Complex Network Theory Applied to the Growth of Kuala Lumpur’s Public Urban Rail Transit Network

Recently, the number of studies involving complex network applications in transportation has increased steadily as scholars from various fields analyze traffic networks. Nonetheless, research on rail network growth is relatively rare. This research examines the evolution of the Public Urban Rail Transit Networks of Kuala Lumpur (PURTNoKL) based on complex network theory and covers both the topological structure of the rail system and future trends in network growth. In addition, network performance when facing different attack strategies is also assessed. Three topological network characteristics are considered: connections, clustering and centrality. In PURTNoKL, we found that the total number of nodes and edges exhibit a linear relationship and that the average degree stays within the interval [2.0488, 2.6774] with heavy-tailed distributions. The evolutionary process shows that the cumulative probability distribution (CPD) of degree and the average shortest path length show good fit with exponential distribution and normal distribution, respectively. Moreover, PURTNoKL exhibits clear cluster characteristics; most of the nodes have a 2-core value, and the CPDs of the centrality’s closeness and betweenness follow a normal distribution function and an exponential distribution, respectively. Finally, we discuss four different types of network growth styles and the line extension process, which reveal that the rail network’s growth is likely based on the nodes with the biggest lengths of the shortest path and that network protection should emphasize those nodes with the largest degrees and the highest betweenness values. This research may enhance the networkability of the rail system and better shape the future growth of public rail networks.     

Topographic Hub Maps of the Human Structural Neocortical Network

Hubs within the neocortical structural network determined by graph theoretical analysis play a crucial role in brain function. We mapped neocortical hubs topographically, using a sample population of 63 young adults. Subjects were imaged with high resolution structural and diffusion weighted magnetic resonance imaging techniques. Multiple network configurations were then constructed per subject, using random parcellations to define the nodes and using fibre tractography to determine the connectivity between the nodes. The networks were analysed with graph theoretical measures. Our results give reference maps of hub distribution measured with betweenness centrality and node degree. The loci of the hubs correspond with key areas from known overlapping cognitive networks. Several hubs were asymmetrically organized across hemispheres. Furthermore, females have hubs with higher betweenness centrality and males have hubs with higher node degree. Female networks have higher small-world indices.     

The organisational structure of protein networks: revisiting the centrality–lethality hypothesis

Protein networks, describing physical interactions as well as functional associations between proteins, have been unravelled for many organisms in the recent past. Databases such as the STRING provide excellent resources for the analysis of such networks. In this contribution, we revisit the organisation of protein networks, particularly the centrality–lethality hypothesis, which hypothesises that nodes with higher centrality in a network are more likely to produce lethal phenotypes on removal, compared to nodes with lower centrality. We consider the protein networks of a diverse set of 20 organisms, with essentiality information available in the Database of Essential Genes and assess the relationship between centrality measures and lethality. For each of these organisms, we obtained networks of high-confidence interactions from the STRING database, and computed network parameters such as degree, betweenness centrality, closeness centrality and pairwise disconnectivity indices. We observe that the networks considered here are predominantly disassortative. Further, we observe that essential nodes in a network have a significantly higher average degree and betweenness centrality, compared to the network average. Most previous studies have evaluated the centrality–lethality hypothesis for Saccharomyces cerevisiae and Escherichia coli; we here observe that the centrality–lethality hypothesis hold goods for a large number of organisms, with certain limitations. Betweenness centrality may also be a useful measure to identify essential nodes, but measures like closeness centrality and pairwise disconnectivity are not significantly higher for essential nodes.     

Fast Fragmentation of Networks Using Module-Based Attacks

In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from a practical point of view. In this contribution, we present a module-based method to efficiently fragment complex networks. The procedure firstly identifies topological communities through which the network can be represented using a well established heuristic algorithm of community finding. Then only the nodes that participate of inter-community links are removed in descending order of their betweenness centrality. We illustrate the method by applying it to a variety of examples in the social, infrastructure, and biological fields. It is shown that the module-based approach always outperforms targeted attacks to vertices based on node degree or betweenness centrality rankings, with gains in efficiency strongly related to the modularity of the network. Remarkably, in the US power grid case, by deleting 3% of the nodes, the proposed method breaks the original network in fragments which are twenty times smaller in size than the fragments left by betweenness-based attack.     

