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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.
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]
A "k-dimensional hole" is a k-dimensional cycle that is not a boundary of a (k+1)-dimensional object. The first few Betti numbers have the following definitions for 0-dimensional, 1-dimensional, and 2-dimensional simplicial complexes: b 0 is the number of connected components; b 1 is the number of one-dimensional or "circular" holes;
If data is a Series, then data['a'] returns all values with the index value of a. However, if data is a DataFrame, then data['a'] returns all values in the column(s) named a. To avoid this ambiguity, Pandas supports the syntax data.loc['a'] as an alternative way to filter using the index.
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 ...
To create a synthetic data point, take the vector between one of those k neighbors, and the current data point. Multiply this vector by a random number x which lies between 0, and 1. Add this to the current data point to create the new, synthetic data point. Many modifications and extensions have been made to the SMOTE method ever since its ...