Node Clustering Coefficient Research Articles

A financial network perspective of financial institutions’ systemic risk contributions

This study considers the effects of the financial institutions’ local topology structure in the financial network on their systemic risk contribution using data from the Chinese stock market. We first measure the systemic risk contribution with the Conditional Value-at-Risk (CoVaR) which is estimated by applying dynamic conditional correlation multivariate GARCH model (DCC-MVGARCH). Financial networks are constructed from dynamic conditional correlations (DCC) with graph filtering method of minimum spanning trees (MSTs). Then we investigate dynamics of systemic risk contributions of financial institution. Also we study dynamics of financial institution’s local topology structure in the financial network. Finally, we analyze the quantitative relationships between the local topology structure and systemic risk contribution with panel data regression analysis. We find that financial institutions with greater node strength, larger node betweenness centrality, larger node closeness centrality and larger node clustering coefficient tend to be associated with larger systemic risk contributions.

AN EVOLVING NETWORK MODEL OF CREDIT RISK CONTAGION IN THE FINANCIAL MARKET

This paper introduces an evolving network model of credit risk contagion containing the average fitness of credit risk contagion, the risk aversion sentiments, and the ability of resist risk of credit risk holders. We discuss the effects of the aforementioned factors on credit risk contagion in the financial market through a series of theoretical analysis and numerical simulations. We find that, on one hand, the infected path distribution of the network gradually increases with the increase in the average fitness of credit risk contagion and the risk aversion sentiments of nodes, but gradually decreases with the increase in the ability to resist risk of nodes. On the other hand, the average fitness of credit risk contagion and the risk aversion sentiments of nodes increase the average clustering coefficient of nodes, whereas the ability to resist risk of nodes decreases this coefficient. Moreover, network size also decreases the average clustering coefficient.

Link prediction with node clustering coefficient

Predicting missing links in incomplete complex networks efficiently and accurately is still a challenging problem. The recently proposed Cannistrai–Alanis–Ravai (CAR) index shows the power of local link/triangle information in improving link-prediction accuracy. Inspired by the idea of employing local link/triangle information, we propose a new similarity index with more local structure information. In our method, local link/triangle structure information can be conveyed by clustering coefficient of common-neighbors directly. The reason why clustering coefficient has good effectiveness in estimating the contribution of a common-neighbor is that it employs links existing between neighbors of a common-neighbor and these links have the same structural position with the candidate link to this common-neighbor. In our experiments, three estimators: precision, AUP and AUC are used to evaluate the accuracy of link prediction algorithms. Experimental results on ten tested networks drawn from various fields show that our new index is more effective in predicting missing links than CAR index, especially for networks with low correlation between number of common-neighbors and number of links between common-neighbors.

Connectome signatures of neurocognitive abnormalities in euthymic bipolar I disorder

ObjectivesConnectomics have allowed researchers to study integrative patterns of neural connectivity in humans. Yet, it is unclear how connectomics may elucidate structure–function relationships in bipolar I disorder (BPI). Expanding on our previous structural connectome study, here we used an overlapping sample with additional psychometric and fMRI data to relate structural connectome properties to both fMRI signals and cognitive performance. Methods42 subjects completed a neuropsychological (NP) battery covering domains of processing speed, verbal memory, working memory, and cognitive flexibility. 32 subjects also had fMRI data performing a Go/NoGo task. ResultsBipolar participants had lower NP performance across all domains, but only working memory reached statistical significance. In BPI participants, processing speed was significantly associated with both white matter integrity (WMI) in the corpus callosum and interhemispheric network integration. Mediation models further revealed that the relationship between interhemispheric integration and processing speed was mediated by WMI, and processing speed mediated the relationship between WMI and working memory. Bipolar subjects had significantly decreased BA47 activation during NoGo vs. Go. Significant predictors of BA47 fMRI activations during the Go/NoGo task were its nodal path length (left hemisphere) and its nodal clustering coefficient (right hemisphere). ConclusionsThis study suggests that structural connectome changes underlie abnormalities in fMRI activation and cognitive performance in euthymic BPI subjects. Results support that BA47 structural connectome changes may be a trait marker for BPI. Future studies are needed to determine if these “connectome signatures” may also confer a biological risk and/or serve as predictors of relapse.