WIPER: Weighted in-Path Edge Ranking for biomolecular association networks

Background: In network biology researchers generate biomolecular networks with candidate genes or proteins experimentally-derived from high-throughput data and known biomolecular associations. Current bioinformatics research focuses on characterizing candidate genes/proteins, or nodes, with network characteristics, e.g., betweenness centrality. However, there have been few research reports to characterize and prioritize biomolecular associations (“edges”), which can represent gene regulatory events essential to biological processes.Method: We developed Weighted In-Path Edge Ranking (WIPER), a new computational algorithm which can help evaluate all biomolecular interactions/associations (“edges”) in a network model and generate a rank order of every edge based on their in-path traversal scores and statistical significance test result. To validate whether WIPER worked as we designed, we tested the algorithm on synthetic network models.Results: Our results showed WIPER can reliably discover both critical “well traversed in-path edges”, which are statistically more traversed than normal edges, and “peripheral in-path edges”, which are less traversed than normal edges. Compared with other simple measures such as betweenness centrality, WIPER provides better biological interpretations. In the case study of analyzing postanal pig hearts gene expression, WIPER highlighted new signaling pathways suggestive of cardiomyocyte regeneration and proliferation. In the case study of Alzheimer’s disease genetic disorder association, WIPER reports SRC:APP, AR:APP, APP:FYN, and APP:NES edges (gene-gene associations) both statistically and biologically important from PubMed co-citation.Conclusion: We believe that WIPER will become an essential software tool to help biologists discover and validate essential signaling/regulatory events from high-throughput biology data in the context of biological networks.Availability: The free WIPER API is described at discovery.informatics.uab.edu/wiper/     

残基相互作用网络特征与木聚糖酶耐热性的关系

残基相互作用网络是体现蛋白质中残基与残基之间协同和制约关系的重要形式。残基相互作用网络的拓扑性质以及社团结构与蛋白质的功能和性质有密切的关系。本文在构建一系列耐热木聚糖酶和常温木聚糖酶的残基相互作用网络后,通过计算网络的度、聚类系数、连接强度、特征路径长度、接近中心性、介数中心性等拓扑参数来确定网络拓扑结构与木聚糖酶耐热性的关系。识别残基相互作用网络的hub点,分析hub点的亲疏水性、带电性以及各种氨基酸在hub点中所占的比例。进一步使用GA-Net算法对网络进行社团划分,并计算社团的规模、直径和密度。网络的高平均度、高连接强度、以及更短的最短路径等表明耐热木聚糖酶残基相互作用网络的结构更加紧密;耐热木聚糖酶网络中的hub节点比常温木聚糖酶网络hub节点具有更多的疏水性残基,hub点中Phe、Ile、Val的占比更高。社团检测后发现,耐热木聚糖酶网络拥有更大的社团规模、较小的社团直径和较大的社团密度。社团规模越大表明耐热木聚糖酶的氨基酸残基更倾向于形成大的社团,而较小的社团直径和较大的社团密度则表明社团内部氨基酸残基的相互作用比常温木聚糖酶更强。     

Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.     

残基相互作用网络特征与木聚糖酶耐热性的关系

残基相互作用网络是体现蛋白质中残基与残基之间协同和制约关系的重要形式。残基相互作用网络的拓扑性质以及社团结构与蛋白质的功能和性质有密切的关系。本文在构建一系列耐热木聚糖酶和常温木聚糖酶的残基相互作用网络后,通过计算网络的度、聚类系数、连接强度、特征路径长度、接近中心性、介数中心性等拓扑参数来确定网络拓扑结构与木聚糖酶耐热性的关系。识别残基相互作用网络的hub点,分析hub点的亲疏水性、带电性以及各种氨基酸在hub点中所占的比例。进一步使用GA-Net算法对网络进行社团划分,并计算社团的规模、直径和密度。网络的高平均度、高连接强度、以及更短的最短路径等表明耐热木聚糖酶残基相互作用网络的结构更加紧密;耐热木聚糖酶网络中的hub节点比常温木聚糖酶网络hub节点具有更多的疏水性残基,hub点中Phe、Ile、Val的占比更高。社团检测后发现,耐热木聚糖酶网络拥有更大的社团规模、较小的社团直径和较大的社团密度。社团规模越大表明耐热木聚糖酶的氨基酸残基更倾向于形成大的社团,而较小的社团直径和较大的社团密度则表明社团内部氨基酸残基的相互作用比常温木聚糖酶更强。     

