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Applications and Kernels>

• General sources of information
  • David Bader's publications in graph computing
  • Paper: "Graph Analytics: Complexity, Scalability, and Architectures"
• Bipartite Matching: Given a graph with two classes of vertices, find an edge subset that connects each of one class vertex to exactly one of the other class.
  • Wikipedia: what are bipartite graphs
  • Wikipedia Graph Matching, with section on bipartite
  • Paper: A n5/2 algorithm for maximum matchings in bipartite: Original paper on Hopcroft-Karp algorithm
  • Hopcroft-Karp algorithm: Wikipedia overview
  • Class note on Matching from Cornell
  • Paper: Multithreaded Algorithms for Maximum Matching in Bipartite Graphs
  • Paper: Parallel algorithms for bipartite matching problems on distributed memory computers
  • Paper: Finding maximum matching for bipartite graphs in parallel
  • Draft: : start on a paper on bipartite matching
• Breadth First Search: explore graph from a root vertex
  • See also Spanning Trees
  • Graph500 Website
  • Applications of BFS
  • More applications of BFS
  • Paper: Introducing the Graph 500
  • R-MAT: A Recursive Model for Graph Mining The algorithm for standard GRAPH500 graph generator
  • Performance Analysis of a Large Memory Application on Multiple Architectures: Architectural analysis of GRAPH500 data
  • Paper:
  • Paper: Direction-optimizing breadth-rst search.Beamer's original hybrid algorithm
  • Paper: Traversing Trillions of Edges in Real-time: Graph Exploration on Large-scale Parallel Machines: Discussion of BFS on BlueGene Q
• Centrality: fining the "most important" vertices
  Wikipedia: Centrality
• Community Detection: Finding subgraphs with some affinity
  • Paper: Community detection in graphs: highly referenced survey
  • Paper: Parallel Community Detection for Massive Graphs
  • Wikipedia: Girvan Newman algorithm
  • Wikipedia: Kernigan-Lin algorithm
• Connected Components: subgraphs where all vertices are reachable
  • Wikipedia See Book 2-5 and 11-4 Algorithm 1
  • Paper: Algorithm 447: efficient algorithms for graph manipulation: the original Hopcroft Tarjan algorithm
• Graph Systems
  • Paper: "Graph Analytics: Complexity, Scalability, and Architectures"
• Higher Order Networks
  • HON website
• Jaccard: compute fraction of neighbor's in common between two vertices
  • Wikipedia
  • Paper: Calculating the Jaccard Similarity Coefficient with Map Reduce for Entity Pairs in Wikipedia: Hadoop
  • Paper:Parallelizing an Algorithm to find Communities using the Jaccard Metric
  • Paper:Asking Hard Graph Questions: scaling study on 1000 node Hadoop
  • Presentation:Jaccard Coefficients as a Potential Graph Benchmark: presentation
  • Paper:Jaccard Coefficients as a Potential Graph Benchmark: includes suggestion for Bloom Filter heuristic
  • Draft: : start on a Jaccard paper, including a suggestion for a Bloom Filter heuristic and a parallel algorithm based on a triangle finder
• Non-Obvious Relationship Analysis: variation of Jaccard with extra search constraints
  • Paper: Comparative performance analysis of a Big Data NORA problem on a variety of architectures
• Page Rank: estimate ``connectiveness'' or centrality of a vertex
  • Wikipedia
  • A nice overview
  • A 1999 paper
  • Presentation on 1st paper
• Shortest Path. Find shortest paths between (specific vertex, all vertices) to (specific vertex, all other vertices)
  • Book 11-5
  • Wikipedia: Dijkstra's algorithm
  • Paper: A Note on Two Problems in Connexion with GraphDijkstra's original paper.
  • Graph500 SSSP BenchmarkSingle source shortest path to all others
  • Paper: A Survey of Shortest-Path Algorithms
  • Web page: Case Study: Shortest-Path Algorithms Includes abstract parallel algorithms
• Spanning Trees: See also BFS
  • See book Chap. 3, esp. 3-10 and 11-4 Algorithm 2
  • Wikipedia: Kruskal's Algorithm for weighted edges
• Stateful Random Walks
  • Paper: Representing higher order dependencies in networks: Notre Dame Authors
  • metapath2vec: Scalable representation learning for heterogeneous networks
  • Draft: Very early discussion

Sample Graph Data Sets

• SNAP: Stanford Large Network Dataset Collection. Wide spectrum of a variety of graph types of various sizes.
• Sample datasets formatted for Neo4j language
• Amazon-hosted Data sets for the Graph Challenge project. Includes pointers to multiple graph generators.
• A Python bipartite graph generator written by Jeremy Speth at ND in summer 2018.
• Hyperlink graphs<\a>
• Neural Connectome Data
  • General Connectome Data
  • Worm data
• Network Data
  • ICON: Colorado Index of Complex Networks
  • KONECT: Koblenz Network Collection
  • Network Repository "Wide variety of applications and domains (e.g., network science, bioinformatics, machine learning, data mining, physics, and social science) and includes relational, attributed, heterogeneous, streaming, spatial, and time series data as well as non-relational machine learning data."
  • Data set for Higher Order Networks. Same gihhub site has code to generate synthetic HON graphs

Programming Paradigms

• Think Like a Vertex Vertex-centric programming paradigm
• From "Think Like a Vertex" to "Think Like a Graph" Followon to above paper.
• Paper: Standards for Graph Algorithm Primitives: first start at thinking of graph algorithms in linear algebra context
• GraphBLAS and Linear Algebra
  • Home page
  • An overview
  • Another overview
  • Math background
  • Tutorial
  • Version 1.2 Specification
  • Suitesparse reference implementation