Path Length Of Network Research Articles

The development of tumour vascular networks

The growth of solid tumours relies on an ever-increasing supply of oxygen and nutrients that are delivered via vascular networks. Tumour vasculature includes endothelial cell lined angiogenesis and the less common cancer cell lined vasculogenic mimicry (VM). To study and compare the development of vascular networks formed during angiogenesis and VM (represented here by breast cancer and pancreatic cancer cell lines) a number of in vitro assays were utilised. From live cell imaging, we performed a large-scale automated extraction of network parameters and identified properties not previously reported. We show that for both angiogenesis and VM, the characteristic network path length reduces over time; however, only endothelial cells increase network clustering coefficients thus maintaining small-world network properties as they develop. When compared to angiogenesis, the VM network efficiency is improved by decreasing the number of edges and vertices, and also by increasing edge length. Furthermore, our results demonstrate that angiogenic and VM networks appear to display similar properties to road traffic networks and are also subject to the well-known Braess paradox. This quantitative measurement framework opens up new avenues to potentially evaluate the impact of anti-cancer drugs and anti-vascular therapies.

The International Affiliation Network of YouTube Trends

Online video, a ubiquitous, visual, and highly shareable medium, is well-suited to crossing geographic, cultural,and linguistic barriers. Trending videos in particular,by virtue of reaching a large number of viewers in a short span of time, are powerful as both influencers and indicators of international communication flows. In this work, we study a large set of videos trending across 57 nations, collected from YouTube over a7-month period. We consider the set as a network of content flowing between nations, then develop conditional co-affiliation, a nation-nation co-affiliation index that enables a meaningful interpretation of network path length and the application of betweenness centrality. We observe a highly-interlinked network with remarkably similar co-affiliation levels between very different nations.However, Arabic-speaking nations appear more isolated, with the U.A.E. emerging as a key bridge. By analyzing video trend lifespans, we show that nations having many globally-popular video trends are reliably not the nation where those trends are strongest: we see no evidence to support the widely discussed idea of cultural exporter or trendsetter nations. We model correlations between co-affiliation and a selection of contextual factors. We note a surprisingly complex interaction between migration and shared video trends. Consistent with existing work on video popularity, we find that long trending times within one nation do not necessarily translate to reaching a wide global audience. This work expands on previous studies of the geographic popularity of videos by incorporating trending data and extending our analysis from video-nation affiliations to nation-nation co-affiliations. Characterizing these relationships is key to understanding the international cultural impact and potential of online video.

Average path length and degree distribution of networks generated by random sequence

Considering that many real networks do not have strict self-similarity property, compared with deterministic evolutionary fractal networks, networks with random sequence structure may be more in accordance with the properties of real networks. In this paper, we generate a hierarchical network by a random sequence based on BRV model. Using the encoding method, we present a way to judge whether two nodes are neighbors and calculate the total path length of the network. We get the degree distribution and limit formula of the average path length of a class of networks, which are obtained by analytical method and iterative calculation.

Infant functional networks are modulated by state of consciousness and circadian rhythm.

Functional connectivity networks are valuable tools for studying development, cognition, and disease in the infant brain. In adults, such networks are modulated by the state of consciousness and the circadian rhythm; however, it is unknown if infant brain networks exhibit similar variation, given the unique temporal properties of infant sleep and circadian patterning. To address this, we analyzed functional connectivity networks calculated from long-term EEG recordings (average duration 20.8 hr) from 19 healthy infants. Networks were subject specific, as intersubject correlations between weighted adjacency matrices were low. However, within individual subjects, both sleep and wake networks were stable over time, with stronger functional connectivity during sleep than wakefulness. Principal component analysis revealed the presence of two dominant networks; visual sleep scoring confirmed that these corresponded to sleep and wakefulness. Lastly, we found that network strength, degree, clustering coefficient, and path length significantly varied with time of day, when measured in either wakefulness or sleep at the group level. Together, these results suggest that modulation of healthy functional networks occurs over ∼24 hr and is robust and repeatable. Accounting for such temporal periodicities may improve the physiological interpretation and use of functional connectivity analysis to investigate brain function in health and disease.