Structural connectivity abnormality in children with acute mild traumatic brain injury using graph theoretical analysis.

The traumatic biomechanical forces associated with mild traumatic brain injury (mTBI) typically impart diffuse, as opposed to focal, brain injury potentially disrupting the structural connectivity between neural networks. Graph theoretical analysis using diffusion tensor imaging was used to assess injury-related differences in structural connectivity between 23 children (age 11-16 years) with mTBI and 20 age-matched children with isolated orthopedic injuries (OI) scanned within 96 h postinjury. The distribution of hub regions and the associations between alterations in regional network measures and symptom burden, as assessed by the postconcussion symptom scale score (PCSS), were also examined. In comparison to the OI group, the mTBI group was found to have significantly higher small-worldness (P < 0.0001), higher normalized clustering coefficients (P < 0.0001), higher normalized characteristic path length (P = 0.007), higher modularity (P = 0.0005), and lower global efficiency (P < 0.0001). A series of hub regions in the mTBI group were found to have significant alterations in regional network measures including nodal degree, nodal clustering coefficient, and nodal between-ness centrality. Correlation analysis showed that PCSS total score acquired at the time of imaging was significantly associated with the nodal degree of two hubs, the superior frontal gyrus at orbital section and the middle frontal gyrus. These findings provide new evidence of acute white matter alteration at both global and regional network level following mTBI in children furthering our understanding of underlying mechanisms of acute neurological insult associated with mTBI.

The Multiple Facets of Influence

This study compares six metrics commonly used to identify influential players in two of Canada’s largest political Twitter communities based on the users, and ranking order of users, identified by each metric. All tweets containing the hashtag #CPC, representing the Conservative Party of Canada (government), and #NDP, representing the New Democratic Party of Canada (official opposition), were collected over a 2-week period in March 2013 and a follower network graph was created. Social network analysis and content analysis were employed to identify influentials. Kendall’s τ was the primary quantitative measure for comparison. Categorization of Twitter profiles of users found within the top 20 most influential lists, according to each metric of influence, made up the qualitative portion of analysis. The authors find that measures of centrality—indegree and eigenvector centrality—identify the traditional political elite (media outlets, journalists, politicians) as influential, whereas measures considering the quality of messages and interactions provide a different group of influencers, including political commentators and bloggers. Finally, the authors investigate the possibility of using the local clustering coefficient of nodes to identify those who are both aware of the traditional elite and embedded in tightly knit communities, similar to the “opinion leader,” described in the Two-Step Flow Hypothesis.

Altered structural brain connectome in young adult fragile X premutation carriers

Fragile X premutation carriers (fXPC) are characterized by 55-200 CGG trinucleotide repeats in the 5' untranslated region on the Xq27.3 site of the X chromosome. Clinically, they are associated with the fragile X-Associated Tremor/Ataxia Syndrome, a late-onset neurodegenerative disorder with diffuse white matter neuropathology. Here, we conducted first-ever graph theoretical network analyses in fXPCs using 30-direction diffusion-weighted magnetic resonance images acquired from 42 healthy controls aged 18-44 years (HC; 22 male and 20 female) and 46 fXPCs (16 male and 30 female). Globally, we found no differences between the fXPCs and HCs within each gender for all global graph theoretical measures. In male fXPCs, global efficiency was significantly negatively associated with the number of CGG repeats. For nodal measures, significant group differences were found between male fXPCs and male HCs in the right fusiform and the right ventral diencephalon (for nodal efficiency), and in the left hippocampus [for nodal clustering coefficient (CC)]. In female fXPCs, CC in the left superior parietal cortex correlated with counting performance in an enumeration task.

