Edge Betweenness Centrality Research Articles

Leveraging Peer Centrality in the Designof Socially-Informed Peer-to-Peer Systems

Social applications mine user social graphs to improve performance in search, provide recommendations, allow resource sharing and increase data privacy. When such applications are implemented on a peer-to-peer (P2P) architecture, the social graph is distributed on the P2P system: the traversal of the social graph translates into a socially-informed routing in the peer-to-peer layer. In this work we introduce the model of a projection graph that is the result of decentralizing a social graph onto a peer-to-peer network. We focus on three social network metrics: degree, node betweenness and edge betweenness centrality and analytically formulate the relation between metrics in the social graph and in the projection graph. We demonstrate with an application scenario on real social networks the usability of the projection graph properties in designing social search applications and unstructured P2P overlays that exhibit improved performance and reduced overhead over baseline scenarios.

Abnormal Brain Network Organization in Body Dysmorphic Disorder

Body dysmorphic disorder (BDD) is characterized by preoccupation with misperceived defects of appearance, causing significant distress and disability. Previous studies suggest abnormalities in information processing characterized by greater local relative to global processing. The purpose of this study was to probe whole-brain and regional white matter network organization in BDD, and to relate this to specific metrics of symptomatology. We acquired diffusion-weighted 34-direction MR images from 14 unmedicated participants with DSM-IV BDD and 16 healthy controls, from which we conducted whole-brain deterministic diffusion tensor imaging tractography. We then constructed white matter structural connectivity matrices to derive whole-brain and regional graph theory metrics, which we compared between groups. Within the BDD group, we additionally correlated these metrics with scores on psychometric measures of BDD symptom severity as well as poor insight/delusionality. The BDD group showed higher whole-brain mean clustering coefficient than controls. Global efficiency negatively correlated with BDD symptom severity. The BDD group demonstrated greater edge betweenness centrality for connections between the anterior temporal lobe and the occipital cortex, and between bilateral occipital poles. This represents the first brain network analysis in BDD. Results suggest disturbances in whole brain structural topological organization in BDD, in addition to correlations between clinical symptoms and network organization. There is also evidence of abnormal connectivity between regions involved in lower-order visual processing and higher-order visual and emotional processing, as well as interhemispheric visual information transfer. These findings may relate to disturbances in information processing found in previous studies.

Methods to find community based on edge centrality

Divisive algorithms are of great importance for community detection in complex networks. One algorithm proposed by Girvan and Newman (GN) based on an edge centrality named betweenness, is a typical representative of this field. Here we studied three edge centralities based on network topology, walks and paths respectively to quantify the relevance of each edge in a network, and proposed a divisive algorithm based on the rationale of GN algorithm for finding communities that removes edges iteratively according to the edge centrality values in a certain order. In addition, we gave a comparison analysis of these measures with the edge betweenness and information centrality. We found the principal difference among these measures in the partition procedure is that the edge centrality based on walks first removes the edge connected with a leaf vertex, but the others first delete the edge as a bridge between communities. It indicates that the edge centrality based on walks is harder to uncover communities than other edge centralities. We also tested these measures for community detection. The results showed that the edge information centrality outperforms other measures, the edge centrality based on walks obtains the worst results, and the edge betweenness gains better performance than the edge centrality based on network topology. We also discussed our method’s efficiency and found that the edge centrality based on walks has a high time complexity and is not suitable for large networks.

Removing spurious interactions in complex networks

Identifying and removing spurious links in complex networks is meaningful for many real applications and is crucial for improving the reliability of network data, which, in turn, can lead to a better understanding of the highly interconnected nature of various social, biological, and communication systems. In this paper, we study the features of different simple spurious link elimination methods, revealing that they may lead to the distortion of networks' structural and dynamical properties. Accordingly, we propose a hybrid method that combines similarity-based index and edge-betweenness centrality. We show that our method can effectively eliminate the spurious interactions while leaving the network connected and preserving the network's functionalities.