A Complex Network Approach for Quantitative Characterization and Robustness Analysis of Sandstone Pore Network Structure

The rational characterization and quantitative analysis of the complex internal pore structure of rock is the foundation to solve many underground engineering problems. In this paper, CT imaging technology is used to directly characterize the three-dimensional pore network topology of sandstone with different porosity. Then, in view of the problem, which is difficult to quantify the detailed topological structure of the sandstone pore networks in the previous study, the new complex network theory is used to characterize the pore structure. PageRank algorithm is based on the number of connections between targets as a measure index to rank the targets, so the network degree distribution, average path length, clustering coefficient, and robustness based on PageRank algorithm and permeability-related topological parameters are studied. The research shows that the degree distribution of sandstone pore network satisfies power law distribution, and it can be characterized by scale-free network model. The permeability of rock is inversely proportional to the average path length of sandstone network. The sandstone pore network has strong robustness to random disturbance, while a small number of pores with special topological properties play a key role in the macroscopic permeability of sandstone. This study attempts to provide a new perspective of quantifying the microstructure of the pore network of sandstone and revealing the microscopic structure mechanism of macroscopic permeability of pore rocks.

Distant connectivity and multiple-step priming in large-scale semantic networks.

We examined 3 different network models of representing semantic knowledge (5,018-word directed and undirected step distance networks, and an association-correlation network) to predict lexical priming effects. In Experiment 1, participants made semantic relatedness judgments for word pairs with varying path lengths. Response latencies for judgments followed a quadratic relationship with network path lengths, replicating and extending a recent pattern reported by Kenett, Levi, Anaki, and Faust (2017) for an 800-word association-correlation network in Hebrew. In Experiment 2, participants identified target words in a progressive demasking task, immediately following a briefly presented prime (120 ms). Response latencies to identify the target showed a linear trend for all network path lengths. Importantly, there were statistically significant differences between relatively distant words in the step distance networks, for example, path lengths 4 and beyond, suggesting that association networks can indeed capture distant functional semantic relationships. Additional comparisons with 2 distributional models (LSA and word2vec) suggested that distributional models also successfully predicted response latencies, although there appear to be fundamental differences in the types of semantic relationships captured by the different models. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Inferring evolutionary pathways and directed genotype networks of foodborne pathogens.

Modelling the emergence of foodborne pathogens is a crucial step in the prediction and prevention of disease outbreaks. Unfortunately, the mechanisms that drive the evolution of such continuously adapting pathogens remain poorly understood. Here, we combine molecular genotyping with network science and Bayesian inference to infer directed genotype networks-and trace the emergence and evolutionary paths-of Salmonella Typhimurium (STM) from nine years of Australian disease surveillance data. We construct networks where nodes represent STM strains and directed edges represent evolutionary steps, presenting evidence that the structural (i.e., network-based) features are relevant to understanding the functional (i.e., fitness-based) progression of co-evolving STM strains. This is argued by showing that outbreak severity, i.e., prevalence, correlates to: (i) the network path length to the most prevalent node (r = -0.613, N = 690); and (ii) the network connected-component size (r = 0.739). Moreover, we uncover distinct exploration-exploitation pathways in the genetic space of STM, including a strong evolutionary drive through a transition region. This is examined via the 6,897 distinct evolutionary paths in the directed network, where we observe a dominant 66% of these paths decrease in network centrality, whilst increasing in prevalence. Furthermore, 72.4% of all paths originate in the transition region, with 64% of those following the dominant direction. Further, we find that the length of an evolutionary path strongly correlates to its increase in prevalence (r = 0.497). Combined, these findings indicate that longer evolutionary paths result in genetically rare and virulent strains, which mostly evolve from a single transition point. Our results not only validate our widely-applicable approach for inferring directed genotype networks from data, but also provide a unique insight into the elusive functional and structural drivers of STM bacteria.

