This package contains pythons files that illustrate application of Four Color Theorem by plotting and coloring several graphs.

1. Graph Artist:
    This program calls graph generator functions from GraphGenrator.py and plots them out using matplotlib pyplot.
    It then uses a simple algorithm to color all the vertices such that no two adjacent vertices have same color.

    The program currently generates and plots the following graphs:
        a. Dodecahedron
        b. Petersen Graph
        c. Cubical Graph

    Dependencies:
        a. matplotlib.pyplot
        b. networkx
        c. geopandas
        d. GraphGenerator.py

    ## GraphGenerator:
        This Python program utilizes the NetworkX library to generate and represent specific graphs. 
        Functions:
            a. generateDodecahedron
            b. generatePetersen
            c. generateCubic
        All three functions reutrn netowrkx graph.

        Dependencies:
            a. networkx

2. WorldMap:
    This program loads a GeoJSON file containing world map data and generates it in form of a network graph using networkx library. All the countries are vertices and have an edge with their neighbours.
    It uses the same algorithm to color the vertices.

    Note:-
        a. "world.geojson" file is being loaded twice in this program. Please ensure the abosolute path to "world.geojson" is mentioned properly. A copy of "world.geojson" is stored in this directory.
    
    Functions:
        a. worldmap:
            Loads a world map dataset and creates a graph using GeoPandas and NetworkX.
            Returns: NetworkX Graph.

        b. draw_graph:
            Visualizes a graph using Matplotlib with nodes colored based on input.
            Parameters:
                mygraph: NetworkX Graph.
                nodecolor: List of node colors.
        c. print_nodes:
            Prints the nodes present in the graph.
            Parameters:
            graph: NetworkX Graph.
        d. set_color_keys:
            Initializes a key-color relation for each node in the graph.
            Parameters:
                graph: NetworkX Graph.
            Returns: 
                Dictionary mapping nodes to colors.
        e. set_graph_color:
            Returns a list of colors corresponding to the nodes in the graph.
            Parameters:
                graph: NetworkX Graph.
                keyColor: Dictionary mapping nodes to colors.
            Returns: 
            List of node colors.
        f. mygraphmain()
            Checks if a graph is planar and visualizes it with colored nodes.
            It calls all the functions in this program.
            Parameters:
            mygraph: NetworkX Graph.
    Dependencies:
        a. networkx
        b. matplotlib.pyplot
        c. geopandas

3. USAMap:
    This program loads a GeoJSON file containing USA map data and generates it in the form of a network graph using the NetworkX library. Each state is a vertex, and edges connect neighboring states. The program applies the same algorithm to color the vertices.
    
    Note:-
        The "states.geojson" file is being loaded twice in this program. Ensure the absolute path to "states.geojson" is correctly specified. A copy of "states.geojson" is stored in this directory.
    
    Functions:
        */Same as WorldMap/*
    
    Dependencies:
        a. networkx
        b. matplotlib.pyplot
        c. geopandas

## Algorithm:
    1. Initialize the color assignment dictionary with all colors set to zero.
    2. Iterate through each node in the graph:
        a. Identify the colors of neighboring nodes.
        b. Assign the first available color from a predefined set (basecolors) that is not present in the neighbors.
    3. Assign display colors to nodes based on the colors obtained from keyColor.

## GEOJson source:
    - https://exploratory.io/map
    - License MIT
    - © 2023 Exploratory, Inc.