Computing Vertex Centrality Measures in Massive Real Networks with a Neural Learning Model

Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such metrics are expensive in terms of computational resources when running real-time applications or massive real world networks. Thus, approximation techniques have been developed and used to compute the measures in such scenarios. In this paper, we demonstrate and analyze the use of neural network learning algorithms to tackle such task and compare their performance in terms of solution quality and computation time with other techniques from the literature. Our work offers several contributions. We highlight both the pros and cons of approximating centralities though neural learning. By empirical means and statistics, we then show that the regression model generated with a feedforward neural networks trained by the Levenberg-Marquardt algorithm is not only the best option considering computational resources, but also achieves the best solution quality for relevant applications and large-scale networks. Keywords: Vertex Centrality Measures, Neural Networks, Complex Network Models, Machine Learning, Regression ModelComment: 8 pages, 5 tables, 2 figures, version accepted at IJCNN 2018. arXiv admin note: text overlap with arXiv:1810.1176

Efficient Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs

Graphs are an important tool to model data in different domains, including social networks, bioinformatics and the world wide web. Most of the networks formed in these domains are directed graphs, where all the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network $G$ and a vertex $r \in V(G)$, we propose a new exact algorithm to compute betweenness score of $r$. Our algorithm pre-computes a set $\mathcal{RV}(r)$, which is used to prune a huge amount of computations that do not contribute in the betweenness score of $r$. Time complexity of our exact algorithm depends on $|\mathcal{RV}(r)|$ and it is respectively $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|)$ and $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|+|\mathcal{RV}(r)|\cdot|V(G)|\log |V(G)|)$ for unweighted graphs and weighted graphs with positive weights. $|\mathcal{RV}(r)|$ is bounded from above by $|V(G)|-1$ and in most cases, it is a small constant. Then, for the cases where $\mathcal{RV}(r)$ is large, we present a simple randomized algorithm that samples from $\mathcal{RV}(r)$ and performs computations for only the sampled elements. We show that this algorithm provides an $(\epsilon,\delta)$-approximation of the betweenness score of $r$. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that in most cases, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also show that our proposed algorithm computes betweenness scores of all vertices in the sets of sizes 5, 10 and 15, much faster and more accurate than the most efficient existing algorithms.Comment: arXiv admin note: text overlap with arXiv:1704.0735

KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation

We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks. The efficiency of the new algorithm relies on two new theoretical contributions, of independent interest. The first contribution focuses on sampling shortest paths, a subroutine used by most algorithms that approximate betweenness centrality. We show that, on realistic random graph models, we can perform this task in time $|E|^{\frac{1}{2}+o(1)}$ with high probability, obtaining a significant speedup with respect to the $\Theta(|E|)$ worst-case performance. We experimentally show that this new technique achieves similar speedups on real-world complex networks, as well. The second contribution is a new rigorous application of the adaptive sampling technique. This approach decreases the total number of shortest paths that need to be sampled to compute all betweenness centralities with a given absolute error, and it also handles more general problems, such as computing the $k$ most central nodes. Furthermore, our analysis is general, and it might be extended to other settings.Comment: Some typos correcte

Hierarchical Multi-resolution Mesh Networks for Brain Decoding

We propose a new framework, called Hierarchical Multi-resolution Mesh Networks (HMMNs), which establishes a set of brain networks at multiple time resolutions of fMRI signal to represent the underlying cognitive process. The suggested framework, first, decomposes the fMRI signal into various frequency subbands using wavelet transforms. Then, a brain network, called mesh network, is formed at each subband by ensembling a set of local meshes. The locality around each anatomic region is defined with respect to a neighborhood system based on functional connectivity. The arc weights of a mesh are estimated by ridge regression formed among the average region time series. In the final step, the adjacency matrices of mesh networks obtained at different subbands are ensembled for brain decoding under a hierarchical learning architecture, called, fuzzy stacked generalization (FSG). Our results on Human Connectome Project task-fMRI dataset reflect that the suggested HMMN model can successfully discriminate tasks by extracting complementary information obtained from mesh arc weights of multiple subbands. We study the topological properties of the mesh networks at different resolutions using the network measures, namely, node degree, node strength, betweenness centrality and global efficiency; and investigate the connectivity of anatomic regions, during a cognitive task. We observe significant variations among the network topologies obtained for different subbands. We, also, analyze the diversity properties of classifier ensemble, trained by the mesh networks in multiple subbands and observe that the classifiers in the ensemble collaborate with each other to fuse the complementary information freed at each subband. We conclude that the fMRI data, recorded during a cognitive task, embed diverse information across the anatomic regions at each resolution.Comment: 18 page