test9.4_Numpy.py

import math
import time
from operator import itemgetter
import numpy as np

'''
Run-Time of this algorithm is essentially
O((n^3)*R), where R is the specified ratio
beforehand of how "fine" the gradient of
movement is for each iteration (so I typically
use spacing = 5000, with an updated step of
1 unit length for all nodes per iteration/round
of simulated movement -- so 5000/1 makes it
O(5000*n^3)
...
However, if you have a way of solving this
as a simplified version of the N-Body Problem,
or even using a GPU with concurrent processing,
you can essentially reduce this down to O(R*n^2)
I think...
'''

def graphConv(filename):
    graph = {}
    size = 0
    with open(filename, 'r') as file:
        for line in file:
            contents = line.split()
            if contents[0] == 'p':
                size = int(contents[2])
                break
    for i in range(1, size + 1):
        graph[i] = []
    with open(filename, 'r') as file:
        for line in file:
            edge = line.split()
            if edge[0] == 'e':
                e1 = int(edge[1])
                e2 = int(edge[2])
                graph[e1].append(e2)
                graph[e2].append(e1)
    return graph
def checkClique(clique, graph):
    flag = True
    for member in range(len(clique)-1):
        neighbors = graph[clique[member]]
        for other in range(member+1, len(clique)):
            if clique[other] not in neighbors:
                flag = False
                break
    print("Return_Set: {0}".format(clique))
    print("Size of Return_Set: {0}".format(len(clique)))
    print("Return_Set is a Clique? -- {0}".format(flag))
def equidistant_vectors(N, spacing):
    dims = N-1
    coords = {}
    first = [0.0]*dims
    second = [float(spacing)] + [0.0]*(dims-1)
    third = [float(spacing/2.0), float(spacing/2.0)*math.sqrt(3)] + [0.0]*(dims-2)
    coords[1] = first
    coords[2] = second
    coords[3] = third
    #initialize N equidistant vectors
    for i in range(4, N+1):
        node_coord = [0.0]*dims
        for dimension in range(0, i-2):
            temp = 0.0
            for prevNode in range(1, i):
                temp += coords[prevNode][dimension]
            temp /= float(i-1)
            node_coord[dimension] = temp
        temp = 0.0
        for prevDims in range(0, i-2):
            temp += (node_coord[prevDims]**2)
        last_dim_solution = math.sqrt(float(spacing)**2 - temp)
        node_coord[i-2] = last_dim_solution
        coords[i] = node_coord
    return coords

def distance(point_list1, point_list2):
    return np.linalg.norm(point_list1 - point_list2)
def unitVector(vector):
    return (vector / np.linalg.norm(vector))
def nextDirection(node, neighbors, coords):
    position = coords[node]
    final = np.zeros(len(position))
    for neighbor in neighbors:
        final += unitVector(coords[neighbor] - position)
    return unitVector(final)
def updatePosition(coords, node, toMoveNext):
    coords[node] += toMoveNext
def hasConverged(distances):
    for key in distances.keys():
        edgeDict = distances[key]
        for edge in edgeDict.keys():
            if edgeDict[edge][1] == False:
                return False
    return True
def updateDistances(coords, distances):
    for node in distances.keys():
        relativesDict = distances[node]
        position = coords[node]
        for relative in relativesDict.keys():
            spacing = relativesDict[relative]
            dist = distance(position, coords[relative])
            spacing[0] = dist
            if dist < 2.0:#Arbitrary value, based on step-distance = 1.0 for unit vector
                spacing[1] = True
            #Can spacing ever grow to be > 2.0 after it's converged?

def avgPosition(coords, nodes):
    average = np.zeros(len(coords[nodes[0]]))
    for node in nodes:
        average += coords[node]
    return (average / float(len(nodes)))

def convergence(coordinates, adjacency, space, onResume = False, resumedCoords = {}):
    #start = time.time()
    nodes = adjacency.keys()
    distances = {}
    if onResume:
        coords = resumedCoords
        for i in range(len(nodes) - 1):
            lesser = nodes[i]
            distances[lesser] = {}
            for j in range(i+1, len(nodes)):
                greater = nodes[j]
                distances[lesser][greater] = [distance(resumedCoords[lesser], resumedCoords[nodes[j]]), False]
                if distances[lesser][greater][0] < 2.0:
                    distances[lesser][greater][1] = True
    else:
        coords = coordinates
        for i in range(len(nodes)-1):
            lesser = nodes[i]
            distances[lesser] = {}
            for j in range(i+1, len(nodes)):
                distances[lesser][nodes[j]] = [space, False]

    iter = 0
    while not hasConverged(distances):
        #startTime = time.time()
        iter += 1
        #print("Round {0}".format(iter))
        moveUpdates = []
        for node in nodes:
            moveUpdates.append(nextDirection(node, adjacency[node], coords))
        for x in range(len(nodes)):
            updatePosition(coords, nodes[x], moveUpdates[x])
        updateDistances(coords, distances)
        #if (iter%100 == 0):
        #    for key in coords.keys():
        #        print("{0}: {1},".format(key, coords[key]))
        #    print("Round {0} ending".format(iter))
        #print(time.time() - startTime)

    #print("Time to Converge: {0}".format(time.time() - start))
    return avgPosition(coords, nodes)

def main(filename, origSize, sample = False, sampleGraph = {}, onResume = False, resumeCoords = {}):
    graph = {}
    if sample:
        for key in sampleGraph.keys():
            temp = []
            for neighbor in sampleGraph[key]:
                temp.append(neighbor)
            graph[key] = temp
    else:
        graph = graphConv(filename)

    #toDel = []
    toDel = [36, 83, 108, 76, 51, 90, 64, 15, 95, 68, 42, 97, 88, 16, 94, 75, 102, 55, 43, 27, 33, 112, 87, 56, 21, 100, 73, 121, 107, 105, 3, 14]
    #toDel = [36, 83, 108, 75, 76, 51, 90, 73, 88, 42, 113, 15, 97, 16, 64, 95, 94, 3, 21, 102, 55, 116, 33, 27, 50, 87, 105, 78, 124, 112, 12, 100, 121, 106, 14, 56, 84, 120, 32, 53, 43, 37, 109, 28, 4,]
    for node in toDel:
        neighbors = graph[node]
        for neighbor in neighbors:
            graph[neighbor].remove(node)
        graph.pop(node, None)

    order = []
    #Typically, spacing is 5000
    spacing = 50000
    coords = equidistant_vectors(origSize, spacing)
    convergencePoints = []
    iterDistances = []
    while True:
        coordsCopy = {}
        for key in coords.keys():
            coordsCopy[key] = np.asarray(coords[key])
        cPoint = convergence(coordsCopy, graph, spacing, onResume, resumeCoords)
        convergencePoints.append(cPoint)
        #print(cPoint)

        distResults = []
        for node in graph.keys():
            distResults.append((node, distance(cPoint, coords[node])))
        distResults = sorted(distResults, key=itemgetter(1), reverse=True)
        iterDistances.append(distResults)
        #print(distResults)
        parsed = []
        for item in distResults:
            parsed.append(item[0])
        order.append(parsed)
        #print(parsed)
        #return distResults[0][0]
        print(order[-1])
        
