Small-world Properties Research Articles

Cognitive Decline Risk Stratification in People with Late-Onset Epilepsy of Unknown Etiology: An Electroencephalographic Connectivity and Graph Theory Pilot Study.

Although people with late onset epilepsy of unknown etiology (LOEU) are at higher risk of cognitive decline compared to the general population, we still lack affordable tools to predict and stratify their risk of dementia. This pilot-study investigates the potential application of electroencephalography (EEG) network small-world (SW) properties in predicting cognitive decline among patients with LOEU. People diagnosed with LOEU and normal cognitive examination at the time of epilepsy diagnosis were included. Cerebrospinal fluid biomarkers, brain imaging, and neuropsychological assessment were performed at the time of epilepsy diagnosis. Baseline EEG was analyzed for SW properties. Patients were followed-up over time with neuropsychological testing to define the trajectory of cognitive decline. Over 5.1 years of follow-up, among 24 patients diagnosed with LOEU, 62.5% were female, mean age was 65.3 years, thirteen developed mild cognitive impairment (MCI), and four developed dementia. Patients with LOEU developing MCI had lower values of SW coefficients in the delta (p = 0.03) band and higher SW values in the alpha frequency bands (p = 0.02) compared to patients having normal cognition at last follow-up. The two separate ANOVAs, for low and alpha bands, confirmed an interaction between SW and cognitive decline at follow-up. A similar gradient was confirmed for patients developing dementia compared to those with normal cognitive function as well as to those developing MCI. Baseline EEG analysis through SW is worth investigating as an affordable, widely available tool to stratify LOEU patients for their risk of cognitive decline.

ANALYSES OF SOME STRUCTURAL PROPERTIES ON A CLASS OF HIERARCHICAL SCALE-FREE NETWORKS

Hierarchical networks as fundamental models to describe the complex networks, have many applications in networks science, engineering technology and so on. In this paper, we first propose a new class of hierarchical networks with fractal structure, which are the networks with triangles compared to traditional hierarchical networks. Second, we study the precise results of some structural properties to derive small-world effect and scale-free feature. Third, it is found that the constructed network is sparse through the average degree and density. Fourth, it is also demonstrated that the degree distributions of hub nodes and the bottom nodes are the power law and exponential, respectively. Finally, we prove that clustering coefficient with a definite value [Formula: see text] tends to stabilize at a lower bound as [Formula: see text] iterates to a certain number, and the average distance of [Formula: see text] has an increasing relationship along with the value of [Formula: see text].

Comorbid depressive symptoms can aggravate the functional changes of the pain matrix in patients with chronic back pain: A resting-state fMRI study.

ObjectiveThe purposes of this study are to explore (1) whether comorbid depressive symptoms in patients with chronic back pain (CBP) affect the pain matrix. And (2) whether the interaction of depression and CBP exacerbates impaired brain function.MethodsThirty-two patients with CBP without comorbid depressive symptoms and thirty patients with CBP with comorbid depressive symptoms were recruited. All subjects underwent functional magnetic resonance imaging (fMRI) scans. The graph theory analysis, mediation analysis, and functional connectivity (FC) analysis were included in this study. All subjects received the detection of clinical depressive symptoms and pain-related manifestations.ResultCompared with the CBP group, subjects in the CBP with comorbid depressive symptoms (CBP-D) group had significantly increased FC in the left medial prefrontal cortex and several parietal cortical regions. The results of the graph theory analyses showed that the area under the curve of small-world property (t = −2.175, p = 0.034), gamma (t = −2.332, p = 0.023), and local efficiency (t = −2.461, p = 0.017) in the CBP-D group were significantly lower. The nodal efficiency in the ventral posterior insula (VPI) (t = −3.581, p = 0.0007), and the network efficiency values (t = −2.758, p = 0.008) in the pain matrix were significantly lower in the CBP-D group. Both the topological properties and the FC values of these brain regions were significantly correlated with self-rating depression scale (SDS) scores (all FDR corrected) but not with pain intensity. Further mediation analyses demonstrated that pain intensity had a mediating effect on the relationship between SDS scores and Pain Disability Index scores. Likewise, the SDS scores mediated the relationship between pain intensity and PDI scores.ConclusionOur study found that comorbid depressive symptoms can aggravate the impairment of pain matrix function of CBP, but this impairment cannot directly lead to the increase of pain intensity, which may be because some brain regions of the pain matrix are the common neural basis of depression and CBP.

