traversed in the graph designed by given input point. For example INPUT {1#2,2#3,3#11,1#11,4#11,4#5,5#6,4#12} should output 7 as result — Krishan Kumar Gorav, Apr 09 '15 at 07:35

score 0 · Answer 1 · answered Apr 10 '15 at 08:12

0

Your definition of the problem is still a bit vague - at least from my point of view. However, I think that you are looking for the longest path in a (directed or undirected?) graph. In general, this is a NP-complete problem. Have a look at this wikepedia entry. This should serve as a starting point for further research.

answered Apr 10 '15 at 08:12

Reinhard

409
2
10

Thanks for your help. Yes I think, this should be NP Complete. But, Is there C# Code or pseudo code to find the NP Complete path in an 2D array or List etc? – Krishan Kumar Gorav Apr 12 '15 at 13:23
Is your graph directed or undirected? Can it contain a cycle or is it an acyclic graph? – Reinhard Apr 16 '15 at 14:03
It is an undirected graph and may contain cycle. But the only condition is, you cannot go back to previous node. – Krishan Kumar Gorav Apr 22 '15 at 06:07
Are you looking for the optimal solution or is a heuristic ok? Waht is the number of nodes for a typical input? – Reinhard Apr 23 '15 at 11:27
Finally I am able to solve this. Thanks for your help. – Krishan Kumar Gorav May 05 '15 at 06:35

score 0 · Answer 2 · answered May 06 '17 at 07:12

Here is the python code that will find the number of maximum components (maximum connected nodes) in a graph. However, it is not optimal solution(a.k.a, slow), but might be useful for you to get started

#!/bin/python
max_count = 0

def count_components(adj_list,r,c,count):
    global max_count
    row  = adj_list[r]

    #count
    connections = 0
    for j in range(len(row)):
        if row[j]==1:
            connections+=1
    count+=connections

    #traverse
    for j in range(len(row)):
        if row[j]==1:            
            adj_list[j][r]=0
            count_components(adj_list,j,r,count)
    #print 'count = {}'.format(count)
    if count>max_count:
        max_count = count

def get_max_num_of_connected_component(adj_list):

    for i in range(len(adj_list)):
        row = adj_list[i]
        for j in range(len(row)):
            if row[j]==1:
                count_components(adj_list,i,j,1)
                break

        #print_adjecency_list(adj_list)
    #print 'max_count = {}'.format(max_count)
    return max_count
def print_adjecency_list(adj_list):
    for i in range(len(adj_list)):
        row = adj_list[i]
        for j in range(len(row)):
            print row[j],
        print
    print
import sys

n, m = raw_input().strip().split(' ')
n, m = [int(n), int(m)]
route = []
for route_i in xrange(m):
    route_temp = map(int,raw_input().strip().split(' '))
    route.append(route_temp)
# Write Your Code Here

# generate NxM adjecency list of 
adjecency_list=[]
for i in range(n):
    row = []
    for j in range(n):
        row.append(0)
    adjecency_list.append(row)

for road in route:
    r = road[0]-1
    c = road[1]-1
    adjecency_row = adjecency_list[r]
    adjecency_row[c]=1
    adjecency_list[r] = adjecency_row

    r = road[1]-1
    c = road[0]-1
    adjecency_row = adjecency_list[r]
    adjecency_row[c]=1
    adjecency_list[r] = adjecency_row

#print_adjecency_list(adjecency_list)

print get_max_num_of_connected_component(adjecency_list)

How to know max number of connected nodes in a graph-without going back to previous node

2 Answers2