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What is a covalence?

What is a covalence? Here are some definitions.

Noun
  1. (chemistry) A form of valence in which electrons are shared between participating atoms
  2. (chemistry) The number of electrons that a particular atom can share (and therefore the number of covalent bonds it can form)
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Examples
It is argued that the terms valence, covalence, hypervalence, oxidation state, and coordination number are often confused and misused in the literature.
We describe a rough estimate that suggests such effects on the degree of covalence are very small.
Covalence, a Geneva-based monitoring organization, recently acknowledged Petro-Canada for its strong ethical practices.

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