        if abs(distResults[0][1] - distResults[-1][1]) < 0.0000001:
            print("   Closest-Farthest Error Difference: {0}".format(abs(distResults[0][1] - distResults[-1][1])))
            break
        else:
            nextToDel = distResults[0][0]
            print("   Closest-Farthest Error Difference: {0}".format(abs(distResults[0][1] - distResults[-1][1])))
            print("   1st_Farthest-2nd Error Difference: {0}".format(abs(distResults[0][1] - distResults[1][1])))
            print("   <DELETING NODE {0}>".format(nextToDel))
            for neighbor in graph[nextToDel]:
                graph[neighbor].remove(nextToDel)
            toDel.append(nextToDel)
            print("   Size of remaining graph: {0}".format(origSize - len(toDel)))
            print("   Deleted so far: {0}".format(toDel))
            graph.pop(nextToDel, None)
            print(time.ctime())

    a = 1
    b = 1
    for point in convergencePoints:
        print("After Iteration {0}: {1}".format(a, point))
        a += 1
    for iterDist in iterDistances:
        print("After Iteration {0}: {1}".format(b, iterDist))
        b += 1
    
    if sample:
        origGraph = sampleGraph
    else:
        origGraph = graphConv(filename)
    clique = []
    for key in origGraph.keys():
        if key not in toDel:
            clique.append(key)
    checkClique(clique, origGraph)
    for ordering in order:
        print(ordering)

#1 Iteration took 0.6 sec
#Size 4 took 3868 simulated rounds
graph1 = {1:[2,3,4], 2:[1,3], 3:[1,2], 4:[1]}
#1 Iteration took 1.74 sec
#Size 7 took 3440 simulated rounds
graph2 = {1:[2,3,4,6], 2:[1,3,5,7], 3:[1,2,4,5], 4:[1,3,5,6,7], 5:[2,3,4,6,7], 6:[1,4,5,7], 7: [2,4,5,6]}
#1 Iteration took 1.3 sec
graph2ver2 = {1:[2,4,6], 2:[1,5,7], 4:[1,5,6,7], 5:[2,4,6,7], 6:[1,4,5,7], 7: [2,4,5,6]}
#1 Iteration took 1.0 sec
graph2ver3 = {1:[4,6], 4:[1,5,6,7], 5:[4,6,7], 6:[1,4,5,7], 7: [4,5,6]}
#1 Iteration took 0.6 sec
graph2ver4 = {4:[5,6,7], 5:[4,6,7], 6:[4,5,7], 7: [4,5,6]}

graph3 = {1: [3, 4], 2: [3, 4, 5], 3: [1, 2], 4: [1, 2, 5], 5: [2, 4]}

graph = graph3
#main("c125.txt", 7, True, graph)

#'''
#(SPACING = 5000)
#1 Iteration took 687 sec (~0.19 seconds/round)
#HOLY SHIT, using Numpy makes this run like 15x faster
#Size 125 took 3526 simulated rounds
#Note to self: Converged at... [2500.1606507561632, 1442.297368316359, 1020.9035173351026, 790.785856318066, 645.8978943025529, 546.780878827789, 473.54237984520347, 416.6814071002168, 372.9346475198153, 337.7651684992841, 306.51289554920527, 282.87369095514794, 261.1904799309855, 242.45481892597658, 226.79674719720086, 213.50343814068427, 202.9363278769302, 192.44613404664068, 181.14223321611146, 171.84367302585264, 165.0118714827357, 156.9617862348561, 151.22024426072954, 144.57052309055285, 138.43254493037603, 133.21253740075556, 128.12656293375687, 125.03317070810411, 120.10125643266791, 115.92598780626956, 111.77610144562067, 107.85094011460671, 106.06061849071692, 102.50518518682027, 97.20686682844537, 96.72556952458811, 93.6688605552854, 92.66237650205935, 90.5313997528022, 87.6097190125494, 83.81641237507291, 83.04803859240326, 81.37941778421214, 80.97639167809864, 78.00210626524475, 76.79105055578769, 74.70182672337468, 73.8700940266351, 70.47985909838101, 68.35085557828651, 68.9494522965366, 67.15506063883844, 67.81642204926685, 64.1803035053063, 63.263473610474975, 62.62974105755576, 61.54690200492055, 60.97076611110323, 61.1350066893735, 57.97261298095041, 57.259912915578475, 55.87062323095282, 54.27455439531492, 55.34835220024454, 53.772732842528974, 54.144291137386176, 51.439188907041995, 51.65807840705602, 51.61842438628762, 49.69983994825094, 49.496681891558346, 47.1304434520029, 48.40525408914543, 45.58119223959545, 44.986307490534685, 46.79760723835413, 45.008888162710534, 45.13633276078471, 45.78243361653749, 43.05593024706185, 43.95763112615007, 40.53187058436222, 42.22093094721457, 42.196137780573785, 41.70535544361472, 40.5149772615826, 39.070176512929145, 39.36026790353056, 37.95235473044288, 39.23086163283957, 39.27864289014676, 37.88714180151359, 36.53653005618709, 36.14553675120005, 37.433319615377776, 35.3705773023133, 37.40330528309892, 37.284444024326774, 34.748258868911506, 36.565506646976985, 34.282233062240955, 33.68497693171059, 35.77969430901654, 33.27500676022936, 33.43224778109444, 33.124239700056954, 30.86281342774412, 32.773403380319564, 33.67990482506363, 33.61056635902326, 31.154523222616273, 30.137018117798718, 32.99954590664156, 31.02700405829687, 29.795995788605772, 30.500453773282228, 30.247979408465053, 30.226916319766907, 29.26186779081025, 29.263168756770042, 29.001778269039683, 29.49490611499247, 28.307327970685638, 29.48597598692083]
DIMACS1 = "c125.txt"
#1 Iteration took ___ sec (~0.84 seconds/round, so predicted -- ~3000 seconds, which is about 50 minutes)
DIMACS2 = "c250.txt"
#1 Iteration took ___ sec (~3.66 seconds/round, so predicted -- ~13,176 seconds, which is about 220 minutes)
DIMACS3 = "c500.txt"

filename = DIMACS1
main(filename, 125)
#'''

#solution1 = [7, 9, 11, 13, 19, 22, 25, 29, 33, 34, 40, 44, 49, 52, 54, 55, 66, 67, 68, 70, 79, 80, 93, 96, 98, 99, 103, 104, 110, 111, 114, 117, 122, 125]
#solution2 = [1, 2, 5, 7, 9, 11, 17, 18, 19, 25, 29, 31, 34, 40, 44, 45, 48, 49, 54, 70, 71, 77, 79, 80, 99, 101, 110, 114, 115, 117, 121, 122, 123, 125]

#   unique1 = [13, 22, 33, 52, 55, 66, 67, 68, 93, 96, 98, 103, 104, 111]
#   unique2 = [1, 2, 5, 17, 18, 31, 45, 48, 71, 77, 101, 115, 121, 123]
#shared = [7, 9, 11, 19, 25, 29, 34, 40, 44, 49, 54, 70, 79, 80, 99, 110, 114, 117, 122, 125]

