# Path: pathpy/Log.py
# class Log:
#     """ A simple logging class, that allows to select what messages should
#         be recorded in the output, and where these message should be directed.
#     """
# 
#     ## the output stream to which log entries will be written
#     output_stream = sys.stdout
# 
#     ## The minimum severity level of messages to be logged
#     min_severity  = Severity.INFO
# 
# 
#     @staticmethod
#     def setMinSeverity(severity):
#         """ Sets the minimum sveerity level a message
#         needs to have in order to be recorded in the output stream.
#         By default, any message which has a severity of at least
#         Severity.INFO will be written to the output stream. All messages
#         with lower priority will be surpressed.
#         """
#         Log.min_severity = severity
# 
# 
#     @staticmethod
#     def setOutputStream(stream):
#         """ Sets the output stream to which all messages will be
#             written. By default, this is sys.stdout, but it can be
#             changed in order to redirect the log to a logfile.
#         """
#         output_stream = stream
# 
# 
#     @staticmethod
#     def add(msg, severity=Severity.INFO):
#         """ Adds a message with the given severity to the log. This message will be written
#             to the log output stream, which by default is sys.stdout. A newline character
#             will be added to the message by default.
#         """
#         if severity >= Log.min_severity:
#             ts = time.strftime("%Y-%m-%d %H:%M:%S", time.gmtime())
#             Log.output_stream.write(ts + ' [' + str(severity) + ']\t' + msg + '\n')
#             Log.output_stream.flush()
# 
# Path: pathpy/Log.py
# class Severity(enum.IntEnum):
#     """ An enumeration that can be used to indicate
#         the severity of log messages, and which can be
#         used tpo filter messages based on severities.
#     """
# 
#     ## Error messages
#     ERROR = 4
# 
#     ## Warning messages
#     WARNING = 3
# 
#     ## Informational messages (default minimum level)
#     INFO = 2
# 
#     ## Messages regarding timing and performance
#     TIMING = 1
# 
#     ## Debug messages (really verbose)
#     DEBUG = 0


import collections as _co
import bisect as _bs
import itertools as _iter
import numpy as _np 
import scipy.sparse as _sparse
import scipy.sparse.linalg as _sla
import scipy.linalg as _la
import scipy as _sp
from pathpy.Log import Log
from pathpy.Log import Severity
                    dist_first[v1][w1] = dist[vk][wk] + self.order - 1

        return dist_first


    def ClosenessCentrality(self):
        """ 
        Calculates the closeness centralities of all nodes.
        If the order of the higher-order network is larger than one 
        centralities calculated based on the higher-order 
        topology will automatically be projected back to first-order 
        nodes.
        """

        dist_first = self.getDistanceMatrixFirstOrder()
        node_centralities = _co.defaultdict( lambda: 0 )   
        
        Log.add('Calculating closeness centralities (k = ' + str(self.order) + ') ...', Severity.INFO)             

        # calculate closeness values
        for v1 in dist_first:
            for w1 in dist_first[v1]:
                if v1 != w1 and dist_first[v1][w1] < _np.inf:
                    node_centralities[v1] += 1.0 / dist_first[v1][w1]
        
        # assign centrality zero to nodes not occurring on higher-order shortest paths
        nodes = self.paths.getNodes()
        for v in nodes:
            node_centralities[v] += 0


# Path: pathpy/Log.py
# class Log:
#     """ A simple logging class, that allows to select what messages should
#         be recorded in the output, and where these message should be directed.
#     """
# 
#     ## the output stream to which log entries will be written
#     output_stream = sys.stdout
# 
#     ## The minimum severity level of messages to be logged
#     min_severity  = Severity.INFO
# 
# 
#     @staticmethod
#     def setMinSeverity(severity):
#         """ Sets the minimum sveerity level a message
#         needs to have in order to be recorded in the output stream.
#         By default, any message which has a severity of at least
#         Severity.INFO will be written to the output stream. All messages
#         with lower priority will be surpressed.
#         """
#         Log.min_severity = severity
# 
# 
#     @staticmethod
#     def setOutputStream(stream):
#         """ Sets the output stream to which all messages will be
#             written. By default, this is sys.stdout, but it can be
#             changed in order to redirect the log to a logfile.
#         """
#         output_stream = stream
# 
# 
#     @staticmethod
#     def add(msg, severity=Severity.INFO):
#         """ Adds a message with the given severity to the log. This message will be written
#             to the log output stream, which by default is sys.stdout. A newline character
#             will be added to the message by default.
#         """
#         if severity >= Log.min_severity:
#             ts = time.strftime("%Y-%m-%d %H:%M:%S", time.gmtime())
#             Log.output_stream.write(ts + ' [' + str(severity) + ']\t' + msg + '\n')
#             Log.output_stream.flush()
# 
# Path: pathpy/Log.py
# class Severity(enum.IntEnum):
#     """ An enumeration that can be used to indicate
#         the severity of log messages, and which can be
#         used tpo filter messages based on severities.
#     """
# 
#     ## Error messages
#     ERROR = 4
# 
#     ## Warning messages
#     WARNING = 3
# 
#     ## Informational messages (default minimum level)
#     INFO = 2
# 
#     ## Messages regarding timing and performance
#     TIMING = 1
# 
#     ## Debug messages (really verbose)
#     DEBUG = 0


# Path: pathpy/HigherOrderNetwork.py
import collections as _co
import bisect as _bs
import itertools as _iter
import numpy as _np 
import scipy.sparse as _sparse
import scipy.sparse.linalg as _sla
import scipy.linalg as _la
import scipy as _sp
from pathpy.Log import Log
from pathpy.Log import Severity

                    dist_first[v1][w1] = dist[vk][wk] + self.order - 1

        return dist_first


    def ClosenessCentrality(self):
        """ 
        Calculates the closeness centralities of all nodes.
        If the order of the higher-order network is larger than one 
        centralities calculated based on the higher-order 
        topology will automatically be projected back to first-order 
        nodes.
        """

        dist_first = self.getDistanceMatrixFirstOrder()
        node_centralities = _co.defaultdict( lambda: 0 )   
        
        Log.add('Calculating closeness centralities (k = ' + str(self.order) + ') ...', Severity.INFO)             

        # calculate closeness values
        for v1 in dist_first:
            for w1 in dist_first[v1]:
                if v1 != w1 and dist_first[v1][w1] < _np.inf:
                    node_centralities[v1] += 1.0 / dist_first[v1][w1]
        
        # assign centrality zero to nodes not occurring on higher-order shortest paths
        nodes = self.paths.getNodes()
        for v in nodes:
            node_centralities[v] += 0


        Log.add('finished.', Severity.INFO)