Summary
Given a formulation of a problem, a compact representation is required both for theoretical purposes — measuring the complexity of algorithms, and for practical purposes — data compression.
The adjacency lists method for representing graphs is compared to the information theoretic lower bounds, and it is shown to be optimal in many instances. For n-vertex labeled planar graphs the adjacency lists method requires 3nlogn + O(n) bits, a linear algorithm is presented to obtain a 3/2nlogn + O(n) representation while nlogn + O(n) is shown to be the minimum.
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References
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Itai, A., Rodeh, M. Representation of graphs. Acta Informatica 17, 215–219 (1982). https://doi.org/10.1007/BF00288971
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DOI: https://doi.org/10.1007/BF00288971