Fractal networks with hierarchical structure: Mean fermat distance and small-world effect

The Fermat point of a triangle is the point with the minimal total distance from the three vertices of the triangle. Meanwhile, the total distance from the three vertices to the Fermat point is called the Fermat distance. In this paper, we discuss the Fermat distance on some networks. We study the mean Fermat distance of an unweighted and undirected hierarchical network [Formula: see text], which is obtained by analytical method and iterative calculation. We then reveal the relation between the mean Fermat distance [Formula: see text] and the mean geodesic distance [Formula: see text] in general networks, namely, [Formula: see text]. The ratio of the mean Fermat distance to the mean geodesic distance of [Formula: see text] tends to [Formula: see text], which is the lower bound of the inequality above. Moreover, the result shows the small-world effect of [Formula: see text]. Finally, we illustrate that the mean Fermat distance is significant in both small-world and scale-free networks.

Early detection of rumors based on source tweet-word graph attention networks.

The massively and rapidly spreading disinformation on social network platforms poses a serious threat to public safety and social governance. Therefore, early and accurate detection of rumors in social networks is of vital importance before they spread on a large scale. Considering the small-world property of social networks, the source tweet-word graph is decomposed from the global graph of rumors, and a rumor detection method based on graph attention network of source tweet-word graph is proposed to fully learn the structure of rumor propagation and the deep representation of text contents. Specifically, the proposed model can adequately capture the contextual semantic association representation of source tweets during the propagation and extract semantic features. For the data sparseness of the early stage of information dissemination, text attention mechanism based on opinion similarity can aggregate and capture more tweet propagation structure features to help improve the efficiency of early detection of rumors. Through the analysis of the experimental results on real public datasets, the rumor detection performance of the proposed method is better than that of other baseline methods. Especially in the early rumor detection tasks, the proposed method can detect rumors with an accuracy of nearly 90% in the early stage of information dissemination. And it still has good robustness with noise interference.

The effect of brain functional network following electroconvulsive therapy in major depressive disorder

PurposeThe purpose of this paper is to examine the changes of brain functional network after electroconvulsive therapy (ECT) treatment in major depressive disorder (MDD).Design/methodology/approachIn this study, resting electroencephalography (EEG) is used to explore the changes in spectral power density, functional connectivity and network topology elicited by an acute open-label course of ECT in a group of 19 MDD subjects. The brain functional network based on Pearson correlation is constructed in a continuous threshold space (0.38–0.59). Complex network theory is used to analyze the network characteristic such as the length of the characteristic path, clustering coefficient, degree, betweenness centrality, global efficiency and small-world architecture.FindingsThe results show that ECT increased the spectral power density of Delta, Theta and Alpha1 bands and the full frequency. ECT increases the functional connectivity in Delta and full frequency and reduces the functional connectivity in Alpha2 band. In the selected threshold space, the clustering coefficient, global efficiency and small-world attributes of the network are changed significantly after ECT.Originality/valueThe findings indicate that resting EEG could effectively characterize the changes of brain functional networks following ECT in MDD. The results provide a theoretical basis to explore the neurophysiological mechanism of ECT in the field of MDD treatment.

Early Development and the Functional Correlation of Brain Structural Connectivity in Preterm-Born Infants.