#Parsed: [36, 83, 108, 75, 76, 51, 90, 73, 88, 42, 113, 15, 97, 16, 64, 95, 94, 3, 68, 103, 33, 17, 116, 50, 12, 81, 100, 89, 55, 14, 63, 38, 105, 78, 21,
#102, 112, 71, 93, 28, 56, 32, 61, 120, 87, 124, 122, 66, 23, 26, 53, 62, 84, 20, 27, 106, 37, 43, 107, 121, 79, 35, 117, 115, 31, 69, 13, 5, 118, 4, 1, 91,
#57, 44, 109, 72, 58, 25, 2, 9, 96, 85, 48, 86, 119, 52, 30, 46, 74, 41, 6, 77, 82, 123, 22, 34, 92, 65, 10, 59, 70, 47, 24, 18, 39, 67, 125, 40, 29, 11, 49,
#98, 80, 7, 110, 99, 101, 19, 8, 45, 111, 104, 54, 114, 60]
#Time from first convergence -- 670 sec
#2nd Convergence -- 681 sec
#etc.    --[670, 681, 652, 634, 632, 620, 610, 598, 586, 576, 566, 559, 548, 540, 529, 520, 509, 507, 514, 496, 476, 468, 470, 468, 449,
#           434, 425, 415, 407, 400, 390, 383, 375, 368, 360, 353, 344, 337, 329, 321, 314, 308, 300, 293, 287, 280, 273, 267, 259, 253,
#           246, 240, 234, 228, 222, 215, 209, 204, 198, 192, 187, 181, 176, 172, 166, 160, 155, 149, 145, 142, 139, 130, 126, 120, 116,
#           112, 107, 104, 100, 95,  92,  88,  83,  79,  76,  72,  68,  65,  62,  58,  55,  52,  49,  46,  44,  41,  38,  36]
# -- so in total, 28,427 seconds (or about 8 hours)

#   Batch of deleted nodes from Vector-Projection-Method, from test8.py:
#[36, 83, 108, 76, 51, 90, 64, 15, 95, 68, 42, 97, 88, 16, 94, 75, 102, 55, 27, 33, 43, 112, 87, 56, 100, 21, 73, 121, 107, 105, 3, 14]
#[113, 61, 109, 50, 124, 84, 72, 32, 37, 4, 57, 78, 20, 116, 28, 12, 53, 120, 106, 65, 98, 46, 115, 23, 62, 30, 118, 74, 52, 39, 111, 6]
#[58, 103, 91, 89, 38, 86, 63, 81, 119, 10, 49, 92, 26]
#   This algorithm's batch of deleted nodes:
#[36, 83, 108, 76, 51, 90, 64, 15, 95, 68*, 97, 42, 88,
# 21 (0.002), 112 (0.0015), 94 (0.3), 55* (0.002), 103* (0.004), 50 (0.00002), 33* (0.0008), 113 (0.001),
# 73 (0.001), 3 (0.35), 121** (0.0016), 102 (0.00007), 100 (0.004), 124 (0.37), 84 (0.0002), 116 (0.0005),
# 75 (0.002), 14 (0.01), 16 (0.4), 105 (0.0008), 27 (0.006), 43 (0.4), 1** (0.007), 28 (0.005), 120 (0.003),
# 20 (0.001), 4 (0.5), 52* (0.0005), 56 (0.001), 32 (0.003), 78 (0.006), 109 (0.54), 98* (0.0008), 65 (0.003),
# 22 (0.004), 57 (0.001), 107 (0.004), 87 (0.62), 122*** (0.0033), 12, 61, 115**, 41, 30, 62, 74, 38, 52, 26,
# 39, 10, 6, 123**, 111*, 101**, 58, 69, 81, 119, 46, 89, 25***, 40***, 60, 79***, 86, 13*, 82, 110***, 24, 66*,
# 23, 59, 118, 106, 37, 8, 63, 91, 45**, 17**, 47, 18**, 80***]


#Returned Set: [2, 5, 7, 9, 11, 19, 29, 31, 34, 35, 44, 48, 49, 54, 67, 70, 71, 72, 77, 85, 92, 93, 96, 99, 104, 114, 117, 125]
#Size: 28

#Returned Orderings:

