In [8]:
import networkx as nx # for drawing graphs
In [9]:
# vertex list
V = [0,1,2,3,4]
E = [(0,2), (1,3)]
In [10]:
G= nx.Graph()
G.add_nodes_from(V)
G.add_edges_from(E)
In [11]:
nx.draw(G)
In [12]:
# make a tree
V = [0,1,2,3,4,5,6]
E = [(0,1), (0,2), (1,3), (1,4), (2,5), (2,6)]
G = nx.Graph()
G.add_nodes_from(V)
G.add_edges_from(E)
In [13]:
nx.draw(G)
In [42]:
# adjacency matrix 
# A[i,j] = 1 if i,j connected by edge
# = 0 otherwise

# edge lists are more convenient
import numpy as np
A = np.array([[0, 1, 1], [1,0,0], [1,0,0]])
H = nx.from_numpy_matrix(A) # create graph from adjacency matrix
nx.draw(H)
In [43]:
def rand_walk(A, v, steps):
    """Given graph correspoding to adj matrix A
    (represented) as numpy array,
    starting vertex v, traverse
    the graph by choosing an edge randomly from
    the possible choices at each vertex."""
    w = v # current vertex
    for n in range(steps):       
        num_vert = len(A[w]) # number of vertices total
        neigh_list = [i for i in range(num_vert) if A[w,i]==1]
        # above is list of neighbors of w 
        
        num_neigh = len(neigh_list) 

        # choose an edge randomly, make this the new w
        w = neigh_list[randint(0,num_neigh-1)]
    return w
In [44]:
A = np.array([[0, 1, 1], [1,0,0], [1,0,0]])
rand_walk(A,0,1)
Out[44]:
1
In [45]:
A = np.array([[0, 1, 1], [1,0,0], [1,0,0]])
rand_walk(A,0,2)
Out[45]:
0