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  2. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. [ 17 ]

  3. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    This book is a classic, developing the theory, then cataloguing many NP-Complete problems. Cook, S.A. (1971). "The complexity of theorem proving procedures". Proceedings, Third Annual ACM Symposium on the Theory of Computing, ACM, New York. pp. 151–158. doi: 10.1145/800157.805047. Karp, Richard M. (1972). "Reducibility among combinatorial ...

  4. List of graph theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_graph_theory_topics

    1 Examples and types of graphs. 2 Graph coloring. 3 Paths and cycles. 4 Trees. Toggle Trees subsection. ... This is a list of graph theory topics, by Wikipedia page.

  5. Shortest path problem - Wikipedia

    en.wikipedia.org/wiki/Shortest_path_problem

    Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

  6. Hamiltonian path - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_path

    A Hamiltonian cycle around a network of six vertices Examples of Hamiltonian cycles on a square grid graph 8x8. In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.

  7. Small-world network - Wikipedia

    en.wikipedia.org/wiki/Small-world_network

    In another example, the famous theory of "six degrees of separation" between people tacitly presumes that the domain of discourse is the set of people alive at any one time. The number of degrees of separation between Albert Einstein and Alexander the Great is almost certainly greater than 30 [ 15 ] and this network does not have small-world ...

  8. Seven Bridges of Königsberg - Wikipedia

    en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

    These changes leave five bridges existing at the same sites that were involved in Euler's problem. In terms of graph theory, two of the nodes now have degree 2, and the other two have degree 3. Therefore, an Eulerian path is now possible, but it must begin on one island and end on the other. [9]

  9. Planar graph - Wikipedia

    en.wikipedia.org/wiki/Planar_graph

    In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [1] [2] Such a drawing is called a plane graph, or a planar embedding of the graph.