orderings = [[36, 83, 108, 75, 76, 51, 90, 73, 88, 42, 113, 15, 97, 16, 64, 95, 94, 3, 68, 103, 33, 17, 116, 50, 12, 81, 100, 89, 55, 14, 63, 38, 105, 78, 21, 102, 112, 71, 93, 28, 56, 32, 61, 120, 87, 124, 122, 66, 23, 26, 53, 62, 84, 20, 27, 106, 37, 43, 107, 121, 79, 35, 117, 115, 31, 69, 13, 5, 118, 4, 1, 91, 57, 44, 109, 72, 58, 25, 2, 9, 96, 85, 48, 86, 119, 52, 30, 46, 74, 41, 6, 77, 82, 123, 22, 34, 92, 65, 10, 59, 70, 47, 24, 18, 39, 67, 125, 40, 29, 11, 49, 98, 80, 7, 110, 99, 101, 19, 8, 45, 111, 104, 54, 114, 60]
,[83, 108, 76, 75, 51, 90, 42, 113, 16, 15, 73, 64, 95, 94, 88, 3, 97, 68, 17, 116, 12, 89, 14, 55, 103, 63, 38, 33, 50, 102, 21, 81, 112, 100, 93, 28, 32, 105, 120, 78, 87, 124, 71, 66, 23, 56, 53, 62, 20, 84, 61, 26, 106, 27, 37, 43, 107, 121, 35, 117, 31, 115, 118, 69, 5, 13, 72, 4, 122, 57, 44, 1, 58, 25, 79, 9, 96, 2, 86, 48, 119, 30, 52, 46, 74, 91, 109, 41, 6, 77, 34, 82, 123, 92, 85, 22, 65, 10, 59, 70, 47, 18, 24, 39, 67, 125, 29, 11, 40, 98, 49, 80, 7, 110, 99, 101, 19, 8, 45, 111, 104, 54, 114, 60]
,[108, 75, 76, 51, 90, 16, 95, 15, 73, 64, 94, 88, 42, 113, 97, 68, 116, 3, 12, 89, 14, 63, 17, 33, 38, 50, 102, 21, 81, 112, 55, 28, 93, 103, 32, 120, 87, 105, 78, 124, 100, 71, 66, 23, 56, 53, 27, 20, 62, 84, 43, 121, 107, 37, 35, 117, 31, 115, 5, 122, 72, 13, 118, 44, 1, 57, 58, 106, 61, 26, 79, 25, 9, 96, 2, 48, 52, 69, 4, 74, 119, 30, 109, 41, 34, 77, 82, 92, 86, 85, 123, 22, 46, 65, 59, 91, 6, 70, 39, 18, 10, 67, 11, 29, 40, 47, 49, 98, 24, 80, 7, 110, 125, 101, 99, 8, 45, 104, 19, 111, 114, 54, 60]
,[76, 51, 90, 75, 16, 95, 64, 15, 88, 42, 113, 97, 73, 94, 68, 116, 12, 89, 17, 63, 50, 3, 102, 81, 21, 112, 55, 93, 33, 14, 103, 38, 87, 120, 105, 78, 100, 124, 71, 28, 56, 23, 53, 27, 43, 32, 62, 84, 121, 107, 37, 35, 117, 122, 66, 72, 31, 118, 44, 57, 20, 26, 106, 61, 25, 2, 96, 13, 5, 115, 48, 69, 119, 52, 74, 1, 4, 109, 58, 79, 77, 9, 34, 82, 123, 85, 92, 22, 86, 30, 41, 65, 91, 46, 59, 6, 70, 39, 18, 10, 11, 29, 67, 40, 47, 49, 24, 98, 80, 110, 125, 101, 99, 8, 45, 7, 19, 104, 111, 114, 54, 60]
,[51, 90, 15, 95, 64, 88, 42, 75, 97, 113, 73, 16, 94, 68, 116, 17, 63, 81, 102, 12, 112, 3, 21, 89, 93, 55, 33, 14, 87, 103, 50, 120, 105, 78, 124, 100, 71, 56, 43, 23, 32, 27, 107, 121, 62, 38, 84, 37, 66, 122, 44, 118, 53, 57, 28, 26, 20, 106, 61, 25, 2, 35, 115, 96, 48, 13, 5, 117, 69, 1, 31, 72, 74, 52, 109, 58, 34, 77, 79, 9, 85, 82, 22, 123, 86, 119, 92, 30, 91, 41, 46, 65, 59, 4, 6, 70, 18, 10, 11, 49, 47, 67, 98, 40, 24, 39, 125, 29, 101, 99, 8, 80, 110, 7, 19, 104, 111, 114, 45, 54, 60]
,[90, 64, 88, 75, 97, 15, 16, 95, 94, 68, 116, 42, 73, 113, 17, 112, 12, 21, 3, 93, 55, 14, 33, 63, 87, 50, 81, 105, 78, 102, 124, 100, 89, 71, 56, 23, 62, 103, 43, 107, 121, 120, 84, 27, 37, 122, 66, 44, 118, 32, 57, 53, 28, 26, 38, 20, 106, 61, 25, 2, 115, 35, 117, 5, 13, 1, 96, 31, 52, 72, 109, 58, 77, 79, 34, 9, 69, 82, 85, 123, 22, 48, 74, 86, 119, 91, 30, 92, 59, 46, 41, 65, 4, 6, 70, 10, 18, 67, 40, 49, 24, 98, 47, 39, 11, 29, 101, 99, 8, 80, 110, 125, 7, 19, 104, 111, 114, 45, 54, 60]
,[64, 88, 15, 16, 94, 95, 68, 75, 42, 97, 113, 116, 17, 21, 112, 12, 73, 3, 55, 14, 50, 87, 33, 102, 81, 124, 100, 89, 71, 93, 62, 23, 56, 103, 107, 63, 120, 43, 37, 121, 27, 78, 105, 32, 57, 118, 26, 28, 53, 84, 38, 106, 20, 61, 25, 1, 5, 115, 117, 13, 122, 96, 66, 44, 31, 52, 72, 109, 79, 2, 34, 9, 82, 69, 85, 35, 22, 48, 123, 74, 86, 46, 119, 59, 30, 92, 65, 41, 4, 58, 6, 77, 70, 10, 91, 18, 67, 40, 49, 47, 98, 24, 39, 11, 101, 29, 99, 8, 125, 80, 7, 19, 104, 111, 114, 110, 45, 54, 60]
,[15, 94, 95, 68, 88, 75, 42, 97, 16, 116, 112, 3, 113, 21, 73, 12, 55, 50, 87, 33, 17, 102, 81, 124, 89, 71, 103, 62, 23, 56, 63, 43, 107, 14, 78, 27, 120, 121, 37, 105, 100, 93, 57, 26, 32, 118, 38, 53, 106, 61, 20, 1, 117, 13, 5, 122, 66, 96, 44, 52, 31, 72, 84, 28, 109, 2, 25, 35, 79, 82, 69, 115, 22, 123, 48, 74, 119, 59, 92, 46, 30, 41, 65, 58, 4, 6, 77, 70, 34, 9, 85, 10, 91, 18, 86, 67, 40, 49, 47, 39, 98, 24, 11, 101, 29, 99, 8, 125, 7, 19, 111, 104, 80, 54, 45, 114, 110, 60]
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,[109, 98, 59, 65, 57, 118, 22, 53, 37, 87, 107, 81, 58, 23, 61, 122, 44, 49, 96, 26, 66, 41, 74, 115, 72, 39, 12, 111, 38, 63, 6, 62, 30, 31, 18, 79, 35, 117, 123, 119, 104, 9, 106, 47, 91, 8, 92, 46, 89, 99, 10, 70, 5, 34, 25, 48, 7, 101, 93, 114, 17, 40, 69, 24, 82, 54, 29, 85, 60, 13, 86, 67, 80, 77, 11, 19, 2, 45, 71, 125, 110]
,[98, 22, 65, 59, 57, 53, 23, 81, 58, 107, 37, 61, 87, 122, 118, 74, 26, 66, 12, 72, 41, 115, 38, 39, 111, 63, 6, 62, 30, 31, 18, 79, 44, 49, 35, 123, 96, 117, 104, 47, 9, 119, 91, 46, 106, 92, 8, 89, 10, 70, 5, 34, 25, 29, 101, 54, 7, 114, 17, 24, 40, 82, 99, 69, 60, 86, 13, 67, 77, 80, 48, 2, 11, 19, 71, 93, 45, 85, 125, 110]
,[65, 22, 23, 57, 53, 81, 107, 61, 87, 122, 118, 59, 74, 12, 66, 72, 115, 39, 58, 111, 63, 62, 30, 41, 37, 6, 31, 44, 49, 18, 79, 35, 96, 117, 47, 104, 9, 91, 119, 106, 26, 46, 38, 92, 89, 10, 8, 70, 5, 34, 114, 7, 25, 101, 29, 54, 40, 17, 24, 123, 82, 99, 69, 13, 86, 67, 77, 80, 48, 2, 71, 11, 93, 45, 85, 19, 60, 110, 125]
,[22, 23, 53, 57, 61, 107, 87, 122, 118, 74, 66, 115, 81, 12, 41, 58, 39, 63, 37, 62, 30, 44, 79, 31, 49, 35, 96, 47, 117, 59, 91, 106, 9, 119, 92, 104, 46, 26, 72, 8, 89, 38, 111, 10, 6, 70, 5, 18, 34, 25, 7, 29, 114, 54, 101, 40, 82, 99, 24, 123, 69, 17, 86, 67, 77, 80, 48, 93, 2, 19, 11, 71, 45, 85, 60, 13, 125, 110]
