Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems- thermotropic liquid crystals and a lyotropic water/surfactant mixtures-graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node-based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.

BACKGROUND: The neurobiological pathogenesis of major depression disorder (MDD) remains largely controversial. Previous literatures with limited sample size utilizing group-level structural covariance networks (SCN) commonly generated mixed findings regarding the topology of brain networks.
METHODS: We analyzed T1 images from a high-powered multisite sample including 1173 patients with MDD and 1019 healthy controls (HCs). We used regional gray matter volume to construct individual SCN by utilizing a novel approach based on the interregional effect size difference. We further investigated MDD-related structural connectivity alterations using topological metrics.
RESULTS: Compared to HCs, the MDD patients showed a shift toward randomization characterized by increased integration. Further subgroup analysis of patients in different stages revealed this randomization pattern was also observed in patients with recurrent MDD, while the first-episode drug naïve patients exhibited decreased segregation. Altered nodal properties in several brain regions which have a key role in both emotion regulation and executive control were also found in MDD patients compared with HCs. The abnormalities in inferior temporal gyrus were not influenced by any specific site. Moreover, antidepressants increased nodal efficiency in the anterior ventromedial prefrontal cortex.
CONCLUSIONS: The MDD patients at different stages exhibit distinct patterns of randomization in their brain networks, with increased integration during illness progression. These findings provide valuable insights into the disruption in structural brain networks that occurs in patients with MDD and might be useful to guide future therapeutic interventions.

Epilepsy is a common symptom in diffuse lower-grade glioma (DLGG). The specific role of white matter (WM) alteration in patients with glioma-related epilepsy (GRE) is largely unknown. This study aims to investigate the reorganization of WM tracts and changes in structural networks related to GRE.
Diffusion-weighted images were collected from 70 patients with left frontal DLGG (GRE = 33, non-GRE = 37) and 41 healthy controls (HC). Tractometry with TractSeg was applied to segment tracts and quantify fractional anisotropy (FA) along each tract. Structural network was constructed using constrained spherical deconvolution and probabilistic tractography. FA and network properties were compared among three groups.
Compared with HC, both GRE and non-GRE showed decreased FA in contralateral inferior fronto-occipital fasciculus, superior longitudinal fasciculus II and arcuate fasciculus, increased nodal efficiency in contralateral nodes of frontal-parietal and limbic networks, whereas decreased degree centrality and betweenness centrality in nodes of dorsal temporal lobe and rostral middle frontal gyrus (rMFG). Additionally, when compared GRE with non-GRE, increased FA in contralateral corticospinal tract (CST) and lower betweenness centrality in paracentral lobule (PCL) in GRE (all p < 0.05 after Bonferroni correction).
This study indicates that patients with left frontal DLGG exhibit complex WM reorganization, and the altered regions mainly concentrated in the language, frontal-parietal and limbic networks. Moreover, the preserved integrity in contralateral CST and server decreased nodal betweenness in PCL may be potential neuroimaging markers underlying the occurrence of presurgical seizures of GRE.

The relationship between the topological characteristics of the white matter (WM) network have been shown to be related to neural development, intelligence, and various diseases; however, few studies have been conducted to explore the relationship between topological characteristics of the WM network and cerebral metabolism. In a recent study we investigated the relationship between WM network topological and metabolic metrics of the cerebral parenchyma in healthy volunteers using the newly developed T2-relaxation-under-spin-tagging (TRUST) magnetic resonance imaging technique and graph theory approaches. Ninety-six healthy adults (25.5 ± 1.8 years of age) were recruited as volunteers in the current study. The cerebral metabolic rate of oxygen (CMRO2), oxygen extraction fraction, and the global topological metrics of the WM network (global efficiency [Eglob], local efficiency, and small-worldliness) were assessed. A stepwise multiple linear regression model was estimated. CMRO2 was entered as the dependent variable. The topological and demographic parameters (age, gender, FIQ, SBP, gray matter volume, and WM volume) were entered as independent variables in the model. The final performing models were comprised of predictors of Eglob, FIQ, and age (adjusted R2 values were 0.489 [L-AAL] and 0.424 [H-1024]). Our study initially revealed a relationship between Eglob and cerebral oxygen metabolism in healthy young adults.