The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying network structure is crucial to understand the brain functioning under both healthy and pathological conditions. Yet, analyzing brain networks is challenging, in part because their structure represents only one possible realization of a generative stochastic process which is in general unknown. Having a formal way to cope with such intrinsic variability is therefore central for the characterization of brain network properties. Addressing this issue entails the development of appropriate tools mostly adapted from network science and statistics. Here, we focus on a particular class of maximum entropy models for networks, i.e. exponential random graph models, as a parsimonious approach to identify the local connection mechanisms behind observed global network structure. Efforts are reviewed on the quest for basic organizational properties of human brain networks, as well as on the identification of predictive biomarkers of neurological diseases such as stroke. We conclude with a discussion on how emerging results and tools from statistical graph modeling, associated with forthcoming improvements in experimental data acquisition, could lead to a finer probabilistic description of complex systems in network neuroscience.

中文翻译：

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复杂大脑网络的统计模型：最大熵方法


大脑是一个高度复杂的系统。这种复杂性大部分源于其各部分之间的混合联系，这些联系产生了丰富的动态和高级认知功能的出现。解开潜在的网络结构对于理解健康和病理条件下的大脑功能至关重要。然而，分析大脑网络具有挑战性，部分原因是它们的结构仅代表了通常未知的生成随机过程的一种可能实现。因此，有一种正式的方法来应对这种内在的变异性对于大脑网络特性的表征至关重要。解决这个问题需要开发适当的工具，这些工具主要改编自网络科学和统计学。在这里，我们关注一类特定的网络最大熵模型，即指数随机图模型，作为识别观察到的全局网络结构背后的局部连接机制的简约方法。回顾了在寻找人脑网络的基本组织特性以及识别中风等神经系统疾病的预测生物标志物方面所做的努力。最后，我们讨论了统计图模型的新兴结果和工具，以及即将到来的实验数据采集改进，如何能够对网络神经科学中的复杂系统进行更精细的概率描述。