Field-Theoretical Approach to Complex Networks

我们建议通过扩展和修改理论物理中用于描述无序介观系统的技术来创建描述复杂网络系统的新工具。我们打算提供一个框架来通用地描述通过属于不同类别的复杂网络系统的随机传播。考虑到动力学无序(由于输入的不可避免的随机性)和猝灭无序(模拟不同拓扑的复杂网络)，我们将建立一组定义在离散流形(网络)上的相关朗之万方程。为了实现普遍的描述，我们将把这些方程转化为有效场论的形式。这将允许我们首先对网络进行分类(关键是同时考虑随机信号的特性和网络拓扑)，从而提出作为这种复杂性的结果而出现的新的普适性类，然后使用强大的场论方法来确定和计算复杂网络上的相关可观测量。

We propose to create new tools for describing complex network systems by extending and modifying techniques used in theoretical physics for the description of disordered mesoscopic systems. We intend to provide a framework for a universal description of stochastic propagation through complex network systems belonging to different classes. Taking into account both dynamical disorder (due to the inevitable stochasticity of the input) and quenched disorder (that models complex networks of different topologies), we will formulate a set of relevant Langevin equations defined on discrete manifolds (networks). To achieve the universal description, we are going to cast these equations into the form of an effective field theory. This would allow us first to classify the networks (crucially, allowing both for the character of random signal and / simultaneously / for the network topology) and thus present new universality classes that emerge as the result of this complexity, and then to use powerful field theoretical methods for determining and calculating relevant observable quantities on the complex network.