Average Shortest Path Length Research Articles

Network Structure of the Master Clock Is Important for Its Primary Function.

A master clock located in the suprachiasmatic nucleus (SCN) regulates the circadian rhythm of physiological and behavioral activities in mammals. The SCN has two main functions in the regulation: an endogenous clock produces the endogenous rhythmic signal in body rhythms, and a calibrator synchronizes the body rhythms to the external light-dark cycle. These two functions have been determined to depend on either the dynamic behaviors of individual neurons or the whole SCN neuronal network. In this review, we first introduce possible network structures for the SCN, as revealed by time series analysis from real experimental data. It was found that the SCN network is heterogeneous and sparse, that is, the average shortest path length is very short, some nodes are hubs with large node degrees but most nodes have small node degrees, and the average node degree of the network is small. Secondly, the effects of the SCN network structure on the SCN function are reviewed based on mathematical models of the SCN network. It was found that robust rhythms with large amplitudes, a high synchronization between SCN neurons and a large entrainment ability exists mainly in small-world and scale-free type networks, but not other types. We conclude that the SCN most probably is an efficient small-world type or scale-free type network, which drives SCN function.

한국어 단어들의 음절 기반 음운이웃 네트워크

This study analyzed the syllable-based phonological neighborhood networks (PNNs) of Korean words. The network-theoretic representation of the lexicon has provided new insights on cross-linguistic and language particular factors in the composition of the phonological lexicon (Vitevitch, 2008; Shoemark et al., 2016, among others). This study draws from the literature the notion of phonological similarity as a network feature, but, unlike previous phonemic approaches, it assumes syllables as the unit of phonological similarity (Mehler et al., 1981; Kwon et al., 2006, 2011). We collected 83,881 polysyllabic words from a Korean corpus. According to the various network measurements on them, the syllable-based PNNs were similar to conventional phonemic-based PNNs in satisfying requirements for small-world networks, being influenced by the lexicon size and having a high value of assortativity by degree. However, they also showed different characteristics from phoneme-based PNNs: syllable-based PNNs had larger giant clusters, average degrees, and cluster coefficients, and they showed smaller values of the average shortest path length. The insights from the PNN analysis are significant since they can help answer empirical questions of phonological word processing and word acquisition.

The interaction of acidophiles driving community functional responses to the re-inoculated chalcopyrite bioleaching process

Re-inoculation was an effective way to improve bioleaching efficiency by enhancing the synergetic effects of biogenic Fe3+ coupling with S0 oxidation. However, the complex microbial interactions after re-inoculation have received far less attention, which was crucial to the bioleaching performances. Herein, the enriched ferrous oxidizers (FeO) or sulfur oxidizers (SO) were inoculated to chalcopyrite microcosm, then they were crossly re-inoculated again to characterize the interspecific interaction patterns. The results showed that the dominant species in Fe groups were Acidithiobacillus ferrooxidans, while A. thiooxidans predominated in S groups. Introducing FeO resulted in a great disturbance by shifting the community diversity and evenness significantly (p < 0.05). In comparison, the communities intensified by SO maintained the original composition and structures. Microbial networks were constructed positively and modularly. The networks intensified by FeO were less connected and complex with less nodes and edges, but showed faster responses to the re-inoculation disturbance reflected by shorter average path length. Interestingly, the genus Leptospirillum were identified as keystones in S groups, playing critical roles in iron-oxidizing with lots of sulfur oxidizers. The introduced sulfur oxidizers enhanced microbial cooperation, formed robust community with strong bio-dissolution capability, and harbored the highest bioleaching efficiency. These findings improved our understanding about the acidophiles interactions, which drive community functional responses to the re-inoculated bioleaching process.

Topological measures for identifying and predicting the spread of complex contagions

The standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.