,[57, 53, 107, 87, 122, 118, 74, 66, 115, 12, 81, 58, 41, 63, 23, 39, 61, 62, 30, 44, 79, 49, 35, 117, 96, 59, 9, 47, 119, 92, 104, 46, 26, 8, 72, 89, 38, 10, 111, 37, 6, 70, 18, 34, 7, 25, 31, 114, 101, 29, 82, 99, 54, 106, 17, 24, 40, 123, 69, 91, 86, 67, 77, 5, 80, 93, 2, 48, 71, 11, 45, 85, 19, 60, 13, 125, 110]
,[107, 87, 122, 12, 115, 66, 81, 58, 23, 39, 53, 61, 63, 41, 62, 30, 79, 35, 96, 117, 118, 47, 59, 9, 119, 46, 92, 74, 26, 72, 104, 89, 8, 38, 111, 10, 37, 6, 70, 34, 7, 44, 31, 25, 49, 114, 101, 82, 99, 54, 29, 24, 123, 17, 106, 40, 91, 69, 86, 67, 77, 18, 80, 5, 93, 2, 71, 11, 45, 85, 19, 60, 13, 125, 110, 48]
,[87, 122, 12, 66, 81, 61, 115, 53, 63, 62, 41, 39, 30, 35, 96, 47, 79, 117, 9, 119, 46, 92, 74, 26, 104, 72, 89, 58, 38, 111, 8, 10, 23, 37, 6, 44, 31, 25, 101, 99, 34, 7, 82, 114, 29, 54, 118, 17, 40, 49, 24, 106, 59, 123, 69, 91, 86, 18, 70, 80, 5, 11, 2, 85, 71, 93, 45, 19, 60, 13, 110, 125, 77, 67, 48]
,[122, 12, 66, 115, 61, 63, 53, 39, 41, 62, 30, 79, 35, 47, 9, 117, 46, 74, 26, 119, 72, 104, 81, 58, 38, 8, 23, 111, 10, 89, 37, 6, 44, 25, 34, 99, 96, 82, 7, 54, 114, 29, 101, 118, 17, 106, 24, 123, 40, 59, 92, 91, 69, 86, 18, 70, 31, 5, 80, 49, 2, 71, 85, 11, 45, 19, 60, 13, 77, 125, 110, 93, 48, 67]
,[12, 66, 61, 115, 63, 41, 62, 30, 79, 35, 47, 9, 117, 46, 74, 119, 104, 26, 38, 81, 53, 23, 111, 8, 89, 10, 37, 39, 6, 44, 25, 96, 99, 54, 114, 34, 82, 118, 7, 24, 101, 17, 40, 29, 123, 92, 72, 91, 69, 86, 58, 18, 70, 31, 5, 71, 2, 80, 85, 49, 45, 106, 11, 19, 59, 60, 13, 125, 77, 110, 93, 48, 67]
,[61, 66, 63, 115, 41, 30, 62, 35, 79, 47, 117, 119, 46, 74, 26, 53, 38, 111, 81, 23, 10, 37, 39, 6, 25, 99, 44, 54, 34, 96, 118, 7, 9, 82, 123, 101, 17, 29, 24, 40, 72, 91, 104, 86, 58, 69, 89, 8, 70, 18, 5, 31, 114, 71, 2, 49, 80, 106, 11, 85, 19, 92, 45, 59, 60, 13, 125, 77, 110, 93, 48, 67]
,[115, 63, 41, 30, 62, 117, 119, 74, 46, 26, 53, 38, 23, 111, 66, 81, 10, 37, 39, 6, 44, 54, 34, 25, 99, 47, 7, 9, 96, 79, 35, 118, 29, 101, 123, 17, 24, 72, 82, 40, 91, 104, 86, 69, 8, 89, 58, 70, 18, 5, 31, 114, 71, 85, 2, 49, 45, 11, 106, 59, 92, 60, 13, 125, 77, 110, 48, 93, 80, 19, 67]
,[41, 62, 30, 117, 46, 53, 26, 74, 38, 63, 23, 10, 111, 37, 81, 39, 6, 47, 99, 34, 9, 7, 44, 54, 118, 25, 29, 17, 24, 82, 104, 40, 79, 72, 91, 101, 86, 119, 123, 66, 69, 58, 8, 89, 70, 18, 5, 31, 114, 71, 35, 96, 85, 49, 45, 2, 11, 106, 59, 92, 60, 13, 125, 77, 93, 110, 48, 80, 19, 67]
,[30, 62, 117, 46, 53, 74, 38, 26, 10, 63, 81, 39, 6, 47, 99, 34, 9, 7, 44, 54, 118, 29, 82, 104, 72, 25, 91, 17, 79, 24, 40, 123, 101, 86, 119, 66, 111, 8, 58, 69, 37, 23, 89, 18, 114, 5, 31, 71, 35, 85, 96, 2, 11, 106, 45, 59, 92, 60, 13, 77, 70, 93, 110, 48, 80, 49, 19, 125, 67]
,[62, 117, 46, 74, 38, 26, 53, 63, 81, 10, 39, 6, 34, 47, 99, 9, 118, 82, 29, 25, 24, 123, 79, 40, 101, 72, 91, 66, 86, 104, 119, 111, 69, 89, 58, 8, 23, 37, 114, 5, 31, 7, 44, 54, 35, 85, 96, 2, 11, 17, 106, 45, 59, 92, 60, 13, 77, 18, 70, 93, 110, 71, 48, 80, 49, 19, 125, 67]
,[74, 46, 38, 26, 53, 63, 81, 10, 39, 6, 9, 99, 29, 117, 25, 79, 123, 118, 82, 40, 101, 72, 104, 91, 66, 86, 8, 23, 69, 119, 37, 89, 58, 111, 47, 34, 5, 31, 7, 54, 44, 35, 96, 85, 114, 106, 11, 45, 24, 2, 17, 59, 92, 13, 60, 77, 71, 70, 48, 110, 80, 49, 19, 125, 18, 93, 67]
,[38, 46, 53, 26, 81, 10, 39, 6, 99, 29, 117, 82, 118, 25, 72, 79, 101, 123, 91, 86, 63, 104, 89, 119, 111, 69, 8, 23, 58, 37, 47, 9, 34, 31, 7, 54, 44, 35, 114, 96, 11, 40, 17, 85, 24, 106, 2, 66, 59, 45, 92, 60, 13, 70, 77, 5, 110, 71, 48, 80, 49, 19, 125, 18, 93, 67]
,[53, 26, 81, 39, 10, 6, 117, 29, 118, 79, 72, 123, 82, 91, 101, 86, 46, 89, 119, 111, 63, 69, 58, 8, 37, 23, 34, 31, 7, 54, 44, 9, 114, 96, 47, 99, 11, 35, 25, 40, 17, 85, 24, 2, 66, 106, 104, 45, 59, 60, 92, 13, 70, 77, 110, 71, 48, 80, 49, 19, 125, 5, 93, 18, 67]
,[26, 39, 10, 6, 117, 79, 72, 118, 123, 101, 86, 89, 63, 82, 111, 81, 69, 119, 37, 58, 8, 23, 46, 34, 9, 31, 29, 7, 96, 114, 54, 11, 99, 47, 40, 17, 25, 85, 35, 104, 24, 91, 106, 59, 45, 66, 92, 60, 13, 70, 77, 71, 44, 110, 48, 80, 49, 2, 19, 125, 5, 93, 18, 67]
,[39, 10, 6, 117, 118, 82, 123, 101, 89, 111, 81, 86, 58, 63, 119, 46, 69, 8, 23, 34, 31, 7, 96, 47, 99, 114, 29, 54, 25, 85, 79, 72, 40, 17, 24, 91, 35, 106, 66, 104, 59, 45, 92, 60, 37, 13, 70, 77, 71, 44, 9, 110, 80, 49, 11, 48, 2, 19, 125, 5, 93, 18, 67]
,[10, 6, 118, 123, 101, 111, 81, 89, 58, 63, 86, 46, 119, 8, 69, 23, 34, 31, 117, 7, 96, 114, 54, 25, 85, 79, 72, 47, 99, 82, 40, 104, 17, 29, 24, 91, 35, 45, 66, 92, 60, 37, 13, 70, 9, 44, 71, 110, 80, 48, 2, 49, 11, 19, 106, 59, 125, 5, 77, 93, 18, 67]
,[6, 123, 101, 111, 81, 86, 89, 69, 8, 63, 58, 23, 119, 46, 31, 96, 7, 114, 117, 25, 85, 47, 99, 72, 82, 79, 40, 17, 24, 35, 104, 45, 66, 91, 60, 92, 118, 37, 13, 70, 9, 44, 110, 54, 34, 80, 48, 2, 29, 49, 11, 19, 106, 59, 125, 5, 77, 71, 93, 18, 67]
,[123, 101, 86, 111, 81, 89, 69, 63, 8, 58, 46, 119, 23, 96, 7, 25, 47, 99, 117, 85, 72, 82, 79, 40, 17, 35, 24, 66, 45, 91, 60, 92, 118, 37, 13, 44, 9, 31, 80, 34, 110, 54, 114, 48, 2, 29, 49, 11, 19, 104, 106, 59, 5, 70, 77, 71, 93, 18, 125, 67]
,[111, 81, 89, 69, 101, 63, 8, 58, 46, 119, 23, 96, 25, 7, 85, 99, 47, 82, 117, 79, 40, 35, 17, 45, 60, 118, 86, 24, 37, 92, 13, 9, 44, 31, 80, 114, 110, 34, 72, 48, 54, 104, 29, 49, 2, 91, 66, 11, 19, 59, 106, 5, 70, 77, 71, 93, 18, 125, 67]