Correlation of the holding behaviour of the holding-based network of Chinese fund management companies based on the node topological characteristics

The data in this paper was collected from the semi-annual reports between 2003 and 2012 which disclosed the Chinese fund management companies' shareholdings in different listed companies. The holdings-based network of Chinese fund management companies is constructed by taking fund management companies as the nodes, the holding of stock of the same listed company at the same period as the edges, and the number of the listed companies holding at the same time as the weight of the edges. Based on the methods such as statistical physics, etc., the stability of the networks at different times is analyzed, and then the correlation of the holding behavior between the nodes with different topological characteristics and three different sets of nodes are calculated and analyzed. Three different sets are the set of nodes in the full graph with a given stock at t-1 (the first type of nodes), the set of nodes in the holing-based network without holding a given stock at t-1 (the second type of nodes), and the set of the new nodes which appear at t (the third type of nodes). The result shows as follows. Firstly, the correlation coefficient of the holding behavior between the node and the second type of nodes rises with the node clustering coefficient increasing; secondly, the node holding behavior is highly correlated with the second type of nodes and with the third type of nodes only when the values of the node average degree and strength are high; finally, the node holding behavior is not related to the third type of nodes at all. This paper propose a new method to study the correlation of stock market, and it is a basis for the further investigation on the structure equivalence network in stock market and also the differences of the importance between the nodes.

Motor Imagery Cognitive Network after Left Ischemic Stroke: Study of the Patients during Mental Rotation Task

Although motor imagery could improve motor rehabilitation, the detailed neural mechanisms of motor imagery cognitive process of stroke patients, particularly from functional network perspective, remain unclear. This study investigated functional brain network properties in each cognitive sub-stage of motor imagery of stroke patients with ischemic lesion in left hemisphere to reveal the impact of stroke on the cognition of motor imagery. Both stroke patients and control subjects participated in mental rotation task, which includes three cognitive sub-stages: visual stimulus perception, mental rotation and response cognitive process. Event-related electroencephalograph was recorded and interdependence between two different cortical areas was assessed by phase synchronization. Both global and nodal properties of functional networks in three sub-stages were statistically analyzed. Phase synchronization of stroke patients significantly reduced in mental rotation sub-stage. Longer characteristic path length and smaller global clustering coefficient of functional network were observed in patients in mental rotation sub-stage which implied the impaired segregation and integration. Larger nodal clustering coefficient and betweenness in contralesional occipitoparietal and frontal area respectively were observed in patients in all sub-stages. In addition, patients also showed smaller betweenness in ipsilesional central-parietal area in response sub-stage. The compensatory effects on local connectedness and centrality indicated the neuroplasticity in contralesional hemisphere. The functional brain networks of stroke patients demonstrated significant alterations and compensatory effects during motor imagery.

Externalities, Transport Networks and the Economic Growth of Urban Clusters

This article uses network analysis tools and new economic geography theory to modify the neo-classical model of regional economic growth, establishes an economic growth model of urban clusters based on externalities and transport networks through a differentiation of transaction costs, and uses the 1990-2008 data of some Chinese cities and the VAR model to test the model. Our empirical study shows that under the influence of transport networks, central cities rely on factor agglomeration for growth, while peripheral cities catch up quickly; that improved transport networks expedite the factor agglomeration of central cities; and that when some newly-added factors are reserved, increasing the node clustering coefficient and reducing peripheral cities’ transport costs will promote these cities’ application of externalities, expedite their economic growth, and facilitate the coordinated growth of central and peripheral cities. Therefore, in building the transport infrastructure, equal emphasis should be placed on linking central cities with peripheral ones and on linking peripheral cities with each other.

Space P-Based Empirical Research on Public Transport Complex Networks in 330 Cities of China

The current empirical studies on public transport network of the cities in China are still limited to several large cities such as Beijing, Shanghai and Guangzhou. And the researches on whether the common topologies of public transport network for cities in different scales do not rely on some extend factors such as population, society or economic, and the researches on the evolutionary mechanisms of public transport network are still limited. This paper studies the public transport networks of 330 cities in China based on the space P concept. Statistical results show that the degree distribution of all networks can be described by an exponential function. It reveals that the evolution mechanism of public transport network is randomly connected instead of preferential attached. All the networks show typical small-world behaviors which characterized by larger clustering coefficient and smaller average shortest path. A transition between the dissortative small networks N<1,000 and assortative large networks N7gt;1,000 is observed. Average clustering coefficient of nodes with degree k decreases with k as a power law, shows that city bus transfer networks are well characterized by hierarchical modularity. The results of this study may provide guidance and reference for researches on evolution mechanism of urban public transport systems and transport network evolution modeling.

