Graph theoretical approach has proved an effective tool to understand, characterize, and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the context of brain networks. Comparing brain networks is indeed mandatory in several network neuroscience applications. Here, we discuss the current state of the art, challenges, and a collection of analysis tools that have been developed in recent years to compare brain networks. We first introduce the graph similarity problem in brain network application. We then describe the methodological background of the available metrics and algorithms of comparing graphs, their strengths, and limitations. We also report results obtained in concrete applications from normal brain networks. More precisely, we show the potential use of brain network similarity to build a “network of networks” that may give new insights into the object categorization in the human brain. Additionally, we discuss future directions in terms of network similarity methods and applications.

Identifying the physiological processes underlying the emergence and maintenance of consciousness is one of the most fundamental problems of neuroscience, with implications ranging from fundamental neuroscience to the treatment of patients with disorders of consciousness (DOCs). One major challenge is to understand how cortical circuits at drastically different spatial scales, from local networks to brain-scale networks, operate in concert to enable consciousness, and how those processes are impaired in DOC patients. In this review, we attempt to relate available neurophysiological and clinical data with existing theoretical models of consciousness, while linking the micro- and macrocircuit levels. First, we address the relationships between awareness and wakefulness on the one hand, and cortico-cortical and thalamo-cortical connectivity on the other hand. Second, we discuss the role of three main types of GABAergic interneurons in specific circuits responsible for the dynamical reorganization of functional networks. Third, we explore advances in the functional role of nested oscillations for neural synchronization and communication, emphasizing the importance of the balance between local (high-frequency) and distant (low-frequency) activity for efficient information processing. The clinical implications of these theoretical considerations are presented. We propose that such cellular-scale mechanisms could extend current theories of consciousness.

The human brain is a dynamic networked system that continually reconfigures its functional connectivity patterns over time. Thus, developing approaches able to adequately detect fast brain dynamics is critical. Of particular interest are the methods that analyze the modular structure of brain networks, that is, the presence of clusters of regions that are densely interconnected. In this paper, we propose a novel framework to identify fast modular states that dynamically fluctuate over time during rest and task. We started by demonstrating the feasibility and relevance of this framework using simulated data. Compared with other methods, our algorithm was able to identify the simulated networks with high temporal and spatial accuracies. We further applied the proposed framework on MEG data recorded during a finger movement task, identifying modular states linking somatosensory and primary motor regions. The algorithm was also performed on dense-EEG data recorded during a picture naming task, revealing the subsecond transition between several modular states that relate to visual processing, semantic processing, and language. Next, we tested our method on a dataset of resting-state dense-EEG signals recorded from 124 patients with Parkinson’s disease. Results disclosed brain modular states that differentiate cognitively intact patients, patients with moderate cognitive deficits, and patients with severe cognitive deficits. Our new approach complements classical methods, offering a new way to track the brain modular states, in healthy subjects and patients, on an adequate task-specific timescale. Author Summary The brain is a dynamic modular network. Thus, exploring the dynamic behavior of the brain can reveal insights about its characteristics during rest and task, in healthy and pathological conditions. In this paper, we propose a new framework that aims to track the dynamic changes of the modular brain organization. The method presents two algorithms that can be applied during task-free or task-related paradigms. Using simulations, we demonstrated the advantages of the proposed algorithm over existing methods. The proposed algorithm was also tested on three datasets recorded from real EEG and MEG acquisitions. Overall, results showed the capacity of the proposed algorithm to track brain network dynamics with good spatial and temporal accuracy.