61 lines
1.7 KiB
Matlab
61 lines
1.7 KiB
Matlab
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% Implementation of the forest fire model by Leskovec et al
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% "Graphs over Time: Densification Laws, Shrinking
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% Diameters and Possible Explanations"
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%
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% Inputs: forward burning probability p in [0,1],
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% backward burning ratio r, in [0,inf),
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% T - number of nodes
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% Outputs: adjacency list of the constructed (directed) graph
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%
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% Other routines used: weightedRandomSample.m
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% GB: last updated, November 28, 2012
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function L = forestFireModel(T,p,r)
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if T==1
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L{1} = []; % a single node, no edges
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return
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elseif T>=2
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L{1} = [2]; L{2} = [1]; % start with a single edge
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end
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for t=3:T
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L{t} = []; % new node arrives
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w = randi(t-1); % pick a node from 1->t-1 uniformly at random
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queue=[w]; visited = [];
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while not(isempty(queue))
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L{t} = [L{t} w]; % connect t to w
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w = queue(1); visited = [visited w];
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outlinks = L{w}; inlinks = [];
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for ll=1:length(L)
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if sum(find(L{ll}==w))>0; inlinks = [inlinks ll]; end
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end
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N = length(unique([outlinks inlinks]));
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x = geornd(1-p,1,1); % mean p/(1-p) => (1-p) probability
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y = geornd(1-r*p,1,1); % mean rp/(1-rp) => (1-rp) probability
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s_in = weightedRandomSample(y,inlinks,ones(size(inlinks))/length(inlinks));
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s_out = weightedRandomSample(x,outlinks,ones(size(outlinks))/length(outlinks));
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ws = unique([s_in s_out]);
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L{t} = unique([L{t} ws]); % add as outlinks to new node
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for ii=1:length(ws)
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if sum(find(visited==ws(ii)))==0; queue = [queue ws(ii)]; end
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end
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queue = queue(2:length(queue)); % remove w from queue
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end
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end
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for ll=1:length(L); L{ll} = setdiff(L{ll},ll); end % remove self-loops
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