Predicting Regional Neurodegeneration from the Healthy Brain Functional Connectome

Neurodegenerative diseases target large-scale neural networks. Four competing mechanistic hypotheses have been proposed to explain network-based disease patterning: nodal stress, transneuronal spread, trophic failure, and shared vulnerability. Here, we used task-free fMRI to derive the healthy intrinsic connectivity patterns seeded by brain regions vulnerable to any of five distinct neurodegenerative diseases. These data enabled us to investigate how intrinsic connectivity in health predicts region-by-region vulnerability to disease. For each illness, specific regions emerged as critical network "epicenters" whose normal connectivity profiles most resembled the disease-associated atrophy pattern. Graph theoretical analyses in healthy subjects revealed that regions with higher total connectional flow and, more consistently, shorter functional paths to the epicenters, showed greater disease-related vulnerability. These findings best fit a transneuronal spread model of network-based vulnerability. Molecular pathological approaches may help clarify what makes each epicenter vulnerable to its targeting disease and how toxic protein species travel between networked brain structures.

The citation networks model with random aging

In citation networks, the age of the articles published plays an important role in deciding the preferential attachment probability of the publishing article. In this article, we consider the aging to be cited of the article decays as (t−ti) −η, where t − ti denotes the time when node i exists in the networks, η is a random variable and denotes the aging decay exponent of the article published. We deduce that the degree distribution of a citation network also shows power-law dependence P(k) ∼ k −γ with exponent γ ≈ 3. At the same time, we study the clustering property of this networks, calculate the clustering coefficient of node i in citation network. We find that the clustering coefficient of node i is larger if its neighbors add into the net earlier. © 2011 Wiley Periodicals, Inc. Complexity, 2012. © 2012 Wiley Periodicals, Inc.

Scale-free property of directed networks with two intrinsic node weights

This paper proposes a network model to understand the scale-free property of directed networks. The proposed model assigns two intrinsic variables (incoming and outgoing weights) to every node. A directed link is established from node i to node j if the sum of the outgoing weight of node i and the incoming weight of node j exceeds a predetermined threshold. The proposed model allows us to know the exact analytical expressions for degree distributions and clustering. We analytically find that the in-degree and out-degree distributions have power-law tails and their scaling exponents are controllable within the range ( 1 , ∞ ) . The average clustering coefficient of nodes with out-degree (or in-degree) n also has a power-law tail as a function of n . We also find that the scaling exponent of the clustering coefficient depends on the correlation between incoming and outgoing weights.

A general geometric growth model for pseudofractal scale-free web

We propose a general geometric growth model for pseudofractal scale-free web (PSW), which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks: degree distribution, second moment of degree distribution, degree correlations, distribution of clustering coefficient, as well as the diameter, which are partially determined by the parameters. Analytical results show that the resulting networks are disassortative and follow power-law degree distributions with a more general degree exponent tuned from 2 to 1 + ln 3 ln 2 ; the clustering coefficient of each individual node is inversely proportional to its degree and the average clustering coefficient of all nodes approaches to a large nonzero value in the infinite network order; the diameter grows logarithmically with the number of network nodes. All these reveal that the networks described by our model have small-world effect and scale-free topology.

Evolution of two properties for scale-free network

Fitness of node can denote its competing power and clustering denotes the transitivity of network. Because the fitness of node is uncertain or fuzzy in some social networks, an explicit form of the degree distribution on fuzzy fitness is derived within a mean field approach. It is a weighted sum of different fuzzy fitness. It can be found that the fuzzy fitness of nodes may lead to multiscaling. Moreover, the clustering coefficient of node decays as power law and clustering coefficient of network behavior not-decrease-but-increase' phenomenon after some time. Some computer simulation results of these models illustrate these analytical results.