Changing structures of B2B networks in the Japanese textile and apparel industry

The aim of the present study was to evaluate how the business-to-business (B2B) networks in the Japanese textile and apparel industry changed between 2005 and 2010 using data on 200 companies. Network analysis was used to study the properties of the B2B networks, and how their structures changed was characterized using the USD/JPY exchange rate. The network analysis revealed power-law properties of the B2B networks, and the core networks characterized by the largest degree centrality exhibited positive correlations with the USD/JPY exchange rate. By contrast, the peripheral networks characterized by the network path length exhibited the negative correlations with the exchange rate USD/JPY. Therefore, the changes that occurred in the B2B networks are explained as the complementarity of comparative advantages originating in the USD/JPY exchange rate. Moreover, the USD/JPY exchange rate affected the B2B networks through not only the complementarity of importing and exporting but also by changing the structures.

Quantitative Controllability Analysis of IEEE Power Network

The previous research on the controllability of complex networks is qualitative issue which can only identify whether the network is controllable or not, and it is difficult to assess the controlled ability of network. In this paper, a quantitative measurement index of network controllability is introduced. And the index is used to study the controllability of the IEEE power network system. The relationship between controllability and network parameters (including the average degree, the clustering coefficient, the average path length) of power network is analyzed by comparing with the ER random network, WS small world network, BA scale-free network and CM network. The results show that the power networks have a small average path length and a higher clustering coefficient, which belong to the small world network. And, the controllability of power networks is larger than the corresponding model networks, indicating that power networks are relatively easier to be controlled.

Sizing complex networks

Among the many features of natural and man-made complex networks the small-world phenomenon is a relevant and popular one. But, how small is a small-world network and how does it compare to others? Despite its importance, a reliable and comparable quantification of the average pathlength of networks has remained an open challenge over the years. Here, we uncover the upper (ultra-long (UL)) and the lower (ultra-short (US)) limits for the pathlength and efficiency of networks. These results allow us to frame their length under a natural reference and to provide a synoptic representation, without the need to rely on the choice for a null-model (e.g., random graphs or ring lattices). Application to empirical examples of three categories (neural, social and transportation) shows that, while most real networks display a pathlength comparable to that of random graphs, when contrasted against the boundaries, only the cortical connectomes prove to be ultra-short.

Altered brain structural topological properties in Parkinson's disease with levodopa-induced dyskinesias

ObjectivesIn this study, the alterations of structural topological properties in Parkinson's disease (PD) patients with levodopa-induced dyskinesias (LIDs) were explored using white matter structural network connectome derived from diffusion tensor imaging (DTI). Methods21 dyskinetic PD patients, 21 non-dyskinetic PD patients and 25 healthy controls were studied in global and nodal topological properties of structural networks after controlling age, gender and education. Afterwards, post hoc analyses were performed to explore further differences. Finally, multiple linear regression analysis was employed to test the associations between significant different properties and the severity of dyskinesias in PD. ResultsDyskinetic PD patients exhibited significant increased global efficiency, local efficiency, clustering coefficient, but decreased shortest path length compared with the non-dyskinetic. Additionally, increased nodal efficiency in bilateral inferior frontal gyrus (IFG), right putamen, right thalamus, and decreased nodal shortest path length in bilateral IFG and right thalamus, were discovered in dyskinetic PD in comparison with non-dyskinetic PD. Notably, a negative correlation between the Abnormal Involuntary Movement Scale (AIMS) scores and shortest path length of whole-brain network was found in PD with LIDs. ConclusionsOur results indicated excessively optimized topological organization of whole-brain structural connectome in PD patients with LIDs. These findings also illustrated that excessively strengthened basal ganglia-thalamocortical nodal structural connections played an important role in the presence of LIDs.

Strong-Weak Pruning for Brain Network Identification in Connectome-Wide Neuroimaging: Application to Amyotrophic Lateral Sclerosis Disease Stage Characterization.