Parietofrontal integrity determines neural modulation associated with grasping imagery after stroke

Chronic stroke patients with heterogeneous lesions, but no direct damage to the primary sensorimotor cortex, are capable of longitudinally acquiring the ability to modulate sensorimotor rhythms using grasping imagery of the affected hand. Volitional modulation of neural activity can be used to drive grasping functions of the paralyzed hand through a brain-computer interface. The neural substrates underlying this skill are not known. Here, we investigated the impact of individual patient's lesion pathology on functional and structural network integrity related to this volitional skill. Magnetoencephalography data acquired throughout training was used to derive functional networks. Structural network models and local estimates of extralesional white matter microstructure were constructed using T(1)-weighted and diffusion-weighted magnetic resonance imaging data. We employed a graph theoretical approach to characterize emergent properties of distributed interactions between nodal brain regions of these networks. We report that interindividual variability in patients' lesions led to differential impairment of functional and structural network characteristics related to successful post-training sensorimotor rhythm modulation skill. Patients displaying greater magnetoencephalography global cost-efficiency, a measure of information integration within the distributed functional network, achieved greater levels of skill. Analysis of lesion damage to structural network connectivity revealed that the impact on nodal betweenness centrality of the ipsilesional primary motor cortex, a measure that characterizes the importance of a brain region for integrating visuomotor information between frontal and parietal cortical regions and related thalamic nuclei, correlated with skill. Edge betweenness centrality, an analogous measure, which assesses the role of specific white matter fibre pathways in network integration, showed a similar relationship between skill and a portion of the ipsilesional superior longitudinal fascicle connecting premotor and posterior parietal visuomotor regions known to be crucially involved in normal grasping behaviour. Finally, estimated white matter microstructure integrity in regions of the contralesional superior longitudinal fascicle adjacent to primary sensorimotor and posterior parietal cortex, as well as grey matter volume co-localized to these specific regions, positively correlated with sensorimotor rhythm modulation leading to successful brain-computer interface control. Thus, volitional modulation of ipsilesional neural activity leading to control of paralyzed hand grasping function through a brain-computer interface after longitudinal training relies on structural and functional connectivity in both ipsilesional and contralesional parietofrontal pathways involved in visuomotor information processing. Extant integrity of this structural network may serve as a future predictor of response to longitudinal therapeutic interventions geared towards training sensorimotor rhythms in the lesioned brain, secondarily improving grasping function through brain-computer interface applications.

Edge betweenness centrality: A novel algorithm for QoS-based topology control over wireless sensor networks

In this paper we propose a novel topology-control algorithm, called edge betweenness centrality (EBC). EBC is based on the concept of betweenness centrality, which has been first introduced in the context of social network analysis (SNA), and measures the “importance” of each node in the network. This information allows us to achieve high quality of service (QoS) in wireless sensor networks by evaluating relationships between entities of the network (i.e., edges), and hence identifying different roles among them (e.g., brokers, outliers), thus controlling information flow, message delivery, latency and energy dissipation among nodes. The experimental evaluation and analysis of EBC in comparison to other state-of-the-art topology control algorithms shows that our algorithm outperforms the competitor ones in all observed cases.

Data Flow Graph Partitioning Algorithms and Their Evaluations for Optimal Spatio-temporal Computation on a Coarse Grain Reconfigurable Architecture

Coarse Grain Reconfigurable Architectures (CGRA) support spatial and temporal computation to speedup execution and reduce reconfiguration time. Thus compilation involves partitioning instructions spatially and scheduling them temporally. The task of partitioning is governed by the opposing forces of being able to expose as much parallelism as possible and reducing communication time. We extend Edge-Betweenness Centrality scheme, originally used for detecting community structures in social and biological networks, for partitioning instructions of a dataflow graph. We also implement several other partitioning algorithms from literature and compare the execution time obtained by each of these partitioning algorithms on a CGRA called REDEFINE. Centrality based partitioning scheme outperforms several other schemes with 6-20% execution time speedup for various Cryptographic kernels. REDEFINE using centrality based partitioning performs 9× better than a General Purpose Processor, as opposed to 7.76× better without using centrality based partitioning. Similarly, centrality improves the execution time comparison of AES-128 Decryption from 11× to 13.2×.

