类似于生物序列比较，比较细胞网络是一个重要的问题，可以为生物学理解和治疗提供见解。由于技术原因，比较大型网络在计算上是不可行的，因此人们一直在寻找度分布等数学方法。通过简单地列出两个网络不同的属性，很容易证明它们是不同的。要证明两个网络是相似的要困难得多，因为这需要证明它们在所有指数级的属性上都是相似的。显然，分析所有网络属性在计算上是不允许的，但是我们在确定网络相似性时施加的约束越多，网络就越有可能真正相似。我们引入了一个新的系统性措施的网络的局部结构，施加了大量的相似性约束的网络进行比较。特别是，我们推广的度分布，它测量的节点的数量'触摸' k边，到分布测量的节点的数量'触摸' k graphlets，其中graphlets是一个大的网络的小连接非同构子图。我们的网络局部结构的新度量由73个具有2-5个节点的小图的小图度分布（GDD）组成，但它很容易扩展到更多数量的约束（即小图）。此外，我们展示了一种方法，将73个GDD组合成一个网络“协议”措施。基于这个新的网络协议措施，我们表明，几乎所有的14个真核PPI网络，包括人类，更好地模拟几何随机图比埃尔多斯-雷尼，随机无标度，或Barabasi-Albert无标度网络。
英文摘要：
Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics such as the degree distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar.
We introduce a new systematic measure of a network's local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes 'touching' k edges, into distributions measuring the number of nodes 'touching' k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions (GDDs) of graphlets with 2-5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets). Furthermore, we show a way to combine the 73 GDDs into a network 'agreement' measure. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, are better modeled by geometric random graphs than by Erdos-Reny, random scale-free, or Barabasi-Albert scale-free networks.
Antifragility Predicts the Robustness and Evolvability of Biological Networks through Multi-class Classification with a Convolutional Neural Network
University of Copenhagen（哥本哈根大学）；Graz University of Technology（格拉茨工业大学）；Sorbonne Université（索邦大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；ITMO University（ITMO大学）
