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# System prepended metadata

title: Research Paper Outline

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###### butterfly, degeneracy, bipartite, counting, research

# Research Paper Outline

1. Introduction
    1. Motivation
        1. What is the problem (high level, larger context, important because...)?
            1. What is the butterfly motif? 2x2 biclique
            2. What is a bipartite network?
    2. Specific problem - Butterfly counting
        1. Why count butterflies? (specific context)
        2. Who else have considered this structure? (background)
        3. Relevant graph definitions
    3. Research Aim
        1. "In this paper, we show..." (key para) "our results are theoretical and applied in nature"
        2. We can demonstrate (approach taken, why our specific results are significant)
            1. the practical applications of this algorithm to industry: bioinformatics - GeneWeaver
            2. how we make computing degeneracy ordering practical
            3. the robustness of our algorithm
    3. Identify differences with the State of the Art (high level)
        1. Butterfly Counting algorithm (Wang 2019)
            1. The time complexity of their algorithm.
            2. Where there exists an opportunity to improve the algorithm.
            3. Our findings (difficulties of this algorithm that needs to be overcome).
        2. Our Approach (inc. what's new about our work compared to others)
            1. Name of our algorithms
            2. Advantages they have
            3. Time complexity
    4. Organisation of this paper (roadmap)

2. Our contribution
    1. "In this section, we present the main contributions of the paper."
    2. Notations and definitions (only those needed to explain the results)
    3. The problems and our idea
        1. Background - set scene, give examples

3. Existing Solutions
    1. Formal descriptions of the 2019 solution

4. Computing degeneracy orderings
    1. Define degeneracy, describe linear-time algorithm
    2. Theoretical algorithm is linear time, but slow in practise
    3. Describe improvement ideas: a) exponential buckets b) empty whole buckets
    4. Present figure with results, discuss

5. Counting C4s using degeneracy
    1. Describe both algorithms, provide pseudo-code
    2. Proof correctness

6. Experiments
    1. Describe data sets
    2. Performance Evaluation

7. Conclusion
                            