Rewiring dynamical networks with prescribed degree distribution for enhancing synchronizability

In this paper, we present an algorithm for enhancing synchronizability of dynamical networks with prescribed degree distribution. The algorithm takes an unweighted and undirected network as input and outputs a network with the same node-degree distribution and enhanced synchronization properties. The rewirings are based on the properties of the Laplacian of the connection graph, i.e., the eigenvectors corresponding to the second smallest and the largest eigenvalues of the Laplacian. A term proportional to the eigenvectors is adopted to choose potential edges for rewiring, provided that the node-degree distribution is preserved. The algorithm can be implemented on networks of any sizes as long as their eigenvalues and eigenvectors can be calculated with standard algorithms. The effectiveness of the proposed algorithm in enhancing the network synchronizability is revealed by numerical simulation on a number of sample networks including scale-free, Watts-Strogatz, and Erdős-Rényi graphs. Furthermore, a number of network's structural parameters such as node betweenness centrality, edge betweenness centrality, average path length, clustering coefficient, and degree assortativity are tracked as a function of optimization steps.

Disassortativity of random critical branching trees

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.

Efficient rewirings for enhancing synchronizability of dynamical networks

In this paper, we present an algorithm for optimizing synchronizability of complex dynamical networks. Starting with an undirected and unweighted network, we end up with an undirected and unweighted network with the same number of nodes and edges having enhanced synchronizability. To this end, based on some network properties, rewirings, i.e., eliminating an edge and creating a new edge elsewhere, are performed iteratively avoiding always self-loops and multiple edges between the same nodes. We show that the method is able to enhance the synchronizability of networks of any size and topological properties in a small number of steps that scales with the network size. For numerical simulations, an optimization algorithm based on simulated annealing is used. Also, the evolution of different topological properties of the network such as distribution of node degree, node and edge betweenness centrality is tracked with the iteration steps. We use networks such as scale-free, Strogatz–Watts and random to start with and we show that regardless of the initial network, the final optimized network becomes homogeneous. In other words, in the network with high synchronizability, parameters, such as, degree, shortest distance, node, and edge betweenness centralities are almost homogeneously distributed. Also, parameters, such as, maximum node and edge betweenness centralities are small for the rewired network. Although we take the eigenratio of the Laplacian as the target function for optimization, we show that it is also possible to choose other appropriate target functions exhibiting almost the same performance. Furthermore, we show that even if the network is optimized taking into account another interpretation of synchronizability, i.e., synchronization cost, the optimal network has the same synchronization properties. Indeed, in networks with optimized synchronizability, different interpretations of synchronizability coincide. The optimized networks are Ramanujan graphs, and thus, this rewiring algorithm could be used to produce Ramanujan graphs of any size and average degree.

Enhancing synchronizability of weighted dynamical networks using betweenness centrality

By considering the eigenratio of the Laplacian of the connection graph as a synchronizability measure, we propose a procedure for weighting dynamical networks to enhance their synchronizability. The method is based on node and edge betweenness centrality measures and is tested on artificially constructed scale-free, Watts-Strogatz, and random networks as well as on some real-world graphs. It is also numerically shown that the same procedure could be used to enhance the phase synchronizability of networks of nonidentical oscillators.

The use of sparsest cuts to reveal the hierarchical community structure of social networks

