Degree

n. rank, extent; unit of measurement of angles; unit of measurement of temperature; academic title received after completing a program of studies at a university or college

Degree, in the sense of measurement, is used to indicate:Comparative degree ("good", "better") and superlative degree ("best")Severity of similar crimes (in some jurisdictions) — for example  first degree murderIntensity of a burn (from first degree to third degree)Level of kinship (consanguinity)Degree of inventiveness in inventions and patents
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Noun
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"
(synonym) grade, level
(hypernym) magnitude
(hyponym) quality, caliber, calibre
(attribute) high
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?"
(synonym) level, stage, point
(hypernym) state
(hyponym) ladder
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"
(synonym) academic degree
(hypernym) award, accolade, honor, honour, laurels
(hyponym) associate degree, associate
4. a unit of temperature on a specified scale; "the game was played in spite of the 40-degree temperature"
(hypernym) temperature unit
(hyponym) degree Centigrade, degree Celsius, C
5. a measure for arcs and angles; "there are 360 degrees in a circle"
(synonym) arcdegree
(hypernym) angular unit
(part-holonym) oxtant
(part-meronym) minute, arcminute, minute of arc
6. the highest power of a term or variable
(hypernym) exponent, power, index
(hyponym) degree of a term
7. the seriousness of something (e.g., a burn or crime); "murder in the second degree"; "a second degree burn"
(hypernym) magnitude

(n.)
Three figures taken together in numeration; thus, 140 is one degree, 222,140 two degrees.
  

(n.)
The point or step of progression to which a person has arrived; rank or station in life; position.
  

(n.)
State as indicated by sum of exponents; more particularly, the degree of a term is indicated by the sum of the exponents of its literal factors; thus, a2b3c is a term of the sixth degree. The degree of a power, or radical, is denoted by its index, that of an equation by the greatest sum of the exponents of the unknown quantities in any term; thus, ax4 + bx2 = c, and mx2y2 + nyx = p, are both equations of the fourth degree.
  

(n.)
One of a series of progressive steps upward or downward, in quality, rank, acquirement, and the like; a stage in progression; grade; gradation; as, degrees of vice and virtue; to advance by slow degrees; degree of comparison.
  

(n.)
Measure of advancement; quality; extent; as, tastes differ in kind as well as in degree.
  

(n.)
Grade or rank to which scholars are admitted by a college or university, in recognition of their attainments; as, the degree of bachelor of arts, master, doctor, etc.
  

(n.)
A step, stair, or staircase.
  

(n.)
A line or space of the staff.
  

(n.)
A division, space, or interval, marked on a mathematical or other instrument, as on a thermometer.
  

(n.)
A certain distance or remove in the line of descent, determining the proximity of blood; one remove in the chain of relationship; as, a relation in the third or fourth degree.
  

(n.)
A 360th part of the circumference of a circle, which part is taken as the principal unit of measure for arcs and angles. The degree is divided into 60 minutes and the minute into 60 seconds.
  

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