Ispolatov I, Krapivsky Pl, Mazo I, Yuryev A
Ariadne Genomics Inc., Rockville, MD 20850, USA.
New J Phys. 2005 Jun 17;7:145. doi: 10.1088/1367-2630/7/1/000.
A population of complete subgraphs or cliques in a protein network model is studied. The network evolves via duplication and divergence supplemented with linking a certain fraction of target-replica vertex pairs. We derive a clique population distribution, which scales linearly with the size of the network and is in a perfect agreement with numerical simulations. Fixing both parameters of the model so that the number of links and abundance of triangles are equal to those observed in the fruitfly protein-binding network, we precisely predict the 4- and 5-clique abundance. In addition, we show that such features as fat-tail degree distribution, various rates of average degree growth and nonaveraging, revealed recently for a particular case of a completely asymmetric divergence, are present in a general case of arbitrary divergence.
研究了蛋白质网络模型中的完全子图或团簇群体。该网络通过复制和分化演化，并辅以连接一定比例的目标 - 复制顶点对。我们推导出团簇群体分布，其与网络规模呈线性比例关系，并且与数值模拟完全吻合。固定模型的两个参数，使得链接数量和三角形丰度与果蝇蛋白质结合网络中观察到的相等，我们精确预测了4团簇和5团簇的丰度。此外，我们表明，最近在完全不对称分化的特定情况下揭示的诸如胖尾度分布、平均度增长的各种速率和非平均化等特征，在任意分化的一般情况下也存在。