Exuberant axon growth and competitive pruning lead to dramatic and comprehensive changes in white matter pathways of the infant brain during the first few postnatal months, yet the development of structural configuration in early infancy has not been fully characterized. This study aimed to investigate the developmental trajectory of structural connectivity reflecting relative fiber density in 43 preterm-born infants aged 0–3 months of corrected age without any complications utilizing probabilistic tractography based on fiber orientation distribution and to explore the potential function correlation associated with the network properties based on the Chinese Communication Development of Infant at 10 months of corrected age. The findings revealed significant increases in global efficiency, local efficiency, normalized clustering coefficient, and small-worldness (padj < 0.001 for each), while the normalized characteristic path length showed a non-significant decrease with age (padj = 0.118). Furthermore, those findings were validated by another parcelation strategy. In addition, the early local efficiency was found to be significantly correlated with words understood at 10 months of corrected age. A unique developmental pattern of structural networks with enhancing efficiency and the small-world property was found in early infancy, which was different from those of neonates or toddlers. In addition, this study revealed a significant correlation between local efficiency and late language comprehension, which indicated that enhanced structural connectivity may lay the structural foundation for language specialization.

Spatial Structure and Development Patterns of Urban Traffic Flow Network in Less Developed Areas: A Sustainable Development Perspective

Sustainable development is a scientific development requirement for economic, social, and ecological development and is particularly important for less developed areas to achieve high quality development. Among them, the traffic flow network is a key contributor to economic activity and an inclusive society, as well as influencing the regional ecology, and is an important way to reflect the connection and structure of cities and towns. Based on the literature related to sustainable development, the article takes the passenger traffic data of highways, railways, and aviation of Inner Mongolia in 2021 as the sample and applies the complex network analysis method to analyze the traffic flow network structure and refine the spatial development patterns. The results show that: (1) The highway network is manifested as the connection between the central urban areas and surrounding banner counties and the connection between the adjacent banner counties. The railroad flow is extended and expanded by the railway line with core cities as the development axis. The internal and external connections of Hohhot are the general form of aviation network. The less developed areas under traffic flow network show obvious pointing of core cities and important node towns. (2) Each traffic flow network has the tendency of scale-free and small-world properties. The influence of key town nodes in the traffic flow network is relatively limited. (3) The town connection patterns under the highway, railway, and air flow networks are “single-core and multi-point”, “axis-spoke”, and “hub-spoke”, respectively. The multiple traffic flows support the development framework of towns in less developed areas. This paper also proposes strategies for the regional transport and urban pattern with complementary advantages and high quality and sustainable development in less developed areas.

Brain Network Alterations in Rectal Cancer Survivors With Depression Tendency: Evaluation With Multimodal Magnetic Resonance Imaging.

Surgery and chemotherapy may increase depression tendency in patients with rectal cancer (RC). Nevertheless, few comprehensive studies are conducted on alterations of brain network induced by depression tendency in patients with RC. Resting-state functional magnetic resonance imaging (rs-fMRI) and diffusion tensor imaging (DTI) data were collected from 42 patients with RC with surgery and chemotherapy and 38 healthy controls (HCs). Functional network (FN) was constructed from extracting average time courses in brain regions, and structural network (SN) was established by deterministic tractography. Graph theoretical analysis was used to calculate network properties. Networks resilient of two networks were assessed. Clinical correlation analysis was explored between altered network parameters and Hamilton depression scale (HAMD) score. This study revealed impaired FN and SN at both local and global levels and changed nodal efficiency and abnormal small-worldness property in patients with RC. On the whole, all FNs are more robust than SN. Moreover, compared with HC, patients with RC show less robustness in both networks. Regions with decreased nodal efficiency were associated with HAMD score. These cognitive dysfunctions are mainly attributable to depression-related brain functional and structural network alterations. Brain network reorganization is to prevent patients with RC from more serious depression after surgery and chemotherapy.

Impaired Functional Homotopy and Topological Properties Within the Default Mode Network of Children With Generalized Tonic-Clonic Seizures: A Resting-State fMRI Study.

