Editing Planar graph (section)

=== Planar graph density ===
The [[meshedness coefficient]] or density {{mvar|D}} of a planar graph, or network, is the ratio of the number {{math|''f'' − 1}} of bounded faces (the same as the [[circuit rank]] of the graph, by [[Mac Lane's planarity criterion]]) by its maximal possible values {{math|2''v'' − 5}} for a graph with {{mvar|v}} vertices:
:<math>D = \frac{f-1}{2v-5}</math>
The density obeys {{math|0 ≤ ''D'' ≤ 1}}, with {{math|1=''D'' = 0}} for 
a completely sparse planar graph (a tree), and {{math|1=''D'' = 1}} for a completely dense (maximal) planar graph.<ref>{{citation
 | last1 = Buhl | first1 = J.
 | last2 = Gautrais | first2 = J.
 | last3 = Sole | first3 = R.V.
 | last4 = Kuntz | first4 = P.
 | last5 = Valverde | first5 = S.
 | last6 = Deneubourg | first6 = J.L.
 | last7 = Theraulaz | first7 = G.
 | doi = 10.1140/epjb/e2004-00364-9
 | issue = 1
 | journal = European Physical Journal B
 | pages = 123–129
 | title = Efficiency and robustness in ant networks of galleries
 | volume = 42
 | year = 2004| bibcode = 2004EPJB...42..123B| s2cid = 14975826
 }}.</ref>