30 lines
816 B
Matlab
30 lines
816 B
Matlab
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% Check whether a sequence of number is graphic, i.e.
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% a graph with this degree sequence exists
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% Source: Erdős, P. and Gallai, T. "Graphs with Prescribed Degrees
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% of Vertices" [Hungarian]. Mat. Lapok. 11, 264-274, 1960.
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%
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% INPUTs: a sequence (vector) of numbers
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% OUTPUTs: boolean, true or false
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%
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% Note: Not generalized to directed graph degree sequences.
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% GB: last updated, Sep 24, 2012
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function B = isGraphic(seq)
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if not(isempty(find(seq<=0))) || mod(sum(seq),2)==1
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% there are non-positive degrees or their sum is odd
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B = false; return;
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end
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n=length(seq);
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seq=-sort(-seq); % sort in decreasing order
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for k=1:n-1
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sum_dk = sum(seq(1:k));
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sum_dk1 = sum(min([k*ones(1,n-k);seq(k+1:n)]));
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if sum_dk > k*(k-1) + sum_dk1; B = false; return; end
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end
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B = true;
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