IntroductionThe aim of the present study was to examine interhemispheric functional connectivity (FC) and topological organization within the default-mode network (DMN) in children with generalized tonic-clonic seizures (GTCS).MethodsResting-state functional MRI was collected in 24 children with GTCS and 34 age-matched typically developing children (TDC). Between-group differences in interhemispheric FC were examined by an automated voxel-mirrored homotopic connectivity (VMHC) method. The topological properties within the DMN were also analyzed using graph theoretical approaches. Consistent results were detected and the VMHC values were extracted as features in machine learning for subject classification.ResultsChildren with GTCS showed a significant decrease in VMHC in the DMN, including the hippocampal formation (HF), lateral temporal cortex (LTC), and angular and middle frontal gyrus. Although the patients exhibited efficient small-world properties of the DMN similar to the TDC, significant changes in regional topological organization were found in the patients, involving the areas of the bilateral temporal parietal junction, bilateral LTC, left temporal pole, and HF. Within the DMN, disrupted interhemispheric FC was found between the bilateral HF and LTC, which was consistent with the VMHC results. The VMHC values in bilateral HF and LTC were significantly correlated with clinical information in patients. Support vector machine analysis using average VMHC information in the bilateral HF and LTC as features achieved a correct classification rate of 89.34% for the classification.ConclusionThese results indicate that decreased homotopic coordination in the DMN can be used as an effective biomarker to reflect seizure effects and to distinguish children with GTCSs from TDC.

Scale-free and small-world properties in an incompatibility hierarchical network

In accordance with a particular iterative method, an incompatibility hierarchical network is introduced and the topological features of the network is investigated, It contains the degree distribution, diameter, clustering coefficient, second moment of distribution and degree correlations. The incompatibility hierarchical network is a simultaneous small-world, scale-free, assortative and divergent, which makes it possible to research the complexity of some real networks.

Reorganized Brain Functional Network Topology in Presbycusis.

PurposePresbycusis is characterized by bilateral sensorineural hearing loss at high frequencies and is often accompanied by cognitive decline. This study aimed to identify the topological reorganization of brain functional network in presbycusis with/without cognitive decline by using graph theory analysis approaches based on resting-state functional magnetic resonance imaging (rs-fMRI).MethodsResting-state fMRI scans were obtained from 30 presbycusis patients with cognitive decline, 30 presbycusis patients without cognitive decline, and 50 age-, sex-, and education-matched healthy controls. Graph theory was applied to analyze the topological properties of brain functional networks including global and nodal metrics, modularity, and rich-club organization.ResultsAt the global level, the brain functional networks of all participants were found to possess small-world properties. Also, significant group differences in global network metrics were observed among the three groups such as clustering coefficient, characteristic path length, normalized characteristic path length, and small-worldness. At the nodal level, several nodes with abnormal betweenness centrality, degree centrality, nodal efficiency, and nodal local efficiency were detected in presbycusis patients with/without cognitive decline. Changes in intra-modular connections in frontal lobe module and inter-modular connections in prefrontal subcortical lobe module were found in presbycusis patients exposed to modularity analysis. Rich-club nodes were reorganized in presbycusis patients, while the connections among them had no significant group differences.ConclusionPresbycusis patients exhibited topological reorganization of the whole-brain functional network, and presbycusis patients with cognitive decline showed more obvious changes in these topological properties than those without cognitive decline. Abnormal changes of these properties in presbycusis patients may compensate for cognitive impairment by mobilizing additional neural resources.

