graph.py

"""!

@brief Graph representation (uses format GRPR).

@authors Andrei Novikov (pyclustering@yandex.ru)
@date 2014-2019
@copyright GNU Public License

@cond GNU_PUBLIC_LICENSE
    PyClustering is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
    
    PyClustering is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
    
    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
@endcond

"""

import warnings

try:
    import matplotlib.pyplot as plt
    from matplotlib import colors
except Exception as error_instance:
    warnings.warn("Impossible to import matplotlib (please, install 'matplotlib'), pyclustering's visualization "
                  "functionality is not available (details: '%s')." % str(error_instance))

from enum import IntEnum

class type_graph_descr(IntEnum):
    """!
    @brief Enumeration of graph description.
    @details Matrix representation is list of lists where number of rows equals number of columns and each element
             of square matrix determines whether there is connection between two vertices. For example:
             [ [0, 1, 1], [1, 0, 1], [1, 1, 0] ].
             
             Vector representation is list of lists where index of row corresponds to index of vertex and elements
             of row consists of indexes of connected vertices. For example:
             [ [1, 2], [0, 2], [0, 1] ].
    
    """
    
    
    GRAPH_UNKNOWN = 0;
    
    
    GRAPH_MATRIX_DESCR = 1;
    
    
    GRAPH_VECTOR_DESCR = 2;


class graph:
    """!
    @brief Graph representation.
    
    """
    
    def __init__(self, data, type_graph = None, space_descr = None, comments = None):
        """!
        @brief Constructor of graph.
        
        @param[in] data (list): Representation of graph. Considered as matrix if 'type_graph' is not specified.
        @param[in] type_graph (type_graph_descr): Type of graph representation in 'data'.
        @param[in] space_descr (list): Coordinates of each vertex that are used for graph drawing (can be omitted).
        @param[in] comments (string): Comments related to graph.
        
        """
        self.__data = data;
        self.__space_descr = space_descr;
        self.__comments = comments;
        
        if (type_graph is not None):
            self.__type_graph = type_graph;
        else:
            self.__type_graph = type_graph_descr.GRAPH_MATRIX_DESCR;
            for row in self.__data:
                if (len(row) != len(self.__data)):
                    self.__type_graph = type_graph_descr.GRAPH_VECTOR_DESCR;
                    break;
                
                for element in row:
                    if ( (element != 0) or (element != 1) ):
                        self.__type_graph = type_graph_descr.GRAPH_VECTOR_DESCR;
    
    
    def __len__(self):
        """!
        @return (uint) Size of graph defined by number of vertices.
        
        """
        return len(self.__data);
    
    
    @property
    def data(self): 
        """!
        @return (list) Graph representation.
        
        """
        return self.__data;
    
    @property
    def space_description(self):
        """!
        @return (list) Space description.
        
        """
        if (self.__space_descr == [] or self.__space_descr is None):
            return None;

        return self.__space_descr;
    
    @property
    def comments(self): 
        """!
        @return (string) Comments.
        
        """
        return self.__comments;
    
    @property
    def type_graph_descr(self):
        """!
        @return (type_graph_descr) Type of graph representation.
        
        """
        return self.__type_graph;
    
    
def read_graph(filename):
    """!
    @brief Read graph from file in GRPR format.
    
    @param[in] filename (string): Path to file with graph in GRPR format.
    
    @return (graph) Graph that is read from file.
    
    """
    
    file = open(filename, 'r');
    
    comments = "";
    space_descr = [];
    data = [];
    data_type = None;
    
    map_data_repr = dict();   # Used as a temporary buffer only when input graph is represented by edges.
    
    for line in file:
        if (line[0] == 'c' or line[0] == 'p'): 
            comments += line[1:]; 
        
        elif (line[0] == 'r'): 
            node_coordinates = [float(val) for val in line[1:].split()];
            if (len(node_coordinates) != 2):
                raise NameError('Invalid format of space description for node (only 2-dimension space is supported)');
                
            space_descr.append( [float(val) for val in line[1:].split()] );
        
        elif (line[0] == 'm'):
            if ( (data_type is not None) and (data_type != 'm') ):
                raise NameError('Invalid format of graph representation (only one type should be used)');
 
            data_type = 'm';
            data.append( [float(val) for val in line[1:].split()] );
        
        elif (line[0] == 'v'):
            if ( (data_type is not None) and (data_type != 'v') ):
                raise NameError('Invalid format of graph representation (only one type should be used)');
            
            data_type = 'v';
            data.append( [float(val) for val in line[1:].split()] );
            
        elif (line[0] == 'e'):
            if ( (data_type is not None) and (data_type != 'e') ):
                raise NameError('Invalid format of graph representation (only one type should be used)');
               
            data_type = 'e';
            vertices = [int(val) for val in line[1:].split()];
            
            if (vertices[0] not in map_data_repr):
                map_data_repr[ vertices[0] ] = [ vertices[1] ];
            else:
                map_data_repr[ vertices[0] ].append(vertices[1])
                
            if (vertices[1] not in map_data_repr):
                map_data_repr[ vertices[1] ] = [ vertices[0] ];
            else:
                map_data_repr[ vertices[1] ].append(vertices[0]);
            
            
        elif (len(line.strip()) == 0): continue;
        
        else: 
            print(line);
            raise NameError('Invalid format of file with graph description');
    
