Python, RuntimeError: dictionary changed size during iteration -

i'm trying create sort of residual network given network, i'm first creating reverse edges doesn't exist in graph, keep getting message

runtimeerror: dictionary changed size during iteration 

first iterating on object being modified during loop:

def gf(graph):    #residual graph  u in graph:     v in graph[u]:         if u in graph[v]:              pass         else:             graph[v][u]=0 #create edge capacity 0  return graph 

where graph graph object of form (i'm new python don't know if best way it)

defaultdict(lambda: defaultdict(lambda:0))

with values graph[u][v] set capacity of edge u,v.

so created copy of graph , tried iterate on object

def gf(graph):    #residual graph  graph_copy=graph.copy()  u in graph_copy:     v in graph_copy[u]:         if u in graph_copy[v]:              pass         else:             graph[v][u]=0   return graph 

but didn't work. tried other ways (create deepcopy; create empty object graph_copy, iterate on graph , set adequate values graph_copy) no luck far. i'm doing wrong?

honestly, don't know causing exception. know, however, is bad idea use nested dictionaries represent graphs. harder iterate over, have discovered, , have more overhead. instead, should use nested list.

if understand current data structure correctly, can represented followed:

graph = {     u0: {v0: 0, v1: 0, ... },     u1: {v0: 0, v1: 0, ... },     ... }  # curly brackets denote dictionaries 

the better representation be:

graph = [     [0, 0, 0, ...],     [0, 0, 0, ...],     ... ]  # brackets denote lists 

this default way encode distance matrix (http://en.wikipedia.org/wiki/distance_matrix) representation of graph. if have coded in other languages c/c++, equivalent of 2-dimensional array.

assuming u & v labels graph vertices, can represented numerical values, i.e. 0 1st node, 1 2nd, , on. accessing value of edge u-v simple doing graph[u][v].

now, let's assume have changed code graph g has n vertices represented nested list/2d array of size nxn, function can rewritten followed:

def gf(g):  # python style guideline recommends lower case variable & function names     vertices_count = len(g)  # size of original graph     gf = []   # initialize new redidual graph     u in range(vertices_count):         gf.append([0]*vertices_count)  # initialize edges         v in range(vertices_count):             if g[u][v] > 0:                 # here if value of edge u-v more zero, e.g. gf[u][v] = formula             else:                 # here if value of edge u-v zero,, e.g. gf[u][v] = 0     return gf