Magnetic resonance imaging allows acquiring functional and structural connectivity data from which high-density whole-brain networks can be derived to carry out connectome-wide analyses in normal and clinical populations. Graph theory has been widely applied to investigate the modular structure of brain connections by using centrality measures to identify the "hub" of human connectomes, and community detection methods to delineate subnetworks associated with diverse cognitive and sensorimotor functions. These analyses typically rely on a preprocessing step (pruning) to reduce computational complexity and remove the weakest edges that are most likely affected by experimental noise. However, weak links may contain relevant information about brain connectivity, therefore, the identification of the optimal trade-off between retained and discarded edges is a subject of active research. We introduce a pruning algorithm to identify edges that carry the highest information content. The algorithm selects both strong edges (i.e. edges belonging to shortest paths) and weak edges that are topologically relevant in weakly connected subnetworks. The newly developed "strong-weak" pruning (SWP) algorithm was validated on simulated networks that mimic the structure of human brain networks. It was then applied for the analysis of a real dataset of subjects affected by amyotrophic lateral sclerosis (ALS), both at the early (ALS2) and late (ALS3) stage of the disease, and of healthy control subjects. SWP preprocessing allowed identifying statistically significant differences in the path length of networks between patients and healthy subjects. ALS patients showed a decrease of connectivity between frontal cortex to temporal cortex and parietal cortex and between temporal and occipital cortex. Moreover, degree of centrality measures revealed significantly different hub and centrality scores between patient subgroups. These findings suggest a widespread alteration of network topology in ALS associated with disease progression.

Structure properties of collaboration network with tunable clustering

A collaboration network model with improved triad formation (ITF) step is proposed and denominated as one-mode collaboration network with tunable clustering. We systematically study its structural features and find this network model can much more accurately reflect cooperative relationship in real society. We acquire expression of nodes degree distribution P(k) that possesses a power-law form with exponent γ whose range is (1,3]. Expression of clustering coefficient C(k) for nodes with degree k is also obtained and composes of a power-law section and a constant section. We verify clustering coefficient of individual nodes increases monotonically with the increase of parameter p that is the probability of ITF step occurring. When specific forms of P(k) and C(k) are given, the model’s average clustering coefficient C can be derived approximately. Finally, we analytically testify average path length L(N) increases with network size N in accordance with logarithmic form. When N is fixed, average path length of entire network decreases with the increase of p. All theoretically predicted results are consistent with simulative experimental results.

Early recovery of interhemispheric functional connectivity after corpus callosotomy.

To investigate whether interhemispheric functional connectivity (FC) recovers in the first year after total callosotomy. Eight epilepsy patients undergoing total callosotomy were recruited. Resting-state functional magnetic resonance imaging was acquired before and after surgery. The precallosotomy and postcallosotomy interhemispheric and intrahemispheric FC was analyzed by using graph theory and voxel-mirrored homotopic connectivity (VMHC). The seizure outcome was scored using the Engel surgical outcome scale. After callosotomy (mean postoperative interval = 4months), the network density, average node degree, characteristic path length, and global efficiency of the whole interhemispheric networks were significantly decreased, compared to those in the precallosotomy networks. However, postcallosotomy interhemispheric FC and homotopic VMHC were not significantly reduced in bilateral frontal and temporal lobes. The network density and average node degree of the intrahemispheric networks were significantly increased. The characteristic path length and global efficiency of intrahemispheric networks were unchanged. The interhemispheric FC may be preserved or recover early within the first postoperative year after total callosotomy, particularly in the frontal and anterior temporal lobes.

Heterogeneity of Networks Promotes Cooperation in the Prisoner’s Dilemma and the Snowdrift Game

Complex networks are ubiquitous in real-world systems. In the last decade, the investigation of complex networks has received much attention. Most of this research suggests that the topological properties of networks have an important influence on the evolution of cooperation. In this paper, we used the prisoner’s dilemma game and snowdrift game as models to study the problem of cooperation evolution on heterogeneous random networks. We found that the heterogeneity of the networks plays a more important role in promoting cooperation than the average clustering coefficient and average path length of the networks do. The higher the heterogeneity of the networks is, the more conducive the emergence and spread of cooperation is. In addition, we found that increasing the average degree of networks would be detrimental for cooperation to thrive.

Reliability evaluation on weighted graph metrics of fNIRS brain networks.

Resting-state fNIRS (R-fNIRS) imaging data has proven to be a valuable technique to quantitatively characterize functional architectures of human brain network. However, whether the brain network metrics derived using weighted brain network model is test-retest (TRT) reliable remains largely unknown. Here, we firstly constructed weighted brain networks on a group of 18 participants, and then applied graph-theory approach to quantify topological parameters of each weighted network. The intraclass correlation coefficient (ICC) was further applied to quantify the TRT reliability of network metrics. We found that the reliability of the weighted network metrics is threshold-sensitive, and most of these network metrics showed fair to excellent reliability. Specifically, the global network metrics, e.g., clustering coefficient, path length, local efficiency and global efficiency were of excellent level reliability (ICC >0.75) on both HbO and HbR signals. The nodal network metrics, e.g., degree and efficiency, generally also showed excellent level reliability on both HbO and HbR signals, and the reliability of these two metrics was better than that of nodal betweenness. Overall, these findings demonstrated that most weighted network metrics derived from fNIRS are TRT reliable and can be used for brain network research.