Identification and classification of hubs in brain networks

Brain regions in the mammalian cerebral cortex are linked by a complex network of fiber bundles. These inter-regional networks have previously been analyzed in terms of their node degree, structural motif, path length and clustering coefficient distributions. In this paper we focus on the identification and classification of hub regions, which are thought to play pivotal roles in the coordination of information flow. We identify hubs and characterize their network contributions by examining motif fingerprints and centrality indices for all regions within the cerebral cortices of both the cat and the macaque. Motif fingerprints capture the statistics of local connection patterns, while measures of centrality identify regions that lie on many of the shortest paths between parts of the network. Within both cat and macaque networks, we find that a combination of degree, motif participation, betweenness centrality and closeness centrality allows for reliable identification of hub regions, many of which have previously been functionally classified as polysensory or multimodal. We then classify hubs as either provincial (intra-cluster) hubs or connector (inter-cluster) hubs, and proceed to show that lesioning hubs of each type from the network produces opposite effects on the small-world index. Our study presents an approach to the identification and classification of putative hub regions in brain networks on the basis of multiple network attributes and charts potential links between the structural embedding of such regions and their functional roles.     

Network structure implied by initial axon outgrowth in rodent cortex: empirical measurement and models

The developmental mechanisms by which the network organization of the adult cortex is established are incompletely understood. Here we report on empirical data on the development of connections in hamster isocortex and use these data to parameterize a network model of early cortical connectivity. Using anterograde tracers at a series of postnatal ages, we investigate the growth of connections in the early cortical sheet and systematically map initial axon extension from sites in anterior (motor), middle (somatosensory) and posterior (visual) cortex. As a general rule, developing axons extend from all sites to cover relatively large portions of the cortical field that include multiple cortical areas. From all sites, outgrowth is anisotropic, covering a greater distance along the medial/lateral axis than along the anterior/posterior axis. These observations are summarized as 2-dimensional probability distributions of axon terminal sites over the cortical sheet. Our network model consists of nodes, representing parcels of cortex, embedded in 2-dimensional space. Network nodes are connected via directed edges, representing axons, drawn according to the empirically derived anisotropic probability distribution. The networks generated are described by a number of graph theoretic measurements including graph efficiency, node betweenness centrality and average shortest path length. To determine if connectional anisotropy helps reduce the total volume occupied by axons, we define and measure a simple metric for the extra volume required by axons crossing. We investigate the impact of different levels of anisotropy on network structure and volume. The empirically observed level of anisotropy suggests a good trade-off between volume reduction and maintenance of both network efficiency and robustness. Future work will test the model's predictions for connectivity in larger cortices to gain insight into how the regulation of axonal outgrowth may have evolved to achieve efficient and economical connectivity in larger brains.     

The importance of bottlenecks in protein networks: correlation with gene essentiality and expression dynamics

It has been a long-standing goal in systems biology to find relations between the topological properties and functional features of protein networks. However, most of the focus in network studies has been on highly connected proteins (“hubs”). As a complementary notion, it is possible to define bottlenecks as proteins with a high betweenness centrality (i.e., network nodes that have many “shortest paths” going through them, analogous to major bridges and tunnels on a highway map). Bottlenecks are, in fact, key connector proteins with surprising functional and dynamic properties. In particular, they are more likely to be essential proteins. In fact, in regulatory and other directed networks, betweenness (i.e., “bottleneck-ness”) is a much more significant indicator of essentiality than degree (i.e., “hub-ness”). Furthermore, bottlenecks correspond to the dynamic components of the interaction network—they are significantly less well coexpressed with their neighbors than nonbottlenecks, implying that expression dynamics is wired into the network topology.     