,[101, 69, 8, 58, 63, 81, 119, 46, 89, 23, 96, 25, 85, 7, 47, 99, 82, 117, 79, 40, 35, 86, 118, 60, 92, 37, 13, 9, 44, 80, 110, 34, 48, 29, 54, 114, 49, 72, 2, 19, 11, 66, 17, 45, 104, 91, 24, 59, 106, 5, 70, 31, 77, 71, 18, 93, 125, 67]
,[58, 69, 8, 81, 46, 23, 89, 119, 7, 85, 99, 47, 82, 117, 25, 40, 35, 79, 86, 118, 60, 63, 92, 37, 13, 96, 44, 9, 80, 34, 110, 48, 54, 29, 114, 49, 19, 2, 66, 11, 45, 17, 91, 24, 59, 106, 31, 5, 70, 71, 77, 72, 93, 18, 104, 125, 67]
,[69, 46, 81, 119, 89, 23, 85, 47, 99, 82, 25, 117, 35, 79, 40, 60, 86, 37, 8, 118, 63, 92, 13, 96, 9, 44, 7, 48, 110, 54, 114, 29, 49, 2, 66, 11, 19, 45, 91, 24, 59, 106, 17, 5, 70, 31, 71, 80, 77, 34, 72, 93, 18, 104, 67, 125]
,[81, 119, 46, 89, 117, 35, 82, 25, 79, 40, 99, 47, 60, 63, 118, 37, 86, 8, 92, 23, 13, 96, 85, 44, 7, 48, 110, 29, 54, 114, 11, 19, 2, 66, 45, 17, 91, 24, 106, 59, 9, 31, 71, 70, 5, 80, 34, 77, 49, 72, 93, 104, 18, 125, 67]
,[119, 46, 89, 47, 99, 82, 117, 79, 25, 40, 118, 63, 60, 37, 8, 92, 86, 23, 13, 96, 44, 85, 48, 110, 35, 54, 29, 19, 2, 66, 11, 17, 106, 91, 59, 24, 31, 9, 71, 7, 80, 34, 77, 5, 70, 114, 49, 72, 45, 18, 93, 104, 125, 67]
,[46, 89, 47, 99, 82, 25, 79, 40, 60, 37, 63, 92, 118, 8, 86, 13, 23, 85, 117, 48, 110, 35, 29, 11, 2, 19, 66, 17, 106, 91, 24, 59, 31, 96, 9, 71, 7, 5, 70, 44, 34, 80, 77, 114, 54, 49, 72, 104, 45, 93, 18, 67, 125]
,[89, 82, 63, 40, 23, 79, 37, 8, 118, 92, 25, 13, 86, 60, 85, 47, 99, 35, 48, 110, 117, 17, 66, 2, 19, 11, 91, 24, 59, 106, 31, 96, 80, 7, 34, 71, 77, 44, 70, 5, 54, 114, 72, 49, 29, 104, 18, 45, 93, 125, 67, 9]
,[25, 79, 60, 37, 40, 63, 92, 8, 118, 13, 86, 23, 117, 48, 110, 35, 11, 19, 2, 66, 47, 82, 99, 17, 24, 91, 59, 106, 5, 70, 71, 7, 44, 34, 80, 85, 77, 114, 54, 29, 49, 72, 45, 104, 93, 18, 31, 9, 67, 125, 96]
,[40, 60, 37, 79, 92, 118, 8, 13, 86, 117, 48, 110, 11, 19, 2, 66, 17, 63, 91, 24, 59, 106, 47, 82, 99, 23, 7, 71, 44, 34, 80, 35, 85, 5, 70, 29, 49, 114, 54, 77, 72, 18, 104, 45, 93, 31, 67, 125, 9, 96]
,[60, 79, 118, 92, 13, 86, 117, 11, 48, 19, 2, 66, 47, 99, 82, 110, 37, 63, 17, 24, 91, 8, 59, 106, 23, 7, 71, 35, 34, 80, 70, 5, 114, 54, 29, 44, 49, 77, 72, 18, 93, 104, 45, 67, 9, 96, 125, 85, 31]
,[79, 118, 13, 86, 117, 47, 82, 99, 11, 48, 2, 63, 66, 37, 110, 59, 91, 24, 8, 92, 23, 106, 71, 7, 35, 34, 77, 80, 19, 5, 29, 70, 114, 54, 44, 49, 18, 45, 72, 17, 104, 93, 125, 31, 96, 85, 9, 67]
,[86, 13, 117, 11, 48, 2, 99, 82, 47, 66, 110, 37, 24, 91, 8, 59, 118, 92, 23, 106, 71, 7, 54, 114, 80, 44, 34, 49, 5, 29, 19, 70, 104, 93, 72, 63, 17, 77, 18, 45, 125, 35, 9, 85, 31, 67, 96]
,[13, 48, 2, 99, 47, 82, 66, 37, 110, 24, 91, 8, 92, 23, 106, 118, 59, 71, 11, 49, 34, 70, 5, 19, 29, 117, 114, 54, 80, 44, 45, 18, 93, 104, 17, 77, 63, 72, 85, 125, 7, 9, 67, 31, 35, 96]
,[82, 99, 47, 110, 24, 91, 92, 66, 8, 37, 23, 118, 106, 59, 34, 19, 117, 29, 49, 70, 5, 11, 114, 80, 54, 2, 44, 48, 18, 72, 45, 93, 63, 77, 104, 17, 35, 85, 125, 71, 31, 7, 96, 67, 9]
,[110, 37, 8, 24, 66, 91, 92, 118, 59, 23, 106, 19, 70, 5, 11, 117, 49, 29, 34, 48, 44, 2, 54, 80, 114, 18, 93, 77, 17, 63, 45, 104, 72, 99, 47, 85, 31, 35, 71, 7, 67, 125, 9, 96]
,[24, 91, 92, 66, 118, 23, 59, 106, 5, 117, 11, 19, 70, 49, 34, 29, 80, 114, 2, 54, 8, 45, 37, 44, 18, 63, 72, 77, 93, 99, 17, 104, 48, 47, 7, 67, 9, 31, 35, 96, 71, 125, 85]
,[66, 92, 118, 23, 59, 106, 5, 34, 29, 49, 117, 11, 19, 70, 80, 2, 44, 18, 45, 17, 37, 63, 77, 54, 93, 47, 72, 91, 104, 8, 48, 99, 96, 71, 9, 125, 114, 35, 31, 7, 85, 67]
,[23, 118, 59, 106, 34, 49, 117, 5, 29, 19, 70, 11, 72, 18, 37, 44, 48, 80, 92, 93, 104, 8, 63, 77, 17, 47, 54, 91, 99, 45, 2, 31, 85, 125, 96, 7, 71, 9, 114, 35, 67]
,[59, 118, 106, 117, 29, 19, 34, 49, 11, 18, 99, 44, 77, 91, 8, 37, 45, 54, 92, 17, 48, 47, 63, 80, 72, 93, 104, 9, 31, 2, 70, 125, 5, 35, 96, 67, 71, 85, 114, 7]
,[118, 106, 117, 19, 34, 29, 8, 54, 91, 92, 93, 37, 45, 48, 99, 104, 17, 18, 44, 72, 77, 80, 47, 63, 2, 5, 35, 114, 125, 11, 67, 85, 96, 31, 9, 49, 71, 7, 70]
,[106, 19, 29, 45, 91, 93, 80, 18, 92, 37, 63, 77, 104, 47, 54, 72, 17, 48, 99, 44, 8, 7, 34, 70, 35, 11, 31, 71, 117, 67, 114, 125, 85, 5, 2, 9, 96, 49]
,[37, 45, 77, 80, 93, 104, 18, 17, 48, 54, 8, 47, 72, 91, 92, 99, 44, 63, 7, 70, 5, 35, 96, 9, 29, 49, 67, 117, 34, 85, 125, 31, 71, 19, 11, 114, 2]
,[8, 77, 44, 72, 91, 80, 92, 93, 45, 47, 99, 17, 63, 18, 104, 54, 5, 35, 9, 48, 29, 31, 34, 125, 7, 71, 19, 67, 70, 85, 96, 11, 114, 117, 49, 2]
,[63, 17, 45, 47, 77, 92, 18, 72, 93, 54, 80, 91, 99, 104, 31, 117, 2, 7, 9, 11, 85, 125, 19, 34, 48, 67, 70, 35, 96, 114, 5, 44, 71, 29, 49]
,[91, 54, 72, 99, 45, 47, 80, 18, 92, 93, 17, 104, 117, 7, 11, 29, 35, 67, 85, 5, 34, 125, 31, 96, 44, 9, 70, 19, 48, 49, 77, 2, 114, 71]
,[45, 93, 17, 47, 80, 92, 104, 18, 99, 72, 117, 35, 125, 11, 71, 114, 48, 31, 54, 77, 2, 5, 44, 49, 85, 7, 29, 34, 96, 9, 67, 70, 19]
,[17, 92, 99, 47, 72, 80, 104, 18, 67, 96, 114, 35, 93, 7, 44, 31, 48, 19, 11, 2, 125, 70, 49, 5, 77, 117, 9, 34, 71, 85, 29, 54]
,[47, 104, 80, 99, 18, 92, 31, 11, 29, 5, 9, 48, 7, 77, 93, 19, 44, 70, 96, 117, 34, 71, 35, 49, 72, 85, 114, 67, 125, 54, 2]
,[18, 80, 104, 92, 29, 49, 48, 117, 35, 5, 11, 72, 125, 77, 93, 7, 67, 9, 44, 54, 96, 19, 31, 114, 85, 70, 71, 2, 34, 99]
,[80, 92, 49, 2, 9, 31, 93, 5, 48, 99, 117, 77, 85, 104, 54, 67, 70, 72, 114, 34, 7, 71, 35, 44, 125, 19, 29, 96, 11]
,[2, 11, 67, 29, 19, 31, 104, 49, 70, 54, 9, 93, 71, 35, 34, 48, 125, 77, 117, 96, 99, 114, 44, 85, 92, 7, 72, 5]]
'''
graph = graphConv(filename)
nodes = {}
for i in range(1, 126):
    nodes[i] = [0, 0]