Comparative analysis between New Acupuncture and Meridians and Acupoints using the complex network approach基于复杂网络的《新针灸学》与《经络腧穴学》比较分析研究

The data relevant to acupoint names and indications were extracted from two key textbooks on acupuncture, namely, New Acupuncture and Meridians and Acupoints. Based on the complex network approach, the acupoint-symptom network was established and changes based on the acupoint number were analyzed to highlight the agreement and congruence between these two textbooks, including indication rules. Using topological data, the reasons for the differences were explained to provide specific ideas and methods for the structural development and standardization of the traditional acupuncture knowledge system. In this study, 386 acupoints, 773 symptoms, and 152,163 acupoint-matched pairs from New Acupuncture and 403 acupoints, 253 symptoms, and 28,755 acupoint-matched pairs from Meridians and Acupoints were included. The results highlighted that there are numerous differences in the acupoint-symptom network between these two textbooks. The model of New Acupuncture displays a more typical small-world effect, which may reflect the advantage of classification by symptoms. Furthermore, many of the variations in acupoint locations and indications between these two textbooks reflect the discipline's development over time.

COMPLEX NETWORKS MODELED ON A KIND OF SIERPIŃSKI-LIKE CARPET

In this paper, we use a kind of Sierpiński-like carpet to construct a special evolving network, whose nodes are all the solid squares in the construction of the carpet up to stage t. In our network, two nodes are neighbors if and only if the intersection of their corresponding squares is a line segment. Using the encoding method in fractal geometry, we show that our evolving network is scale-free and has the small-world effect, but is not fractal scaling.

Spatial and Temporal Evolution of the Chinese Artificial Intelligence Innovation Network

Sustainable development has become a concern of all countries globally, and Artificial Intelligence technology emerges at this historic moment. However, few researchers have studied the innovation activities of the Artificial Intelligence industry from the macro-level. This paper focuses on the topological structure and the spatial pattern of the AI patent citation network in China over from 2000–2016. Our main research results are as follows: The network has experienced a striking growth in terms of the size and the number of linkages since 2000, but it has also developed unequally across regions. In the later stages, the network has formed a scale-free network that exhibits small-world property. The network nodes have shown an assortative trait property while weighted preferential attachment has not been significant. In addition, the high values of centrality and numerous linkages between nodes concentrate in the eastern part of China, especially in the Yangtze River Delta, Pearl River Delta, and Bohai Rim. Our results suggest that the AI innovation policies should expand the targets of technological exchange and cultivate more nodes as intermediaries of local knowledge transmission necessary to expand the network and develop the AI industry.

Examining the interconnectedness and early warning signals of systemic risks of shadow banks: an application to the Indian shadow bank crisis

PurposeThe paper models the financial interconnectedness and systemic risk of shadow banks using Granger-causal network-based measures and takes the Indian shadow bank crisis of 2018–2019 as a systemic event.Design/methodology/approachThe paper employs pairwise linear Granger-causality tests adjusted for heteroskedasticity and return autocorrelation on a rolling window of weekly returns data of 52 financial institutions from 2016 to 2019 to construct network-based measures and calculate network centrality. The Granger-causal network-based measure ranking of financial institutions in the pre-crisis period (explanatory variable) is rank-regressed with the ranking of financial institutions based on maximum percentage loss suffered by them during the crises period (dependent variable).FindingsThe empirical result demonstrated that the shadow bank complex network during the crisis is denser, more interconnected and more correlated than the tranquil period. The closeness, eigenvector, and PageRank centrality established the systemic risk transmitter and receiver roles of institutions. The financial institutions that are more central and hold prestigious positions due to their incoming links suffered maximum loss. The shadow bank network also showed small-world phenomena similar to social networks. Granger-causal network-based measures have out-of-sample predictive properties and can predict the systemic risk of financial institutions.Research limitations/implicationsThe study considers only the publicly listed financial institutions. Also, the proposed measures are susceptible to the size of the rolling window, frequency of return and significance level of Granger-causality tests.Practical implicationsSupervisors and financial regulators can use the proposed measures to monitor the development of systemic risk and swiftly identify and isolate contagious financial institutions in the event of a crisis. Also, it is helpful to policymakers and researchers of an emerging economy where bilateral exposures' data between financial institutions are often not present in the public domain, plus there is a gap or delay in financial reporting.Originality/valueThe paper is one of the first to study systemic risk of shadow banks using a financial network comprising of commercial banks and mutual funds. It is also the first one to study systemic risk of Indian shadow banks.