We show that good community structures can be obtained by partitioning a social network in a succession of divisive sparsest cuts. A network flow algorithm based on fundamental principles of graph theory is introduced to identify the sparsest cuts and an underlying hierarchical community structure of the network via maximum concurrent flow. Matula [Matula, David W., 1985. Concurrent flow and concurrent connectivity in graphs. In: Alavi, Y., et al. (Eds.), Graph Theory and its Applications to Algorithms and Computer Science. Wiley, New York, NY, pp. 543–559.] established the maximum concurrent flow problem (MCFP), and papers on divisive vs. agglomerative average-linkage hierarchical clustering [e.g., Matula, David W., 1983. Cluster validity by concurrent chaining. In: Felsenstein, J. (Ed.), Numerical Taxonomy: Proc. of the NATO Adv. Study Inst., vol. 1. Springer-Verlag, New York, pp. 156–166 (Proceedings of NATO ASI Series G); Matula, David W., 1986. Divisive vs. agglomerative average linkage hierarchical clustering. In: Gaul, W., and Schader, M. (Eds.), Classification as a Tool of Research. Elsevier, North-Holland, Amsterdam, pp. 289–301; Thompson, Byron J., 1985. A flow rerouting algorithm for the maximum concurrent flow problem with variable capacities and demands, and its application to cluster analysis. Master Thesis. School of Engineering and Applied Science, Southern Methodist University] provide the basis for partitioning a social network by way of sparsest cuts and/or maximum concurrent flow. The MCFP extends the [Ford Jr., Lester R., Fulkerson, Delbert R., 1956. Maximal flow through a network. Canadian Journal of Mathematics 8, 399–404; Ford Jr., Lester R., Fulkerson, Delbert R., 1962. Flows in Networks. Princeton University Press, Princeton, NJ] source–sink max-flow problem to all-pairs maximum concurrent flow. The density of an ( S, T)-cut is |( S, T)\\/(| S|•| T|) where |( S, T)| is the number of edges (equivalently, links or bonds) between communities S and T with | S|•| T| being the maximum number of edges possible. The minimum density cut in the network is the sparsest cut. When the edges are weighted, the density is the average weight of the ( S, T)-cut edges, with absent edges treated as edges of zero weight. Sparsest cuts (i.e., minimum density) of the remaining components are iteratively determined via linear programming until a multipartite cut is identified that is more constraining to concurrent flow than any sparsest cut. Empirical results on real-world networks with known hierarchical structures and random networks with embedded communities are used to compare this sparsest-cut community structure criterion to the weighted Girvan–Newman community structure criterion [e.g., Newman, M.E.J., 2004. Analysis of weighted networks. Physical Review E 70, 056131] that is based on edge betweenness centrality. A new measure of accuracy M is defined to evaluate the results of the graph partitionings found by these criteria.

Homogeneity of Load Distribution Plays a Key Role in Global Synchronizability of Complex Networks

Many structure parameters have been suggested to predict the synchronizability of complex networks. They were qualitatively suitable for certain networks but failed for others. Based on the coupled oscillator model, we find that the homogeneity of load distribution determines the synchronizability of complex networks, and the standard deviation of edge betweenness centrality is coincident with synchronizability for various complex networks. These results suggest that in order for a network to hence to synchronize more effectively, the load distribution must be more homogeneous.

Fractality and self-similarity in scale-free networks

Fractal scaling and self-similar connectivity behaviour of scale-free (SF) networks are reviewed and investigated in diverse aspects. We first recall an algorithm of box-covering that is useful and easy to implement in SF networks, the so-called random sequential box-covering. Next, to understand the origin of the fractal scaling, fractal networks are viewed as comprising of a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a spanning tree specifically based on the edge-betweenness centrality or load. We show that the skeleton is a non-causal tree, either critical or supercritical. We also study the fractal scaling property of the k-core of a fractal network and find that as k increases, not only does the fractal dimension of the k-core change but also eventually the fractality no longer holds for large enough k. Finally, we study the self-similarity, manifested as the scale-invariance of the degree distribution under coarse-graining of vertices by the box-covering method. We obtain the condition for self-similarity, which turns out to be independent of the fractality, and find that some non-fractal networks are self-similar. Therefore, fractality and self-similarity are disparate notions in SF networks.