Identification of focal epileptic regions from electroencephalographic data: Feigenbaum graphs

In the study of problems related to epilepsy analyzing electroencephalograms data is of much importance to help, one hand, to its diagnosis, and, another hand in the possibility of diminishing errors in surgery. We do this analysis making the Feigenbaum graphs for real electroencephalographic signals data sets and calculating characteristic networks (graph) quantities, such as average clustering, degree distribution, and average shortest path length. We manage to characterize two different data sets from each other, from data sets corresponding to focal and non-focal neuronal activity both time out of an epileptic seizure. This method enables us to identify sets of data from epileptic focal zones and suggest our approach could be used to aid physicians with diagnosing epilepsy from electroencephalographic data and/or in an exact establishment of the epileptic focal region for surgery.

Graph optimization algorithm for low-latency interconnection networks

In various industrial products including parallel computing systems, it is expected that the performance of the whole system will be improved by applying a network topology with smaller diameter and average shortest path length (ASPL). Such network topologies can be defined as the order/degree problem in graph theory by modeling a network topology as an undirected graph. Although previous research indicates that the random graph has both small diameter and ASPL due to the small-world effect, there is still room for improvement. In this paper, we propose an algorithm for the order/degree problem that optimizes random graphs. The feature of the proposed algorithm is that by giving symmetry to the graph, the solution search performance is improved and the calculation time for obtaining the diameter and APSL is greatly reduced. The proposed algorithm is evaluated using various graphs, including a huge graph with one million vertices presented by Graph Golf, an international competition for the order/degree problem. The results show that the proposed algorithm can generate a network topology with sufficiently small diameter and APSL. In addition, we also simulate the latency, performance of the parallel benchmarks, and bisection on the generated network topologies. The results show that the generated network topology performs better than the random topology and a conventional k-ary n-cube topology.

Analysis of Network Robustness in Weighted and Unweighted Approaches: A Case Study of the Air Transport Network in the Belt and Road Region

Aviation transport is one of the most important and critical infrastructures in today’s global economy. Failure in its proper operations can seriously impact regional economic development, which is why it is important to evaluate network robustness. Previous analyses of robustness have mainly been conducted with an unweighted approach. In the development of air transport, however, the demand for route configuration has gradually decreased, while the demand for flight adjustments has increased. Consequently, the aviation network has developed unevenly, so adhering to a uniform approach for evaluating network robustness may lead to inaccurate results. Therefore, we examined which centrality sequence is the most sensitive to network robustness in both unweighted and weighted approaches. The air transport network selected for the case study comprised the six subregions of the Eurasian landmass of the Belt and Road region. The study results showed the following: (a) in the network constructed as an unweighted one, betweenness, and degree centrality had higher priorities in preserving network functionalities than eigenvector and closeness centrality; (b) in the network constructed as a weighted one, recursive power had a higher priority in preserving network functionalities than recursive centrality; and (c) no particular centrality measurement had a significant advantage in representing the totality of robustness. The betweenness centrality sequence was sensitive to the average shortest path length and global efficiency; the recursive power sequence was sensitive to the clustering coefficient, while degree centrality was sensitive to graph diversity. The findings of this study support the decisions about managing air transportation in the Belt and Road region.

Structural Differences of the Semantic Network in Adolescents with Intellectual Disability

The semantic network structure is a core aspect of the mental lexicon and is, therefore, a key to understanding language development processes. This study investigated the structure of the semantic network of adolescents with intellectual disability (ID) and children with typical development (TD) using network analysis. The semantic networks of the participants (nID = 66; nTD = 49) were estimated from the semantic verbal fluency task with the pathfinder method. The groups were matched on the number of produced words. The average shortest path length (ASPL), the clustering coefficient (CC), and the network’s modularity (Q) of the two groups were compared. A significantly smaller ASPL and Q and a significantly higher CC were found for the adolescents with ID in comparison with the children with TD. Reasons for this might be differences in the language environment and differences in cognitive skills. The quality and quantity of the language input might differ for adolescents with ID due to differences in school curricula and because persons with ID tend to engage in different out-of-school activities compared to TD peers. Future studies should investigate the influence of different language environments on the language development of persons with ID.