Grooming network cohesion and the role of individuals in a captive chimpanzee group

Social network analysis offers new tools to study the social structure of primate groups. We used social network analysis to investigate the cohesiveness of a grooming network in a captive chimpanzee group (N = 17) and the role that individuals may play in it. Using data from a year-long observation, we constructed an unweighted social network of preferred grooming interactions by retaining only those dyads that groomed above the group mean. This choice of criterion was validated by the finding that the properties of the unweighted network correlated with the properties of a weighted network (i.e. a network representing the frequency of grooming interactions) constructed from the same data. To investigate group cohesion, we tested the resilience of the unweighted grooming network to the removal of central individuals (i.e. individuals with high betweenness centrality). The network fragmented more after the removal of individuals with high betweenness centrality than after the removal of random individuals. Central individuals played a pivotal role in maintaining the network's cohesiveness, and we suggest that this may be a typical property of affiliative networks like grooming networks. We found that the grooming network correlated with kinship and age, and that individuals with higher social status occupied more central positions in the network. Overall, the grooming network showed a heterogeneous structure, yet did not exhibit scale-free properties similar to many other primate networks. We discuss our results in light of recent findings on animal social networks and chimpanzee grooming.     

Identification of retinoblastoma related genes with shortest path in a protein-protein interaction network

This paper presents a new method for identifying retinoblastoma related genes by integrating gene expression profile and shortest path in a functional linkage graph. With the existing protein-protein interaction data from STRING, a weighted functional linkage graph is constructed. 119 consistently differentially expressed genes between retinoblastoma and normal retina were obtained from the overlap of two gene expression studies of retinoblastoma. Then the shortest paths between each pair of these 119 genes were determined with Dijkstra's algorithm. Finally, all the genes present on the shortest paths were extracted and ranked according to their betweenness and the 119 shortest genes with a betweenness greater than 100 and with a p-value less than 0.05 were selected for further analysis. We also identified 53 retinoblastoma related miRNAs from published miRNA array data and most of the 238 (119 consistently differentially expressed genes and 119 shortest path genes) retinoblastoma genes were shown to be target genes of these 53 miRNAs. Interestingly, the genes we identified from both the gene expression profiles and the functional protein association network included more cancer genes than did the genes identified from the gene expression profiles alone. In addition, these genes also had greater functional similarity to the reported cancer genes than did the genes identified from the gene expression profiles alone. This study shows promising results and proves the efficiency of the proposed methods.     

Algorithms for identifying Boolean networks and related biological networks based on matrix multiplication and fingerprint function.

Due to the recent progress of the DNA microarray technology, a large number of gene expression profile data are being produced. How to analyze gene expression data is an important topic in computational molecular biology. Several studies have been done using the Boolean network as a model of a genetic network. This paper proposes efficient algorithms for identifying Boolean networks of bounded indegree and related biological networks, where identification of a Boolean network can be formalized as a problem of identifying many Boolean functions simultaneously. For the identification of a Boolean network, an O(mnD+1) time naive algorithm and a simple O (mnD) time algorithm are known, where n denotes the number of nodes, m denotes the number of examples, and D denotes the maximum in degree. This paper presents an improved O(momega-2nD + mnD+omega-3) time Monte-Carlo type randomized algorithm, where omega is the exponent of matrix multiplication (currently, omega < 2.376). The algorithm is obtained by combining fast matrix multiplication with the randomized fingerprint function for string matching. Although the algorithm and its analysis are simple, the result is nontrivial and the technique can be applied to several related problems.     

Eigenvector Centrality Mapping for Analyzing Connectivity Patterns in fMRI Data of the Human Brain

Functional magnetic resonance data acquired in a task-absent condition (“resting state”) require new data analysis techniques that do not depend on an activation model. In this work, we introduce an alternative assumption- and parameter-free method based on a particular form of node centrality called eigenvector centrality. Eigenvector centrality attributes a value to each voxel in the brain such that a voxel receives a large value if it is strongly correlated with many other nodes that are themselves central within the network. Google''s PageRank algorithm is a variant of eigenvector centrality. Thus far, other centrality measures - in particular “betweenness centrality” - have been applied to fMRI data using a pre-selected set of nodes consisting of several hundred elements. Eigenvector centrality is computationally much more efficient than betweenness centrality and does not require thresholding of similarity values so that it can be applied to thousands of voxels in a region of interest covering the entire cerebrum which would have been infeasible using betweenness centrality. Eigenvector centrality can be used on a variety of different similarity metrics. Here, we present applications based on linear correlations and on spectral coherences between fMRI times series. This latter approach allows us to draw conclusions of connectivity patterns in different spectral bands. We apply this method to fMRI data in task-absent conditions where subjects were in states of hunger or satiety. We show that eigenvector centrality is modulated by the state that the subjects were in. Our analyses demonstrate that eigenvector centrality is a computationally efficient tool for capturing intrinsic neural architecture on a voxel-wise level.     

