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20 records · Page 2Linked to original sources

Core-periphery identification in massive networks

Modern networks can be huge with millions or even billions of nodes and edges. Thus, algorithms must be capable of scaling to such large networks in order to be practically useful. In this work, we are interested in developing an algorithm to identify core-periphery structure in massive networks. Core-periphery structure is a meso-scale feature where nodes are grouped into a densely connected core or sparsely connected periphery. To identify such structures in large networks, we propose a divide-and-conquer algorithm. The key feature of our algorithm is leveraging the edge list representation of the network, instead of the adjacency matrix, as it tends to be faster and makes a more efficient use of memory. We apply the proposed algorithm to synthetic and real-world data, notably demonstrating its performance on a real-world network with almost 14 million edges without loading the entire network into memory.

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Symmetry-driven embedding of networks in hyperbolic space

Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embeddings algorithms have been proposed to invert these models and assign hyperbolic coordinates to network data. Current algorithms for finding these coordinates, however, do not quantify uncertainty in the inferred coordinates. We present BIGUE, a Markov chain Monte Carlo (MCMC) algorithm that samples the posterior distribution of a Bayesian hyperbolic random graph model. We show that the samples are consistent with current algorithms while providing added credible intervals for the coordinates and all network properties. We also show that some networks admit two or more plausible embeddings, a feature that an optimization algorithm can easily overlook.

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