OPTWEB: A Lightweight Fully Connected Inter-FPGA Network for Efficient Collectives

Modern FPGA accelerators can be equipped with many high-bandwidth network I/Os, e.g., 64 x 50 Gbps, enabled by onboard optics or co-packaged optics. Some dozens of tightly coupled FPGA accelerators form an emerging computing platform for distributed data processing. However, a conventional indirect packet network using Ethernet's Intellectual Properties imposes an unacceptably large amount of the logic for handling such high-bandwidth interconnects on an FPGA. Besides the indirect network, another approach builds a direct packet network. Existing direct inter-FPGA networks have a low-radix network topology, e.g., 2-D torus. However, the low-radix network has the disadvantage of a large diameter and large average shortest path length that increases the latency of collectives. To mitigate both problems, we propose a lightweight, fully connected inter-FPGA network called OPTWEB for efficient collectives. Since all end-to-end separate communication paths are statically established using onboard optics, raw block data can be transferred with simple link-level synchronization. Once each source FPGA assigns a communication stream to a path by its internal switch logic between memory-mapped and stream interfaces for remote direct memory access (RDMA), a one-hop transfer is provided. Since each FPGA performs input/output of the remote memory access between all FPGAs simultaneously, multiple RDMAs efficiently form collectives. The OPTWEB network provides 0.71-μsec start-up latency of collectives among multiple Intel Stratix 10 MX FPGA cards with onboard optics. The OPTWEB network consumes 31.4 and 57.7 percent of adaptive logic modules for aggregate 400-Gbps and 800-Gbps interconnects on a custom Stratix 10 MX 2100 FPGA, respectively. The OPTWEB network reduces by 40 percent the cost compared to a conventional packet network.

Characterization and influencing factors of the pig movement network in Hunan Province, China

In terms of pig production in China, Hunan was the third largest province where the number of hogs accounted for 9.0 % of the national number of hogs in 2017. To propose the precise strategy for supervision of pig movements in Hunan Province, a weighted directed one-mode network was constructed using the data from the electronic animal health certificate platform in 2017. The nodes were designed as districts in Hunan and edges as flows of pig movement between districts. Social network analysis was used to analyse network characteristics and generalized linear models were performed to ascertain the socioeconomic factors that affect the pig movement network. During 2017, the pig movement network within the Hunan Province was composed of 122 nodes and 8562 directed connections, with a total of 510,973 shipments and 17,815,040 pigs moved. The network displayed a small-world topology, which had a higher clustering coefficient (0.4 vs. 0.1) and shorter average shortest path length (1.8 vs. 3.7) compared with equivalent random networks. The degree centrality positively correlated with closeness centrality (r = 0.99, P < 0.001) as well as betweenness centrality (r = 0.91, P < 0.001). After restricting the cross-regional pig movements in areas with the top 10 % of degree centrality, the number of pigs was reduced by nearly 50 % in the network, whereas the number of pigs was reduced by 94.0 % when movement restrictions were implemented in areas with the top 50 % of degree centrality. Observed network metrics showed an upward trend during the months of 2017, peaking in November and December. Generalized linear models showed that the size of the human population and per capita gross domestic product were the most important socioeconomic drivers of pig movements. The pig movement network in Hunan Province is a small-world network in which the introduction and spread of diseases may be quicker. More human, material, and financial resources should be allocated to areas with higher centrality. Swine movements were seasonal, and the inspection and quarantine work should be reinforced in the fourth quarter, especially in November and December. Pig movements were more active in areas with larger populations and advanced economy, and stricter supervision in these areas should be implemented. Our findings contribute to understanding the movement of pigs and the associated influencing factors in a big pig producing province in China, and the supervision strategies proposed in this study can be extended to other regions in China if proved to be viable.

