G.remove_edges_from(G.selfloop_edges())

G = removeSingletons(G)

orig_core_nums = nx.core_number(G)

H = G.copy(); H_nodes = set(G.nodes())

current_core_nums = orig_core_nums.copy()

peak_numbers = {}

# Each iteration of the while loop finds a k-contour

while(len(H.nodes()) > 0):

# degen_core is the degeneracy of the graph

degen_core = nx.k_core(H) # Degen-core

# Nodes in the k-contour. Their current core number is their peak number.

kcontour_nodes = degen_core.nodes()

for n in kcontour_nodes:

peak_numbers[n] = current_core_nums[n]

# Removing the kcontour (i.e. degeneracy) and re-computing core numbers.

H_nodes = H_nodes.difference(set(kcontour_nodes))

H = G.subgraph(list(H_nodes))

current_core_nums = nx.core_number(H)

# Initializing node_CNdrops_mountainassignment

# 'node_CNdrops_mountainassignment' is a dict where keys are nodeIDS

# Each value is tuple of the maximum drop in core number observed for this node and the mountain to which it is assigned.

node_CNdrops_mountainassignment = {}

for n in G.nodes():

node_CNdrops_mountainassignment[n] = [0, -1] #diff in core number, assignment to a mountain

H = G.copy()

H_nodes = set(G.nodes())

current_core_nums = orig_core_nums.copy()

current_d = max(current_core_nums.values())

# 'current_plotmountain_id' keeps track of numbering of the plot-mountains

current_plotmountain_id = 0

peak_numbers = {}

# Each iteration of the while loop finds a k-contour

while(len(H.nodes()) > 0):

# degen_core is the degeneracy of the graph

degen_core = nx.k_core(H) # Degen-core

# Note that the actual mountains may consist of multiple components.

# To analyze each component, use the following line to find the components

# components_of_mountain = nx.connected_component_subgraphs(induced_subgraph_of_mountain)

# But in the mountain plot we plot the separate components related to a k-contour as a single mountain.

# Nodes in the k-contour. Their current core number is their peak number.

kcontour_nodes = degen_core.nodes()

for n in kcontour_nodes:

peak_numbers[n] = current_core_nums[n]

# Removing the kcontour (i.e. degeneracy) and re-computing core numbers.

H_nodes = H_nodes.difference(set(kcontour_nodes))

H = G.subgraph(list(H_nodes))

new_core_nums = nx.core_number(H)

for n in kcontour_nodes:

# For the nodes in kcontour, its removal causes its core number to drop to 0.

# Checking is this drop is greater than the drop in core number observed for these nodes in previous iterations

if current_core_nums[n] - 0 > node_CNdrops_mountainassignment[n][0]:

node_CNdrops_mountainassignment[n][0] = current_core_nums[n]

node_CNdrops_mountainassignment[n][1] = current_plotmountain_id

for n in new_core_nums:

# Checking is this drop is greater than the drop in core number observed for these nodes in previous iterations

if current_core_nums[n] - new_core_nums[n] > node_CNdrops_mountainassignment[n][0]:

node_CNdrops_mountainassignment[n][0] = current_core_nums[n] - new_core_nums[n]

node_CNdrops_mountainassignment[n][1] = current_plotmountain_id

current_plotmountain_id += 1

current_core_nums = new_core_nums.copy()

# Creating a dictionary of dictionary,

# such that a key represents the ID of a mountain

# and the value represents the a dictionary of nodes assigned to that mountain.

# eg. permountain_ID_core_peak_numbers[0] is a dict of mountain 0.

# Keys of the inner dictionary are nodes and value is a tuple <nodeID, corenumber, peak number>

permountain_ID_corenumber_peaknumber = {}

for n in orig_core_nums.keys():

if node_CNdrops_mountainassignment[n][1] not in permountain_ID_corenumber_peaknumber:

permountain_ID_corenumber_peaknumber[node_CNdrops_mountainassignment[n][1]] = {}

permountain_ID_corenumber_peaknumber[node_CNdrops_mountainassignment[n][1]][n] = (n, orig_core_nums[n],peak_numbers[n])

# Initializing node_CNdrops_mountainassignment

# 'node_CNdrops_mountainassignment' is a dict where keys are nodeIDS

# Each value is tuple of the maximum drop in core number observed for this node and the mountain to which it is assigned.