Fractality in complex networks: Critical and supercritical skeletons

Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a box-covering algorithm that is a modified version of the original algorithm introduced by Song [Nature (London) 433, 392 (2005)]; this algorithm enables easy implementation. Fractal networks are viewed as comprising a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a special type of spanning tree based on the edge betweenness centrality; it provides a scaffold for the fractality of the network. When the skeleton is regarded as a branching tree, it exhibits a plateau in the mean branching number as a function of the distance from a root. For nonfractal networks, on the other hand, the mean branching number decays to zero without forming a plateau. Based on these observations, we construct a fractal network model by combining a random branching tree and local shortcuts. The scaffold branching tree can be either critical or supercritical, depending on the small worldness of a given network. For the network constructed from the critical (supercritical) branching tree, the average number of vertices within a given box grows with the lateral size of the box according to a power-law (an exponential) form in the cluster-growing method. The critical and supercritical skeletons are observed in protein interaction networks and the World Wide Web, respectively. The distribution of box masses, i.e., the number of vertices within each box, follows a power law Pm(M) approximately M(-eta). The exponent eta depends on the box lateral size l(B). For small values of l(B), eta is equal to the degree exponent gamma of a given scale-free network, whereas eta approaches the exponent tau=gamma/(gamma-1) as l(B) increases, which is the exponent of the cluster-size distribution of the random branching tree. Finally, we study the perimeter H(alpha) of a given box alpha, i.e., the number of edges connected to different boxes from a given box alpha as a function of the box mass M(B,alpha). It is obtained that the average perimeter over the boxes with box mass M(B) is likely to scale as <H(M(B))> approximately M(B), irrespective of the box size l(B).

An algorithm for modularity analysis of directed and weighted biological networks based on edge-betweenness centrality

Modularity analysis is a powerful tool for studying the design of biological networks, offering potential clues for relating the biochemical function(s) of a network with the 'wiring' of its components. Relatively little work has been done to examine whether the modularity of a network depends on the physiological perturbations that influence its biochemical state. Here, we present a novel modularity analysis algorithm based on edge-betweenness centrality, which facilitates the use of directional information and measurable biochemical data.

Inhomogeneous substructures hidden in random networks

We study the structure of the load-based spanning tree (LST) that carries the maximum weight of the Erdös-Rényi (ER) random network. The weight of an edge is given by the edge-betweenness centrality, the effective number of shortest paths through the edge. We find that the LSTs present very inhomogeneous structures in contrast to the homogeneous structures of the original networks. Moreover, it turns out that the structure of the LST changes dramatically as the edge density of an ER network increases, from scale free with a cutoff, scale free, to a starlike topology. These would not be possible if the weights are randomly distributed, which implies that topology of the shortest path is correlated in spite of the homogeneous topology of the random network.

Skeleton and Fractal Scaling in Complex Networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.

Underlying Scale-Free Trees in Complex Networks

We investigate the properties of two relatively different spanning trees of complex networks, so-called communication kernel and response network. First, for the communication kernel, we construct spanning trees carrying a maximum total weight of edges that is given by average traffic, which is defined as edge betweenness centrality. It is found that the resulting spanning tree plays an important role in communication between vertices. We also find that the degree distribution of spanning trees shows scale-free behavior for many model and real-world networks and the degree of the spanning trees has strong correlation with their original network topology. For the response network, we launch an attack on a single vertex which can drastically change the communication pattern between vertices of networks. By using minimum spanning tree technique, we construct the response network based on the measurement of the betweenness centrality changes due to a vertex removal. We find that the degree distribution of the response network indicates the scale-free behavior as well as that of the communication kernel. Interestingly, these two minimum spanning trees from different methods not only have same scale-free behavior but overlap each other in their structures. This fact indicates that the complex network has a concrete skeleton, scale-free tree, as a basic structure.

Distance, dissimilarity index, and network community structure

We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, Phys. Rev. E 67, 041908 (2003)], the concept of network random walking is introduced and a distance measure defined. Here we calculate, based on this distance measure, the dissimilarity index between nearest-neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized. Each community is characterized by an upper and a lower dissimilarity threshold. The algorithm is applied to several artificial and real-world networks, and excellent results are obtained. In the case of artificially generated random modular networks, this method outperforms the algorithm based on the concept of edge betweenness centrality. For yeast's protein-protein interaction network, we are able to identify many clusters that have well defined biological functions.