Hunting for vital nodes in complex networks using local information

Complex networks in the real world are often with heterogeneous degree distributions. The structure and function of nodes can vary significantly, with vital nodes playing a crucial role in information spread and other spreading phenomena. Identifying and taking action on vital nodes enables change to the network’s structure and function more efficiently. Previous work either redefines metrics used to measure the nodes’ importance or focuses on developing algorithms to efficiently find vital nodes. These approaches typically rely on global knowledge of the network and assume that the structure of the network does not change over time, both of which are difficult to achieve in the real world. In this paper, we propose a localized strategy that can find vital nodes without global knowledge of the network. Our joint nomination (JN) strategy selects a random set of nodes along with a set of nodes connected to those nodes, and together they nominate the vital node set. Experiments are conducted on 12 network datasets that include synthetic and real-world networks, and undirected and directed networks. Results show that average degree of the identified node set is about 3–8 times higher than that of the full node set, and higher-degree nodes take larger proportions in the degree distribution of the identified vital node set. Removal of vital nodes increases the average shortest path length by 20–70% over the original network, or about 8–15% longer than the other decentralized strategies. Immunization based on JN is more efficient than other strategies, consuming around 12–40% less immunization resources to raise the epidemic threshold to tau sim 0.1. Susceptible-infected-recovered simulations on networks with 30% vital nodes removed using JN delays the arrival time of infection peak significantly and reduce the total infection scale to 15%. The proposed strategy can effectively identify vital nodes using only local information and is feasible to implement in the real world to cope with time-critical scenarios such as the sudden outbreak of COVID-19.

Pathway-based protein-protein association network to explore mechanism of α-glucosidase inhibitors from Scutellaria baicalensis Georgi against type 2 diabetes.

Natural products have been widely used in the treatment of type 2 diabetes (T2D). However, their mechanisms are often obscured due to multi‐components and multi‐targets. The authors constructed a pathway‐based protein–protein association (PPA) network for target proteins of 13 α‐glucosidase inhibitors (AGIs) identified from Scutellaria baicalensis Georgi (SBG), designed to explore the underlying mechanisms. This network contained 118 nodes and 1167 connections. An uneven degree distribution and small‐world property were observed, characterised by high clustering coefficient and short average path length. The PPA network had an inherent hierarchy as C(k)∼k −0.71. It also exhibited potential weak disassortative mixing pattern, coupled with a decreased function Knn (k) and negative value of assortativity coefficient. These properties indicated that a few nodes were crucial to the network. PGH2, GNAS, MAPK1, MAPK3, PRKCA, and MAOA were then identified as key targets with the highest degree values and centrality indices. Additionally, a core subnetwork showed that chrysin, 5,8,2′‐trihydroxy‐7‐methoxyflavone, and wogonin were the main active constituents of these AGIs, and that the serotonergic synapse pathway was the critical pathway for SBG against T2D. The application of a pathway‐based protein–protein association network provides a novel strategy to explore the mechanisms of natural products on complex diseases.

Robustness evaluation for real traffic network from complex network perspective

Robustness is a critical characteristic of ubiquitous real networked systems which are often very vulnerable to the random failures or targeted attacks. In this work, we aim to evaluate the robustness of a traffic network which is constructed from real trajectory data. First, we divide a city into grids which are considered as nodes and a link is established if there is at least one taxi dispatch order from one grid to another. Second, we propose two categories of attack strategies: node attacks (e.g. random node failure, and degree, in-degree, out-degree, closeness, clustering coefficient, PageRank-based targeted attacks) and link attacks (e.g. random link failure and link weight, link degree, link betweenness-based targeted attacks). Third, we suppose all elements (i.e. node or link) are simultaneously or iteratively removed, and evaluate the network robustness by employing the relative size of the giant components, average clustering coefficient and average shortest path length. The results show that the degree-based targeted attacks are the most destructive among all attacks, and no matter node or link, the betweenness-based attack is the most effective method to be beneficial to the target index. Moreover, most methods with recalculations take priority over the ones without recalculations.