node_CNdrops_mountainassignment = {}

for n in G.nodes():

node_CNdrops_mountainassignment[n] = [0, -1] #diff in core number, assignment to a mountain

H = G.copy()

H_nodes = set(G.nodes())

current_core_nums = orig_core_nums.copy()

current_d = max(current_core_nums.values())

# 'current_plotmountain_id' keeps track of numbering of the plot-mountains

current_plotmountain_id = 0

peak_numbers = {}

# Each iteration of the while loop finds a k-contour

while(len(H.nodes()) > 0):

# degen_core is the degeneracy of the graph

degen_core = nx.k_core(H) # Degen-core

# Note that the actual mountains may consist of multiple components.

# To analyze each component, use the following line to find the components

# components_of_mountain = nx.connected_component_subgraphs(induced_subgraph_of_mountain)

# But in the mountain plot we plot the separate components related to a k-contour as a single mountain.

# Nodes in the k-contour. Their current core number is their peak number.

degen_core_comps = nx.connected_component_subgraphs(degen_core)

for comp in degen_core_comps:

kcontour_nodes = comp.nodes()

for n in kcontour_nodes:

peak_numbers[n] = current_core_nums[n]

# Removing the kcontour (i.e. degeneracy) and re-computing core numbers.

H_nodes = H_nodes.difference(set(kcontour_nodes))

H = G.subgraph(list(H_nodes))

new_core_nums = nx.core_number(H)

for n in kcontour_nodes:

# For the nodes in kcontour, its removal causes its core number to drop to 0.

# Checking is this drop is greater than the drop in core number observed for these nodes in previous iterations

if current_core_nums[n] - 0 > node_CNdrops_mountainassignment[n][0]:

node_CNdrops_mountainassignment[n][0] = current_core_nums[n]

node_CNdrops_mountainassignment[n][1] = current_plotmountain_id

for n in new_core_nums:

# Checking is this drop is greater than the drop in core number observed for these nodes in previous iterations

if current_core_nums[n] - new_core_nums[n] > node_CNdrops_mountainassignment[n][0]:

node_CNdrops_mountainassignment[n][0] = current_core_nums[n] - new_core_nums[n]

node_CNdrops_mountainassignment[n][1] = current_plotmountain_id

current_plotmountain_id += 1

current_core_nums = new_core_nums.copy()

# Creating a dictionary of dictionary,

# such that a key represents the ID of a mountain

# and the value represents the a dictionary of nodes assigned to that mountain.

# eg. permountain_ID_core_peak_numbers[0] is a dict of mountain 0.

# Keys of the inner dictionary are nodes and value is a tuple <nodeID, corenumber, peak number>

permountain_ID_corenumber_peaknumber = {}

for n in orig_core_nums.keys():

if node_CNdrops_mountainassignment[n][1] not in permountain_ID_corenumber_peaknumber:

permountain_ID_corenumber_peaknumber[node_CNdrops_mountainassignment[n][1]] = {}

permountain_ID_corenumber_peaknumber[node_CNdrops_mountainassignment[n][1]][n] = (n, orig_core_nums[n],peak_numbers[n])

### Part 1 ####

# Sorting the nodes in each mountain

# The final ordering is such that nodes are ordered in descending order of core number

# The nodes with same core umber in a mountain are ordered (in descending order) of their peak number

# Arranging the values in arrays, of x and y axis to be plotted based on above ordering

x_vals = []; y_vals = []; y_vals2 = []; nodecount=0

mountain_breaks_x_vals = []

mountain_breaks_y_vals = []

for id in permountain_ID_core_peak_numbers:

mountaindict = permountain_ID_core_peak_numbers[id]

unsorted_tuples = mountaindict.values()

sortedbypeaknumber_tuples = sorted(unsorted_tuples, key=lambda xyv: xyv[2], reverse=True)

sortedbyCOREnumber_tuples = sorted(sortedbypeaknumber_tuples, key=lambda xyv: xyv[1], reverse=True)

# node_ordering_permountain[id] = [x for x, y, z in sortedbyCOREnumber_tuples]

nodelist_this_mountain = [x for x, y, z in sortedbyCOREnumber_tuples]

for i in range(len(nodelist_this_mountain)):

x_vals.append(nodecount); nodecount+=1

y_vals.append(orig_core_nums[nodelist_this_mountain[i]])

y_vals2.append(peak_numbers[nodelist_this_mountain[i]])

mountain_breaks_x_vals.append(nodecount)

mountain_breaks_y_vals.append(y_vals[-1])