Analysis of the Football Transfer Market Network

Using publicly available data from the football database transfermarkt.co.uk, it is possible to construct a trade network between football clubs. This work regards the network of the flow of transfer fees between European top league clubs from eight countries between 1992 and 2020 to analyse the network of each year’s transfer market. With the transfer fees as weights, the market can be represented as a weighted network in addition to the classic binary network approach. This opens up the possibility to study various topological quantities of the network, such as the degree and disparity distributions, the small-world property and different clustering measures. This article shows that these quantities stayed rather constant during the almost three decades of transfer market activity, even despite massive changes in the overall market volume.

Complex spiking neural networks with synaptic time-delay based on anti-interference function.

The research on a brain-like model with bio-interpretability is conductive to promoting its information processing ability in the field of artificial intelligence. Biological results show that the synaptic time-delay can improve the information processing abilities of the nervous system, which are an important factor related to the formation of brain cognitive functions. However, the synaptic plasticity with time-delay of a brain-like model still lacks bio-interpretability. In this study, combining excitatory and inhibitory synapses, we construct the complex spiking neural networks (CSNNs) with synaptic time-delay that more conforms biological characteristics, in which the topology has scale-free property and small-world property, and the nodes are represented by an Izhikevich neuron model. Then, the information processing abilities of CSNNs with different types of synaptic time-delay are comparatively evaluated based on the anti-interference function, and the mechanism of this function is discussed. Using two indicators of the anti-interference function and three kinds of noise, our simulation results consistently verify that: (i) From the perspective of anti-interference function, an CSNN with synaptic random time-delay outperforms an CSNN with synaptic fixed time-delay, which in turn outperforms an CSNN with synaptic none time-delay. The results imply that brain-like networks with more bio-interpretable synaptic time-delay have stronger information processing abilities. (ii) The synaptic plasticity is the intrinsic factor of the anti-interference function of CSNNs with different types of synaptic time-delay. (iii) The synaptic random time-delay makes an CSNN present better topological characteristics, which can improve the information processing ability of a brain-like network. It implies that synaptic time-delay is a factor that affects the anti-interference function at the level of performance.

Reorganization of prefrontal network in stroke patients with dyskinesias: evidence from resting-state functional near-infrared spectroscopy.

Stroke usually causes multiple functional disability. To develop novel rehabilitation strategies, it is quite necessary to improve the understanding of post-stroke brain plasticity. Here, we use functional near-infrared spectroscopy to investigate the prefrontal cortex (PFC) network reorganization in stroke patients with dyskinesias. The PFC hemodynamic signals in the resting state from 16 stroke patients and 10 healthy subjects are collected and analyzed with the graph theory. The PFC networks for both groups show small-world attributes. The stroke patients have larger clustering coefficient and transitivity and smaller global efficiency and small-worldness than healthy subjects. Based on the selected network features, the established support vector machine model classifies the two groups of subjects with an accuracy rate of 88.5%. Besides, the clustering coefficient and local efficiency negatively correlate with patients' motor function. This study suggests that the PFC of stroke patients with dyskinesias undergoes specific network reorganization.

Complexity and robustness of weighted circuit network of placement

The research on artificial networks is of great significance for understanding and improving the functionality of the artificial system. In this paper, we study the complexity and robustness of the weighted circuit network of the placement. The result on circuit benchmarks shows that the network behaves as a small-world property of the broad-scale class, and the large-scale circuit tends to be with a strong small-world property. The correlation between network efficiency and circuit scale presents a power-law distribution. The networks represent diverse robustness to different attack strategies due to their inherent characteristics. Especially IS (Initial Strength) attack strategy outperforms ID (Initial Degree) attack strategy for large-scale networks.