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degree

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degree [n]
 
1)a position on a scale of intensity or amount or quality; "a moderate degree of intelligence"; "a high level of care is required"; "it is all a matter of degree"
    Synonyms :grade level 
    See Also: magnitude  high  low  mild  intense  caliber  intensity  depth  high  low  extreme  amplitude_level  moderateness  immoderateness 
 
2)a specific identifiable position in a continuum or series or especially in a process; "a remarkable degree of frankness"; "at what stage are the social sciences?"
    Synonyms :level point stage 
    See Also: state  ladder  acme  extent  end_point  standard_of_life  plane  state_of_the_art  ultimacy  quickening  climax 
 
3)an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study; "he earned his degree at Princeton summa cum laude"
    Synonyms :academic_degree 
    See Also: accolade  makings  associate  baccalaureate  honours  master's_degree  doctor's_degree  law_degree  honorary_degree 
 
4)a unit of temperature on a specified scale; "the game was played in spite of the 40-degree temperature"
    Synonyms :
    See Also: temperature_unit  c  degree_fahrenheit 
 
5)a measure for arcs and angles; "there are 360 degrees in a circle"
    Synonyms :arcdegree 
    See Also: angular_unit  oxtant  sextant  quadrant  arcminute 
 
6)the highest power of a term or variable
    Synonyms :
    See Also: exponent  degree_of_a_term  degree_of_a_polynomial  first_degree 
 
7)the seriousness of something (e.g., a burn or crime); "murder in the second degree"; "a second degree burn"
    Synonyms :
    See Also: magnitude 
 

From The Free On-line Dictionary of Computing: (http://www.foldoc.org/, Editor Denis Howe)

The degree (or valency) of a node in a graph is the number of edges joined to it.








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