### Part 2 ####

## The plotting

ax = plt.gca()

plt.fill_between(x_vals, y_vals, 0, color = 'lightblue') # Area under the core number values (blue line)

plt.plot(x_vals, y_vals, label = 'Core Number', color = 'blue')

plt.scatter(x_vals, y_vals2, color = 'r', label = 'Peak Number')

for i in range(len(mountain_breaks_x_vals)):

if i == len(mountain_breaks_x_vals) - 1:

plt.plot([mountain_breaks_x_vals[i]-1, mountain_breaks_x_vals[i]-1],[0, mountain_breaks_y_vals[i]], color = 'black', label = 'Boundary Between Mountains')

else:

plt.plot([mountain_breaks_x_vals[i]-1, mountain_breaks_x_vals[i]-1],[0, mountain_breaks_y_vals[i]], color = 'black')

plt.ylabel('Core Number or Peak Number', fontsize=20); plt.xlabel('Individual nodes', fontsize=20)

plt.legend(fontsize=18,bbox_to_anchor=(1.01, 1), prop={'size':18})

plt.xlim(0, len(orig_core_nums.keys()))

plt.ylim(0, max([orig_core_nums[x] for x in orig_core_nums]))

ax.tick_params(axis='x', labelsize=18); ax.tick_params(axis='y', labelsize=18)

# plt.show()

plt.savefig(graphname+'_mountainplot_withcomponents_and_mountainmarkers.pdf', bbox_inches='tight')

### Part 1 ####

# Sorting the nodes in each mountain

# The final ordering is such that nodes are ordered in descending order of core number

# The nodes with same core umber in a mountain are ordered (in descending order) of their peak number

# Arranging the values in arrays, of x and y axis to be plotted based on above ordering

x_vals = []; y_vals = []; y_vals2 = []; nodecount=0

for id in permountain_ID_core_peak_numbers:

mountaindict = permountain_ID_core_peak_numbers[id]

unsorted_tuples = mountaindict.values()

sortedbypeaknumber_tuples = sorted(unsorted_tuples, key=lambda xyv: xyv[2], reverse=True)

sortedbyCOREnumber_tuples = sorted(sortedbypeaknumber_tuples, key=lambda xyv: xyv[1], reverse=True)

# node_ordering_permountain[id] = [x for x, y, z in sortedbyCOREnumber_tuples]

nodelist_this_mountain = [x for x, y, z in sortedbyCOREnumber_tuples]

for i in range(len(nodelist_this_mountain)):

x_vals.append(nodecount); nodecount+=1

y_vals.append(orig_core_nums[nodelist_this_mountain[i]])

y_vals2.append(peak_numbers[nodelist_this_mountain[i]])

### Part 2 ####

## The plotting

ax = plt.gca()

plt.fill_between(x_vals, y_vals, 0, color = 'lightblue') # Area under the core number values (blue line)

plt.plot(x_vals, y_vals, label = 'Core Number', color = 'blue')

plt.scatter(x_vals, y_vals2, color = 'r', label = 'Peak Number')

plt.ylabel('Core Number or Peak Number', fontsize=20); plt.xlabel('Individual nodes', fontsize=20)

plt.legend(fontsize=18,bbox_to_anchor=(1.01, 1), prop={'size':18})

plt.xlim(0, len(orig_core_nums.keys()))

plt.ylim(0, max([orig_core_nums[x] for x in orig_core_nums]))

ax.tick_params(axis='x', labelsize=18); ax.tick_params(axis='y', labelsize=18)

# plt.show()

plt.savefig(graphname+'_mountainplot.pdf', bbox_inches='tight')

G.remove_edges_from(G.selfloop_edges())

G = removeSingletons(G)

orig_core_nums = nx.core_number(G)

permountain_ID_corenumber_peaknumber, peak_numbers = get_kpeak_mountainassignment(G, orig_core_nums)

G.remove_edges_from(G.selfloop_edges())

G = removeSingletons(G)

orig_core_nums = nx.core_number(G)

permountain_ID_corenumber_peaknumber, peak_numbers = get_kpeak_mountainassignment_component(G, orig_core_nums)

degrees=G.degree()

for node in degrees.keys():

if degrees[node]==0:

G.remove_node(node)