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In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see holes in graph theory). Every chordal graph is a strangulated graph , a graph in which every peripheral cycle is a triangle, because peripheral cycles are a special case of induced cycles.
A triangle-free graph is a graph with no induced cycle of length three. The cographs are exactly the graphs with no induced path of length three. The chordal graphs are the graphs with no induced cycle of length four or more. The even-hole-free graphs are the graphs containing no induced cycles with an even number of vertices.
More precisely, the definition may allow the graph to have induced cycles of length four, or may also disallow them: the latter is referred to as even-cycle-free graphs. [ 1 ] Addario-Berry et al. (2008) demonstrated that every even-hole-free graph contains a bisimplicial vertex (a vertex whose neighborhood is the union of two cliques ), which ...
NetworkX has applications in any field that studies data as graphs or networks, such as mathematics, physics, biology, computer science and social science. [20] The nodes in a NetworkX graph can be specialized to hold any data, and the data stored in edges is arbitrary, further making it widely applicable to different fields. It is able to read ...
Data science is multifaceted and can be described as a science, a research paradigm, a research method, a discipline, a workflow, and a profession. [4] Data science is "a concept to unify statistics, data analysis, informatics, and their related methods" to "understand and analyze actual phenomena" with data. [5]
The mutability of these types of graphs, is studied in the field of graph rewriting. The nomenclature term graph is associated with the field of term graph rewriting , [ 2 ] which involves the transformation and processing of expressions by the specification of rewriting rules, [ 3 ] whereas abstract semantic graph is used when discussing ...
In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...