for order in orderings:
    size = len(order)
    for i in range(len(order)):
        nodes[order[i]][1] += 1
        nodes[order[i]][0] += (size - i)

frequency = []
for node in nodes.keys():
    frequency.append((node, float(nodes[node][0] / float(nodes[node][1]))))
frequency = sorted(frequency, key=itemgetter(1))
#print(frequency)
graph = graphConv(filename)
print(graph[60])
'''
'''
clique = [2, 5, 7, 9, 11, 19, 29, 31, 34, 35, 44, 48, 49, 54, 67, 70, 71, 72, 77, 85, 92, 93, 96, 99, 104, 114, 117, 125]
graph = graphConv(filename)
additional = []
for key in graph.keys():
    if key not in clique:
        neighbors = graph[key]
        flag = True
        for member in clique:
            if member not in neighbors:
                flag = False
                break
        if flag:
            additional.append(key)
checkClique(additional, graph)
'''
#space5000 = [36, 83, 108, 75, 76, 51, 90, 73, 88, 42, 113, 15, 97, 16, 64, 95, 94, 3, 68, 103, 33, 17, 116, 50, 12, 81, 100, 89, 55, 14, 63, 38, 105, 78, 21, 102, 112, 71, 93, 28, 56, 32, 61, 120, 87, 124, 122, 66, 23, 26, 53, 62, 84, 20, 27, 106, 37, 43, 107, 121, 79, 35, 117, 115, 31, 69, 13, 5, 118, 4, 1, 91, 57, 44, 109, 72, 58, 25, 2, 9, 96, 85, 48, 86, 119, 52, 30, 46, 74, 41, 6, 77, 82, 123, 22, 34, 92, 65, 10, 59, 70, 47, 24, 18, 39, 67, 125, 40, 29, 11, 49, 98, 80, 7, 110, 99, 101, 19, 8, 45, 111, 104, 54, 114, 60]
#space15000 = [36, 83, 108, 75, 76, 51, 90, 73, 88, 97, 42, 113, 15, 64, 16, 95, 94, 3, 103, 68, 17, 33, 116, 50, 12, 81, 100, 89, 55, 63, 14, 102, 38, 21, 105, 78, 112, 71, 32, 56, 87, 93, 120, 28, 61, 124, 122, 66, 53, 62, 26, 43, 27, 23, 84, 107, 20, 106, 37, 121, 79, 35, 1, 5, 117, 69, 13, 31, 115, 72, 91, 118, 44, 58, 4, 57, 109, 25, 85, 2, 96, 9, 86, 30, 119, 74, 48, 46, 52, 6, 41, 34, 77, 92, 82, 123, 10, 22, 65, 59, 70, 24, 47, 39, 18, 125, 29, 11, 40, 67, 49, 98, 80, 19, 7, 99, 110, 101, 8, 45, 104, 111, 114, 60, 54]

