def calculate(graph):
deg_seq = gp.degree_sequence(graph)
valencies = []
for i in range(0, nx.number_of_nodes(graph)):
if deg_seq[i] not in valencies:
valencies.append(deg_seq[i])
return len(valencies)
def annihilation_number(G):
r"""Return the annihilation number of the graph.
The annihilation number of a graph G is defined as:
.. math::
a(G) = \max\{t : \sum_{i=0}^t d_i \leq m\}
where
.. math::
{d_1 \leq d_2 \leq \cdots \leq d_n}
is the degree sequence of the graph ordered in non-decreasing order and *m*
is the number of edges in G.
Parameters
----------
G : NetworkX graph
An undirected graph.
Returns
-------
int
The annihilation number of the graph.
"""
D = degree_sequence(G)
D.sort() # sort in non-decreasing order
n = len(D)
m = number_of_edges(G)
# sum over degrees in the sequence until the sum is larger than the number of edges in the graph
for i in reversed(range(n + 1)):
if sum(D[:i]) <= m:
return i
def degree_ranking(Ma):
G = nx.from_numpy_matrix(Ma)
deg = np.asarray(gp.degree_sequence(G))
deg = (np.amax(deg) + 1) - deg #higher degree comes first
deg_rank = np.argsort(deg)
return deg_rank
def sub_k_domination_number(G, k):
r"""Return the sub-k-domination number of the graph.
The *sub-k-domination number* of a graph G with *n* nodes is defined as the
smallest positive integer t such that the following relation holds:
.. math::
t + \frac{1}{k}\sum_{i=0}^t d_i \geq n
where
.. math::
{d_1 \geq d_2 \geq \cdots \geq d_n}
is the degree sequence of the graph.
Parameters
----------
G : NetworkX graph
An undirected graph.
k : int
A positive integer.
Returns
-------
int
The sub-k-domination number of a graph.
See Also
--------
slater
Examples
--------
>>> G = nx.cycle_graph(4)
>>> nx.sub_k_domination_number(G, 1)
True
References
----------
D. Amos, J. Asplund, B. Brimkov and R. Davila, The sub-k-domination number
of a graph with applications to k-domination, *arXiv preprint
arXiv:1611.02379*, (2016)
"""
# check that k is a positive integer
if not float(k).is_integer():
raise TypeError("Expected k to be an integer.")
k = int(k)
if k < 1:
raise ValueError("Expected k to be a positive integer.")
D = degree_sequence(G)
D.sort(reverse=True)
n = len(D)
for i in range(n + 1):
if i + (sum(D[:i]) / k) >= n:
return i
# if above loop completes, return None
return None
def annihilation_number(G):
# TODO: Add documentation
D = degree_sequence(G)
D.sort() # sort in non-decreasing order
m = number_of_edges(G)
# sum over degrees in the sequence until the sum is larger than the number of edges in the graph
S = [D[0]]
while(sum(S) <= m):
S.append(D[len(S)])
return len(S) - 1
def sub_total_domination_number(G):
# TODO: Add documentation
D = degree_sequence(G)
D.sort(reverse = True)
n = len(D)
for i in range(n + 1):
if sum(D[:i]) >= n:
return i
# if above loop completes, return None (should not occur)
return None
def sub_k_domination_number(G, k):
"""Return the sub-k-domination number of the graph.
The *sub-k-domination number* of a graph G with *n* nodes is defined as the
smallest positive integer t such that the following relation holds:
.. math::
t + \frac{1}{k}\sum_{i=0}^t d_i \geq n
where
.. math::
{d_1 \geq d_2 \geq \cdots \geq \d_n}
is the degree sequence of the graph.
Parameters
----------
G : graph
A Networkx graph.
k : int
A positive integer.
Returns
-------
sub : int
The sub-k-domination number of a graph.
See Also
--------
slater
Examples
--------
>>> G = nx.cycle_graph(4)
>>> nx.sub_k_domination_number(G, 1)
True
References
----------
D. Amos, J. Asplund, and R. Davila, The sub-k-domination number of a graph
with applications to k-domination, *arXiv preprint arXiv:1611.02379*, (2016)
"""
# TODO: add check that k >= 1 and throw error if not
D = degree_sequence(G)
D.sort(reverse = True)
n = len(D)
for i in range(n + 1):
if i + (sum(D[:i]) / k) >= n:
return i
# if above loop completes, return None (should not occur)
return None
def sub_total_domination_number(G):
r"""Return the sub-total domination number of the graph.
The sub-total domination number is defined as:
.. math::
sub_{t}(G) = \min\{t : \sum_{i=0}^t d_i \geq n\}
where
.. math::
{d_1 \geq d_2 \geq \cdots \geq d_n}
is the degree sequence of the graph ordered in non-increasing order and *n*
is the order of the graph.
This invariant was defined and investigated by Randy Davila.
Parameters
----------
G : NetworkX graph
An undirected graph.
Returns
-------
int
The sub-total domination number of the graph.
References
----------
R. Davila, A note on sub-total domination in graphs. *arXiv preprint
arXiv:1701.07811*, (2017)
"""
D = degree_sequence(G)
D.sort(reverse=True)
n = len(D)
for i in range(n + 1):
if sum(D[:i]) >= n:
return i
# if above loop completes, return None
return None
def calculate(graph):
sequence = (gp.degree_sequence(graph))
return sum(sequence) / len(sequence)
def calculate(graph):
return min(gp.degree_sequence(graph))
def test_depth_of_complete_graph_is_order_minus_1(self):
for i in range(2, 12):
G = gp.complete_graph(i)
hh = gp.HavelHakimi(gp.degree_sequence(G))
assert hh.depth() == G.order() - 1
def test_initial_sequence(self):
G = gp.complete_graph(4)
hh = gp.HavelHakimi(gp.degree_sequence(G))
assert hh.get_initial_sequence() == [3, 3, 3, 3]
def test_elimination_sequence_of_complete_graph(self):
G = gp.complete_graph(4)
hh = gp.HavelHakimi(gp.degree_sequence(G))
e = [3, 2, 1, 0]
assert hh.get_elimination_sequence() == e
def test_process_of_compete_graph(self):
G = gp.complete_graph(4)
hh = gp.HavelHakimi(gp.degree_sequence(G))
p = [[3, 3, 3, 3], [2, 2, 2], [1, 1], [0]]
assert hh.get_process() == p