    # In case of edge representation result should be copied.
    if (data_type == 'e'):
        for index in range(len(map_data_repr)):
            data.append([0] * len(map_data_repr));
            
            for index_neighbour in map_data_repr[index + 1]:
                data[index][index_neighbour - 1] = 1;
    
    file.close();
    
    # Set graph description
    graph_descr = None;
    if (data_type == 'm'): graph_descr = type_graph_descr.GRAPH_MATRIX_DESCR;
    elif (data_type == 'v'): graph_descr = type_graph_descr.GRAPH_VECTOR_DESCR;
    elif (data_type == 'e'): graph_descr = type_graph_descr.GRAPH_MATRIX_DESCR;
    else:
        raise NameError('Invalid format of file with graph description');
    
    if (space_descr != []):
        if (len(data) != len(space_descr)):
            raise NameError("Invalid format of file with graph - number of nodes is different in space representation and graph description");
    
    return graph(data, graph_descr, space_descr, comments);



def draw_graph(graph_instance, map_coloring = None):
    """!
    @brief Draw graph.

    @param[in] graph_instance (graph): Graph that should be drawn.
    @param[in] map_coloring (list): List of color indexes for each vertex. Size of this list should be equal to size of graph (number of vertices).
                                    If it's not specified (None) than graph without coloring will be dwarn.
    
    @warning Graph can be represented if there is space representation for it.
    
    """
    
    if (graph_instance.space_description is None):
        raise NameError("The graph haven't got representation in space");
    
    if (map_coloring is not None):
        if (len(graph_instance) != len(map_coloring)):
            raise NameError("Size of graph should be equal to size coloring map");
        
    
    fig = plt.figure();
    axes = fig.add_subplot(111);
    
    available_colors = ['#00a2e8', '#22b14c', '#ed1c24',
                        '#fff200', '#000000', '#a349a4',
                        '#ffaec9', '#7f7f7f', '#b97a57',
                        '#c8bfe7', '#880015', '#ff7f27',
                        '#3f48cc', '#c3c3c3', '#ffc90e',
                        '#efe4b0', '#b5e61d', '#99d9ea',
                        '#7092b4', '#ffffff'];
              
    if (map_coloring is not None):
        if (len(map_coloring) > len(available_colors)):
            raise NameError('Impossible to represent colored graph due to number of specified colors.');
    
    x_maximum = -float('inf');
    x_minimum = float('inf');
    y_maximum = -float('inf');
    y_minimum = float('inf');
    
    for i in range(0, len(graph_instance.space_description), 1):
        if (graph_instance.type_graph_descr == type_graph_descr.GRAPH_MATRIX_DESCR):
            for j in range(i, len(graph_instance.space_description), 1):    # draw connection between two points only one time
                if (graph_instance.data[i][j] == 1):
                    axes.plot([graph_instance.space_description[i][0], graph_instance.space_description[j][0]], [graph_instance.space_description[i][1], graph_instance.space_description[j][1]], 'k-', linewidth = 1.5);
                    
        elif (graph_instance.type_graph_descr == type_graph_descr.GRAPH_VECTOR_DESCR):
            for j in graph_instance.data[i]:
                if (i > j):     # draw connection between two points only one time
                    axes.plot([graph_instance.space_description[i][0], graph_instance.space_description[j][0]], [graph_instance.space_description[i][1], graph_instance.space_description[j][1]], 'k-', linewidth = 1.5);   
            
        color_node = 'b';
        if (map_coloring is not None):
            color_node = colors.hex2color(available_colors[map_coloring[i]]);
        
        axes.plot(graph_instance.space_description[i][0], graph_instance.space_description[i][1], color = color_node, marker = 'o', markersize = 20);
    
        if (x_maximum < graph_instance.space_description[i][0]): x_maximum = graph_instance.space_description[i][0];
        if (x_minimum > graph_instance.space_description[i][0]): x_minimum = graph_instance.space_description[i][0];  
        if (y_maximum < graph_instance.space_description[i][1]): y_maximum = graph_instance.space_description[i][1]; 
        if (y_minimum > graph_instance.space_description[i][1]): y_minimum = graph_instance.space_description[i][1];
    
    plt.xlim(x_minimum - 0.5, x_maximum + 0.5);
    plt.ylim(y_minimum - 0.5, y_maximum + 0.5);
    
    plt.show();