A longitudinal study into the effects of material incentives on knowledge-sharing networks and information lifecycles in an online forum

ABSTRACT The purpose of this study is to examine the effect of material incentives on the knowledge-sharing networks and information lifecycles of a public online forum. The users’ interaction data were collected from two similar sub-forums, and one of them provided material incentives for sharing knowledge. After collecting user behaviors for one natural year, the interaction data from 18,079 main posts and 326,024 replies were coded using social network analysis. Results showed that both sub-forums have significant small-world effects, but the effect is more obvious in the incentive intervention, with higher density, larger network cohesion, shorter average path length, and larger power-law index. Also, the material incentives made the whole interactive network more connected, with less isolated clusters. According to the K-core analysis, marginal users in the incentive intervention relied less on core users and had been motivated toward the network center. However, the information lifecycle for both conditions was about 46 days, with no significant difference. These findings indicated that the material incentives have a significant spatial effect that helps widening knowledge-sharing scopes and deepening the interaction, while it has limited time-line effects on prolonging knowledge-sharing sustainability.

Exploring the conformational dynamics and flexibility of intrinsically disordered HIV-1 Nef protein using molecular dynamic network approaches.

The online version contains supplementary material available at 10.1007/s13205-021-02698-8.

Bypass Schemes of Urban Transit Station Based on Complex Network Theory

To study detour scheme after failure of urban transit station, urban transit network model is constructed by considering the reciprocal of urban transit line departure time interval as the weight. In accordance with the characteristics of the traffic flow, the network is studied under different time intervals, namely, morning, evening, and flat rush hours. First, an urban transit network topological characteristic index analysis model was constructed by combining ABC management method to identify the key elements of each indicator. Second, on the basis of the research on topological characteristic indicators, average path length and global efficiency of the network were used to measure the urban transit network connectivity, and an urban transit network station failure optimization scheme was designed. The optimization effect was judged by the changes in the two index values before and after the bus stop detour in accordance with the number of stations in the bypass area, namely, two stations, one station, and zero stations. Finally, the reliability of the model is studied, considering the urban transit network in Huangdao District of Qingdao. Through the analysis of node degree, second-order node degree, centrality, and other indicators, the urban transit network in Huangdao District of Qingdao was found to have evident small-world characteristics, and the top ranking stations of node degree value and centrality index are mainly distributed in the new urban edge planning area and the urban center area. In addition, for stations with the same rank, the node centrality value at each time interval has the following order: morning rush hours> evening rush hours> flat rush hours. The top 10 urban transit stations with node degree value are selected as the failure stations for optimization analysis. Results show that the average shortest path length of the optimized network decreases, the global efficiency of the network increases, and the optimized scheme is reliable.

Global Network Organization of the Fetal Functional Connectome.

Recent advances in brain imaging have enabled non-invasive in vivo assessment of the fetal brain. Characterizing brain development in healthy fetuses provides baseline measures for identifying deviations in brain function in high-risk clinical groups. We examined 110 resting state MRI data sets from fetuses at 19 to 40weeks' gestation. Using graph-theoretic techniques, we characterized global organizational features of the fetal functional connectome and their prenatal trajectories. Topological features related to network integration (i.e., global efficiency) and segregation (i.e., clustering) were assessed. Fetal networks exhibited small-world topology, showing high clustering and short average path length relative to reference networks. Likewise, fetal networks' quantitative small world indices met criteria for small-worldness (σ > 1, ω = [-0.5 0.5]). Along with this, fetal networks demonstrated global and local efficiency, economy, and modularity. A right-tailed degree distribution, suggesting the presence of central areas that are more highly connected to other regions, was also observed. Metrics, however, were not static during gestation; measures associated with segregation-local efficiency and modularity-decreased with advancing gestational age. Altogether, these suggest that the neural circuitry underpinning the brain's ability to segregate and integrate information exists as early as the late 2nd trimester of pregnancy and reorganizes during the prenatal period. Significance statement. Mounting evidence for the fetal origins of some neurodevelopmental disorders underscores the importance of identifying features of healthy fetal brain functional development. Alterations in prenatal brain connectomics may serve as early markers for identifying fetal-onset neurodevelopmental disorders, which in turn provide improved surveillance of at-risk fetuses and support the initiation of early interventions.

