Keck Graduate Institute of Applied Life Sciences, 535 Watson Drive, Claremont, CA 91711, USA.
Biol Direct. 2010 May 6;5:32. doi: 10.1186/1745-6150-5-32.
Much work in systems biology, but also in the analysis of social network and communication and transport infrastructure, involves an in-depth analysis of local and global properties of those networks, and how these properties relate to the function of the network within the integrated system. Most often, systematic controls for such networks are difficult to obtain, because the features of the network under study are thought to be germane to that function. In most such cases, a surrogate network that carries any or all of the features under consideration, while created artificially and in the absence of any selective pressure relating to the function of the network being studied, would be of considerable interest.
Here, we present an algorithmic model for growing networks with a broad range of biologically and technologically relevant degree distributions using only a small set of parameters. Specifying network connectivity via an assortativity matrix allows us to grow networks with arbitrary degree distributions and arbitrary modularity. We show that the degree distribution is controlled mainly by the ratio of node to edge addition probabilities, and the probability for node duplication. We compare topological and functional modularity measures, study their dependence on the number and strength of modules, and introduce the concept of anti-modularity: a property of networks in which nodes from one functional group preferentially do not attach to other nodes of that group. We also investigate global properties of networks as a function of the network's growth parameters, such as smallest path length, correlation coefficient, small-world-ness, and the nature of the percolation phase transition. We search the space of networks for those that are most like some well-known biological examples, and analyze the biological significance of the parameters that gave rise to them.
Growing networks with specified characters (degree distribution and modularity) provides the opportunity to create surrogates for biological and technological networks, and to test hypotheses about the processes that gave rise to them. We find that many celebrated network properties may be a consequence of the way in which these networks grew, rather than a necessary consequence of how they work or function.
系统生物学，以及社会网络、通信和交通基础设施分析等领域的许多工作都涉及到对这些网络的局部和全局特性的深入分析，以及这些特性如何与网络在集成系统中的功能相关。通常情况下，很难对这些网络进行系统控制，因为所研究的网络的特征被认为与该功能有关。在大多数情况下，考虑到与正在研究的网络的功能有关的任何选择压力，具有所考虑的任何或所有特征的替代网络是非常重要的，而这种网络是人工创建的，并且不存在这种选择压力。
在这里，我们提出了一种算法模型，该模型可以使用少量参数生成具有广泛生物学和技术相关性的度分布的网络。通过使用关联矩阵指定网络的连通性，我们可以生成具有任意度分布和任意模块性的网络。我们表明，度分布主要由节点与边添加概率的比值以及节点复制的概率控制。我们比较了拓扑和功能模块性度量，研究了它们对模块数量和强度的依赖性，并引入了反模块性的概念：一种网络的特性，其中一个功能组的节点优先不与该组的其他节点连接。我们还研究了网络的全局特性作为网络生长参数的函数，例如最短路径长度、相关系数、小世界特性和渗流相变的性质。我们在网络空间中搜索那些最类似于一些著名的生物学实例的网络，并分析产生它们的参数的生物学意义。
用指定的特征（度分布和模块性）生成网络，为创建生物学和技术网络的替代物，并测试产生它们的过程的假设提供了机会。我们发现，许多著名的网络特性可能是这些网络生长方式的结果，而不是它们工作或功能的必然结果。