Screened nonbonded interactions in native proteins manipulate optimal paths for robust residue communication

A protein structure is represented as a network of residues whereby edges are determined by intramolecular contacts. We introduce inhomogeneity into these networks by assigning each edge a weight that is determined by amino acid pair potentials. Two methodologies are utilized to calculate the average path lengths (APLs) between pairs: to minimize i), the maximum weight in the strong APL, and ii), the total weight in the weak APL. We systematically screen edges that have higher than a cutoff potential and calculate the shortest APLs in these reduced networks, while keeping chain connectivity. Therefore, perturbations introduced at a selected region of the residue network propagate to remote regions only along the nonscreened edges that retain their ability to disseminate the perturbation. The shortest APLs computed from the reduced homogeneous networks with only the strongest few nonbonded pairs closely reproduce the strong APLs from the weighted networks. The rate of change in the APL in the reduced residue network as compared to its randomly connected counterpart remains constant until a lower bound. Upon further link removal, this property shows an abrupt increase toward a random coil behavior. Under different perturbation scenarios, diverse optimal paths emerge for robust residue communication.     

Reconstructing an ultrametric galled phylogenetic network from a distance matrix

Given a distance matrix M that specifies the pairwise evolutionary distances between n species, the phylogenetic tree reconstruction problem asks for an edge-weighted phylogenetic tree that satisfies M, if one exists. We study some extensions of this problem to rooted phylogenetic networks. Our main result is an O(n(2) log n)-time algorithm for determining whether there is an ultrametric galled network that satisfies M, and if so, constructing one. In fact, if such an ultrametric galled network exists, our algorithm is guaranteed to construct one containing the minimum possible number of nodes with more than one parent (hybrid nodes). We also prove that finding a largest possible submatrix M' of M such that there exists an ultrametric galled network that satisfies M' is NP-hard. Furthermore, we show that given an incomplete distance matrix (i.e. where some matrix entries are missing), it is also NP-hard to determine whether there exists an ultrametric galled network which satisfies it.     

A network perspective on the topological importance of enzymes and their phylogenetic conservation

Background  

A metabolic network is the sum of all chemical transformations or reactions in the cell, with the metabolites being interconnected by enzyme-catalyzed reactions. Many enzymes exist in numerous species while others occur only in a few. We ask if there are relationships between the phylogenetic profile of an enzyme, or the number of different bacterial species that contain it, and its topological importance in the metabolic network. Our null hypothesis is that phylogenetic profile is independent of topological importance. To test our null hypothesis we constructed an enzyme network from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database. We calculated three network indices of topological importance: the degree or the number of connections of a network node; closeness centrality, which measures how close a node is to others; and betweenness centrality measuring how frequently a node appears on all shortest paths between two other nodes.     

Better tired than lost: Turtle ant trail networks favor coherence over short edges

Creating a routing backbone is a fundamental problem in both biology and engineering. The routing backbone of the trail networks of arboreal turtle ants (Cephalotes goniodontus) connects many nests and food sources using trail pheromone deposited by ants as they walk. Unlike species that forage on the ground, the trail networks of arboreal ants are constrained by the vegetation. We examined what objectives the trail networks meet by comparing the observed ant trail networks with networks of random, hypothetical trail networks in the same surrounding vegetation and with trails optimized for four objectives: minimizing path length, minimizing average edge length, minimizing number of nodes, and minimizing opportunities to get lost. The ants’ trails minimized path length by minimizing the number of nodes traversed rather than choosing short edges. In addition, the ants’ trails reduced the opportunity for ants to get lost at each node, favoring nodes with 3D configurations most likely to be reinforced by pheromone. Thus, rather than finding the shortest edges, turtle ant trail networks take advantage of natural variation in the environment to favor coherence, keeping the ants together on the trails.