Public goods games on random hyperbolic graphs with mixing

Understanding the evolution of cooperation in structured populations remains one of the fundamental challenges of the 21st century, with far-reaching implications for the wellbeing of modern human societies. Studies over the past two decades showed that the structure of the network of contacts plays a crucial role in determining whether cooperation prevails or not. An important step to more realistic networks was made with the shift from regular grids and lattices to complex social networks at the turn of the century. Real networks exhibit a high mean local clustering coefficient, short average path lengths, and community structure. Recent studies have revealed that random geometric graphs in hyperbolic spaces exhibit properties that are frequently found in real networks. We here study the public goods game on random geometric graphs in hyperbolic spaces, and we consider assortative and disassortative mixing with different frequencies. We show that in hyperbolic spaces heterogeneous networks promote the evolution of public cooperation in comparison to the more homogeneous networks. We also confirm that assortative and disassortative mixing on random hyperbolic networks both impair the evolutionary success of cooperators, regardless of the network architecture. The differences between the two mixing protocols are most expressed at low mixing frequencies, whilst at high mixing frequencies the two almost converge.

Effects of COVID-19 on Urban Population Flow in China.

The COVID-19 epidemic has become a Public Health Emergency of International Concern. Thus, this sudden health incident has brought great risk and pressure to the city with dense population flow. A deep understanding of the migration characteristics and laws of the urban population in China will play a very positive role in the prevention and control of the epidemic situation. Based on Baidu location-based service (LBS) big data, using complex networks method and geographic visualization tools, this paper explores the spatial structure evolution of population flow network (PFN) in 368 cities of China under different traffic control situations. Effective distance models and linear regression models were established to analyze how the population flow across cities affects the spread of the epidemic. Our findings show that: (1) the scope of population flow is closely related to the administrative level of the city and the traffic control policies in various cities which adjust with the epidemic situation; The PFN mainly presents the hierarchical structure dominated by the urban hierarchy and the regional isolation structure adjacent to the geographical location.(2) through the analysis network topology structure of PFN, it is found that only the first stage has a large clustering coefficient and a relatively short average path length, which conforms to the characteristics of small world network. The epidemic situation has a great impact on the network topology in other stages, and the network structure tends to be centralized. (3) The overall migration scale of the whole country decreased by 36.85% compared with the same period of last year’s lunar calendar, and a further reduction of 78.52% in the nationwide traffic control stage after the festival. (4) Finally, based on the comparison of the effective distance and the spatial distance from the Wuhan to other destination cities, it is demonstrated that there is a higher correlation between the effective distance and the epidemic spread both in Hubei province and the whole country.

Small world and stability analysis of industrial coupling symbiosis network of ecological industrial park of oil and gas resource cities

This paper analyzes the small cosmopolitan and stability of the industrial coupling symbiotic network of eco-industrial parks of oil and gas resource-based cities. Taking Daqing A Ecological Industrial Park as an example, we constructed the characteristic index system and calculated the topological parameters such as the agglomeration coefficient and the average shortest path length of the industrial coupling symbiotic network. Based on the complex network theory we analyzed the characteristics of the scaled world, constructed the adjacency matrix of material and information transfers between enterprises, drew the network topology diagram. We simulated the system analysis and analyzed the stability of the industrial coupling symbiotic network of the eco-industrial park using the network efficiency and node load and maximum connected subgraph. The analysis results are as follows: the small world degree δ of Daqing A Eco-industrial Park is 0.891, which indicates that the industrial coupled symbiotic network has strong small world characteristics; the average path is 1.268, and the agglomeration coefficient is 0.631. The probability of edge connection between two nodes in a symbiotic network is 63.1%, which has a relatively high degree of aggregation, indicating that energy and material exchanges are frequent among all enterprises in the network, the degree of network aggregation is high, and the dependence between nodes is high; when the tolerance parameter is 0 to 0.3, the network efficiency and the maximum connected subgraphs show a sharp change trend, indicating that the topology of the industrial coupling symbiotic network of the eco-industrial park changes drastically when the network is subjected to deliberate attacks. It is easy to cause the breakage of material flow and energy flow in the industrial park, which leads to the decline of the stability of the industrial coupling symbiotic network of the eco-industrial park.