README Graph

Design Choices:

    -Types of Decorations I used:

        -_vertexCost: This was a decorator in which I paired a vertex and an integer to keep track of the cost of
            visiting a vertex when constructing a Minimum Spanning Tree
        -_previousVertex: This was a decorator in which I paired a vertex an another vertex, and this decorator kept
            track of what a vertex's previous vertex was in a minimum spanning tree (the node visited directly before it)
        -_vertexEntry: This was a decorator in which I paired a vertex and an <Integer, Vertex> Entry, with the purpose
            of this decorator being to keep track of which entry a vertex was located at in the priority queue
        -_inPriorityQueue: This was a decorator in which I paired a vertex and a boolean, specifically to reference
            whether a vertex had been visited and added to a minimum spanning tree/removed from the queue already

    - Created an ArrayList in PageRank to keep track of the sinks of a graph called _graphSinks

    - Created helper methods for the mathematical calculation of updating a vertex's PageRank

    - Checked for ending conditions of PageRank in one helper method

    - Handled sinks by distributing the sum of sink PageRanks over the overall number of vertices

    - Created a _unique_indices ArrayList that I popped from to ensure that vertices always had a unique index
        on the graph

Known Bugs:

    - None!

Handin:

    - This is my final handin

Test Case Explanations:

    -GraphTest:
        Exception Tests: This was a large category of tests in which I checked whether exceptions were properly thrown
            in cases where there were null vertices, null edges, non-existing edges/vertices, or the wrong type of graph
        Tested the following methods strictly for functionality in a valid graph:
            -removeVertex()
            -areAdjacent() - Both Directed and Undirected
            -connectingEdge()
            -incomingEdges() - Both Directed and Undirected
            -outgoingEdges() - Both Directed and Undirected
            -opposite()
            -endVertices()
            -clear()
            -getNumVertices()

    -MyPageRankTest:
        -emptyTest() - Tests PageRank on an empty graph
        -oneNodeTest() - Tests PageRank on an graph with just one vertex
        -twoNodeTest() - Tests PageRank on an graph with just one edge
        -twoTrees() - Tests PageRank on a graph with two disconnected trees
        -lotsOfSinks() - Tests PageRank on graph with multiple vertices that have only incoming edges

    -MsfTest:
        -emptyGraphTest() - Tests Prim-Jarnik on an empty graph
        -oneVertexTest() - Tests Prim-Jarnik on graph with just one vertex
        -oneEdgeTest() - Tests Prim-Jarnik on a graph with just one edge
        -twoSeparateTrees() - Tests Prim-Jarnik on a graph with two disconnected trees
        -multipleValidPathsTest() - Tests Prim-Jarnik on a graph where there are multiple valid MSFs

Conceptual Question:

    - In order to alter the search results to prevent the spread of false information for certain blacklisted sites, I
    propose the following algorithm:

        - Let us say there exists a list of blacklisted sites on a certain topic. For this proposed algorithm, let us
        also construct a "whitelist" of a few, scientifically-accredited sites that provide valuable information on the
        topic. This would not be particularly difficult, as there are a few types of sites that would qualify for being
        on said whitelist (ex. official university sites, governmental organizations, etc.)

        - My solution algorithm would create outgoing edges from each individual blacklisted site to every whitelisted
        site, and would also gradually remove incoming edges to blacklisted sites! This would have the following benefits:

            -Blacklisted sites are prevented from becoming sinks, and thereby lose a certain amount of PageRank that
            they would have had otherwise. They would also have multiple outgoing edges going to different nodes,
            significantly decreasing their PageRank.

            -Whitelisted sites are given a bonus for provided verified, accredited information, and this PageRank bonus
            does not come from ambiguous sites but instead directly from sites that contain false information, keeping
            the PageRank at a total of 1, while simultaneously rewarding correct information and punishing false
            information

            -Finally, this gives us the ability to manually ensure that a blacklisted page is never listed above a
            whitelisted page (this algorithm could include a checking method that makes sure all whitelisted sites are
            ranked above blacklisted sites, and if not, switches their PageRanks) - doing this would ensure that
            the blacklisted sites are not censored or removed, because that would be ethically inconsiderate, but
            ensures that they are much more difficult to find for those looking for reliable information on the topic.