noun, plural complexities for 2.
the state or quality of being complex; intricacy: the complexity of urban life.
something complex: the complexities of foreign policy.

1715–25; complex + -ity

intercomplexity, noun, plural intercomplexities.
overcomplexity, noun
supercomplexity, noun, plural supercomplexities. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
complexity (kəmˈplɛksɪtɪ)
n , pl -ties
1.  the state or quality of being intricate or complex
2.  something intricate or complex; complication

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

1721, "composite nature," from complex (adj.) + -ity. Meaning "intricacy" is from 1790. As a noun, from 1794.
Online Etymology Dictionary, © 2010 Douglas Harper
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Computing Dictionary

complexity definition

The level in difficulty in solving mathematically posed problems as measured by the time, number of steps or arithmetic operations, or memory space required (called time complexity, computational complexity, and space complexity, respectively).
The interesting aspect is usually how complexity scales with the size of the input (the "scalability"), where the size of the input is described by some number N. Thus an algorithm may have computational complexity O(N^2) (of the order of the square of the size of the input), in which case if the input doubles in size, the computation will take four times as many steps. The ideal is a constant time algorithm (O(1)) or failing that, O(N).
See also NP-complete.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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Example sentences
Given the complexity of the issues, none of these questions can yet be answered
Think about your colleagues' lives, in all their complexity.
Evolution borrowed those tools for a new task: building bodies of increasing
New research confirms that social complexity enriches cognitive growth.
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