Cascading failures with coupled map lattices on Watts–Strogatz networks

In this paper, we present a cascading failure model based on coupled map lattices, in which a given number of crucial nodes are perturbed at the same time. By comparing the effect of five attacking strategies: random strategy, high-degree strategy, high-clustering coefficient strategy, high-betweenness strategy and high-closeness strategy (HCS) on Watts–Strogatz (WS) small-world networks, we found that HCS outperforms the other attacking strategies with different number of perturbed nodes. The efficiency of HCS on WS small-world networks is explored extensively. The results show that increasing the rewiring probability can reduce the range of cascading failures, but it will enhance the propagation speed of cascades. Furthermore, a more compact network structure will lead to a faster cascading failure propagation speed, and the propagation speed of cascades is inversely proportional to the characteristic path length of WS small-world networks. Our work will highlight a better understanding of cascading failures on complex networks.

Urban Transit Network Properties Evaluation and Optimization Based on Complex Network Theory

Urban public transportation contributes greatly to sustainable urban development. An urban public transportation network is a complex system. It is meaningful for theory and practice to analyze the topological structure of an urban public transportation network and explore the spatial structure of an urban transportation network so as to mitigate and prevent traffic congestion and achieve sustainability. By examining the Xi’an bus network, the degree distribution, average path length, aggregation coefficient, and betweenness centrality of the bus station network were computed using models in complex network theory. The results show that the node degrees of the Xi’an bus network are unevenly distributed and present a polarization diagram with long average path length and high aggregation. A model based on betweenness and its solution method was developed to improve the public transportation network’s sustainability and discuss the possibility of optimizing the sustainability by network analyzing methods.

Adaptive rewiring in weighted networks

Human connectome studies suggest that the brain has a modular small world network structure with rich-club effect. Such structure emerges spontaneously in simple model neural networks, (e.g. coupled maps), through adaptive rewiring according to the dynamic functional connectivity. The utility of adaptive rewiring has so far exclusively been demonstrated for unweighted networks; it is anything but guaranteed to work as well for weighted networks. We investigate adaptive rewiring in weighted networks, comparing various right-skewed, symmetrical, and left-skewed fixed weight distributions. We examine how network clustering, path length, modularity, and rich club coefficients develop for weakly, intermediate and strongly coupled networks. At low coupling strength, the weight distribution, as well as episodes of functional synchrony, have a significant effect on network evolution. With increased coupling strengths, all weighted networks robustly develop architectures similar to the unweighted ones. Adaptive rewiring appears relatively ineffective in networks with (biologically implausibly) extreme right-skewed weight distributions but performed most economically in biologically plausible log-normal distributions.

Dynamic Analysis for the Average Shortest Path Length of Mobile Ad Hoc Networks Under Random Failure Scenarios

In general, the mobile ad hoc networks (MANETs) are built on the basis of the random distribution of the nodes, while the nodes of real networks usually have the characteristics of location preference choice. The evolving network model based on local-area choice is proposed for MANET based on the complex network theory. The proposed model of the topology not only considers the scale-free nature of the network and the actual mobility of MANET but also considers the consumption of the node energy. Random failures often occur in MANET. Most of the existing research focuses on the changes in network topology caused by random node failures. In order to describe the impact of random edge failures on the topology of MANET, we focus on the average shortest path length (ASPL) which is an important feature of the network topology and propose the formula for calculating the ASPL of the MANET after the random edge failure. The experimental simulation analyzes the change of the ASPL of MANET in the random failure scenario (after random edge deletion). By comparing with the actual scene results, the proposed estimation formula which describes this change more accurately is proved. The formula proposed in this paper provides a general framework for studying the shortest path of MANET.