Data Structures & Graph Variants

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Abstractions about data structures and specialized graph forms, including tree and heap structures such as the 2-3 heap, radix tree and random binary tree, specialized graph families like the complement graph, lollipop graph and Moore graph, and structural measures built on them such as dendrograms and cophenetic correlation.

17 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• 2–3 Heap — In computer science, a 2–3 heap is a data structure that implements a priority queue.
• Biased Graph — A graph with selected balanced cycles satisfying the theta rule: no theta subgraph has exactly two balanced cycles.
• Complement graph — In the mathematical field of graph theory, the complement or inverse of a graph is a graph on the same vertices such that two distinct vertices are adjacent (connected) in if and only if they are not adjacent in .
• Cophenetic correlation — In statistics, and especially in biostatistics, cophenetic correlation (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points.
• Dendrogram — A dendrogram is a tree diagram that represents nested grouping or branching relations, especially the sequence of cluster merges or splits in hierarchical clustering.
• Game complexity — The state-space complexity of a game is the number of legal game positions reachable from the initial position of the game.
• Graph operations — In the mathematical field of graph theory, graph operations are operations which produce new graphs from initial ones.
• Graph Toughness — The minimum ratio of vertices removed to components left over all fragmenting vertex sets of a finite graph, with complete graphs assigned infinity.
• Lollipop Graph — In the mathematical discipline of graph theory, the (m,n)-lollipop graph is a special type of graph consisting of a complete graph (clique) on m vertices and a path graph on n vertices, connected with a bridge.
• Maximal independent set — In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set.
• Moore graph — In graph theory, a Moore graph is a regular graph whose girth (the shortest cycle length) is more than twice its diameter (the distance between the farthest two vertices).
• Network Motif — A small connected graph pattern that occurs significantly more often in a network than under a stated randomized comparison.
• Radix tree — In computer science, a radix tree (also radix trie or compact prefix tree or compressed trie) is a data structure that represents a space-optimized trie (prefix tree) in which each node that is the only child is merged with its parent.
• Random Binary Tree — In computer science and probability theory, a random binary tree is a binary tree selected at random from some probability distribution on binary trees.
• Skew-symmetric graph — In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points.
• Tree Decomposition — In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph.
• Tree toplology — A tree topology, or star-bus topology, is a hybrid network topology in which star networks are interconnected via bus networks.