def worstGraph(n, k):
    size = (k*(n-1)) + n
    retGraph = {}
    for i in range(1, (size - n + 1)):
        neighbors = []
        unMod = i%(n-1)
        for j in range(1, (size-n+1)):
            if (j%(n-1)) != unMod:
                neighbors.append(j)
        if i == 1:
            neighbors.append(size)
        retGraph[i] = neighbors
    for x in range((size-n+1), (size+1)):
        neighbors = []
        for y in range((size-n+1), (size+1)):
            if y != x:
                neighbors.append(y)
        if x == size:
            neighbors.append(1)
        retGraph[x] = neighbors
    return retGraph


'''
#newGraph = worstGraph(6, 5)
#main(filename, 31, True, newGraph)

For worstGraph(6, 5), the "final convergent point":
(I put "" around that, because all those of the 6-clique (beside that
one connected to one of the 5 5-cliques) were still like 1500 units of
distance away from all those of the 5 5-cliques, and it didn't look like
it was going to converge any time soon (or rather, it was... but like at
decimal pace every 100 rounds))
cPoint = np.asarray([2447.77430702,1413.22315507,999.29967628,774.05420082,629.99564124,
                   534.48907473,462.88111676,408.22277385,365.12554891,328.16183206,
                   301.68480958,277.50966271,256.92402362,239.18324925,221.59612608,
                   210.29682284,198.26974599,187.54440414,177.92024385,167.0796803,
                   161.46290208,154.28314509,147.71486538,141.68312157,678.88482027,
                   653.25722289,629.49441109,607.39996387,586.80411413,574.28835721])
 -- which, by the way, was the convergent coordinate of node 31 after approx. 5700 rounds...

 Returned ordered distance from this convergent point:
[(21, 3790.2893136411608), (11, 3790.2893136361836), (16, 3790.2893136360913), (6, 3790.2893136344651), (10, 3788.2277809625589), (15, 3788.2277809625289), (12, 3788.2277809615584), (22, 3788.2277809615334), (8, 3788.2277809608322), (5, 3788.2277809601205), (3, 3788.2277809596826), (4, 3788.2277809595148), (7, 3788.2277809594166), (13, 3788.2277809586099), (20, 3788.2277809585817), (19, 3788.2277809581474), (17, 3788.2277809567599), (14, 3788.2277809566917), (18, 3788.227780956312), (9, 3788.2277809558213), (2, 3788.2277809557427), (23, 3788.2277809556413), (25, 3788.2277809550019), (24, 3788.227780954755), (1, 3718.6573908609635), (30, 3230.5991892704192), (26, 3230.5991892682646), (28, 3230.5991892666366), (27, 3230.5991892638694), (29, 3230.5991892621059), (31, 3223.1046395430294)]
[[21, 11, 16, 6, 10, 15, 12, 22, 8, 5, 3, 4, 7, 13, 20, 19, 17, 14, 18, 9, 2, 23, 25, 24, 1, 30, 26, 28, 27, 29, 31]]


 -- ...And also, the convergent coordinate of node 1 after approx. 5700 rounds... --
cPoint = np.asarray([  2.49909152e+03,   1.44285116e+03,   1.02024984e+03,   7.90282129e+02,
                       6.44991458e+02,   5.45392320e+02,   4.72323604e+02,   4.16550265e+02,
                       3.72573884e+02,   3.36722501e+02,   3.07668617e+02,   2.83013965e+02,
                       2.62020017e+02,   2.43927361e+02,   2.27885504e+02,   2.14349370e+02,
                       2.02090524e+02,   1.91158498e+02,   1.81348875e+02,   1.72207264e+02,
                       1.64483436e+02,   1.57169366e+02,   1.50478211e+02,   1.44333630e+02,
                       2.58063098e+00,   2.48321332e+00,   2.39288423e+00,   2.30889706e+00,
                       2.23060647e+00,   6.99362104e+00])

 Returned ordered distance from this convergent point:
[(30, 3602.9807906750025), (26, 3602.9807906698661), (27, 3602.9807906681704), (28, 3602.9807906677161), (29, 3602.9807906673755), (31, 3598.1534738824198), (21, 3464.4202613508569), (6, 3464.4202611179608), (16, 3464.4202611137816), (11, 3464.4202605544215), (3, 3464.1170687424428), (4, 3464.1170681282956), (22, 3464.1170673360666), (8, 3464.1170672805733), (19, 3464.1170672418098), (14, 3464.1170671279974), (7, 3464.1170671180766), (9, 3464.1170671108885), (15, 3464.1170670336514), (24, 3464.1170670212005), (18, 3464.1170669032431), (12, 3464.1170668324703), (5, 3464.1170668253558), (17, 3464.1170668051341), (13, 3464.117066796141), (25, 3464.1170665806817), (20, 3464.117066543397), (10, 3464.1170665022091), (2, 3464.1170664905644), (23, 3464.1170664819037), (1, 3462.8055461361373)]
[[30, 26, 27, 28, 29, 31, 21, 6, 16, 11, 3, 4, 22, 8, 19, 14, 7, 9, 15, 24, 18, 12, 5, 17, 13, 25, 20, 10, 2, 23, 1]]


 -- AND, the average of both node 1 and 31's coordinates after 5700 rounds... --
cPoint = np.asarray([ 2473.43291351  1428.03715754  1009.77475814   782.16816491   637.49354962
   539.94069737   467.60236038   412.38651943   368.84971646   332.44216653
   304.67671329   280.26181386   259.47202031   241.55530512   224.74081504
   212.32309642   200.180135     189.35145107   179.63455942   169.64347215
   162.97316904   155.72625555   149.09653819   143.00837578   340.73272563
   327.8702181    315.94364766   304.85443047   294.5173603    290.64098912])

 Returned ordered distance from this convergent point:
[(21, 3550.6356305619893), (6, 3550.635630444795), (16, 3550.6356304436244), (11, 3550.6356301707842), (3, 3549.3874626517886), (4, 3549.3874623520028), (22, 3549.3874619664816), (8, 3549.3874619390281), (19, 3549.3874619186781), (14, 3549.3874618623627), (7, 3549.3874618589757), (9, 3549.3874618535488), (15, 3549.3874618194382), (24, 3549.3874618092132), (18, 3549.387461752483), (12, 3549.3874617207466), (5, 3549.3874617165075), (17, 3549.3874617048459), (13, 3549.387461701444), (25, 3549.3874615943773), (20, 3549.3874615780933), (10, 3549.3874615601167), (2, 3549.3874615507966), (23, 3549.3874615465161), (1, 3511.7631593423275), (30, 3336.447784198017), (26, 3336.4477841942007), (28, 3336.4477841922517), (27, 3336.4477841911566), (29, 3336.4477841898743), (31, 3330.2130466929502)]
[[21, 6, 16, 11, 3, 4, 22, 8, 19, 14, 7, 9, 15, 24, 18, 12, 5, 17, 13, 25, 20, 10, 2, 23, 1, 30, 26, 28, 27, 29, 31]]

'''