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.

We aimed at identifying the potential relationship between the dynamical properties of the human functional network at rest and one of the most prominent traits of personality, namely resilience. To tackle this issue, we used resting-state EEG data recorded from 45 healthy subjects. Resilience was quantified using the 10-item Connor-Davidson Resilience Scale (CD-RISC). By using a sliding windows approach, brain networks in each EEG frequency band (delta, theta, alpha, and beta) were constructed using the EEG source-space connectivity method. Brain networks dynamics were evaluated using the network flexibility, linked with the tendency of a given node to change its modular affiliation over time. The results revealed a negative correlation between the psychological resilience and the brain network flexibility for a limited number of brain regions within the delta, alpha, and beta bands. This study provides evidence that network flexibility, a metric of dynamic functional networks, is strongly correlated with psychological resilience as assessed from personality testing. Beyond this proof-of-principle that reliable EEG-based quantities representative of personality traits can be identified, this motivates further investigation regarding the full spectrum of personality aspects and their relationship with functional networks. Author Summary In this study, we investigated the possible correlation between one of the most important personality traits, resilience , with a metric of dynamic functional networks called flexibility . From EEG resting-state recordings in N = 45 volunteers, we unveiled such a correlation and identified the brain regions involved in psychological resilience, from frequency-specific networks.