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Lancichinetti-Fortunato-Radicchi (LFR) benchmark is an algorithm that generates benchmark networks (artificial networks that resemble real-world networks). They have a priori known communities and are used to compare different community detection methods.〔Hua-Wei Shen (2013). "Community Structure of Complex Networks". Springer Science & Business Media. 11-12.〕 The advantage of LFR over other methods is that it accounts for the heterogeneity in the distributions of node degrees and of community sizes.〔A. Lancichinetti, S. Fortunato, and F. Radicchi.(2008) Benchmark graphs for testing community detection algorithms. Physical Review E, 78. http://arxiv.org/pdf/0805.4770v4.pdf〕 ==The algorithm== The node degrees and the community sizes are distributed according to power law, with different exponents. LFR assumes that both the degree and the community size have power law distributions with different exponents, γ and β, respectively. N is the number of nodes and the average degree is One can generate a LFR benchmark network in the following steps. Step 1: Generate a network with nodes following a power law distribution with exponent γ and choose extremes of the distribution and to get desired average degree is Step 2: (1 − µ) fraction of links of every node is with nodes of the same community, while fraction µ is with the other nodes. Step 3: Generate community sizes from a power law distribution with exponent β. The sum of all sizes must be equal to N. The minimal and maximal community sizes and must satisfy the definition of community so that every non-isolated node is in at least in one community: Step 4: Initially, no nodes are assigned to communities. Then, each node is randomly assigned to a community. As long as the number of neighboring nodes within the community does not exceed the community size a new node is added to the community, otherwise stays out. In the following iterations the “homeless” node is randomly assigned to some community. If that community is complete, i.e. the size is exhausted, a randomly selected node of that community must be unlinked. Stop the iteration when all the communities are complete and all the nodes belong to at least one community. Step 5: Implement rewiring of nodes keeping the same node degrees but only affecting the fraction of internal and external links such that the number of links outside the community for each node is approximately equal to the mixing parameter µ.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lancichinetti-Fortunato-Radicchi Benchmark」の詳細全文を読む スポンサード リンク
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