Survey on Sensor Holes: A Cause-Effect-Solution Perspective☆

‘Hubs-repelling’ Laplacian and related diffusion on graphs/networks

In this work, we introduce a new Laplacian matrix, referred to as the hubs-attracting Laplacian, accounting for diffusion processes on networks where the hopping of a particle occurs with higher pr...

/pdf/hubs-attracting-laplacian-and-related-synchronization-on-15zk9actuh.pdf

Hubs-attracting Laplacian and Related Synchronization on Networks

Graph clustering, i.e., partitioning nodes or data points into non-overlapping clusters, can be beneficial in a large varieties of computer vision and machine learning applications. However, main graph clustering schemes such as spectral clustering cannot be applied to a large network due to prohibitive computational complexity required. While there exist methods applicable to large networks, these methods do not offer convincing comparisons against known ground truth. For the first time, this work conducts clustering algorithm performance evaluations on large networks (consisting of one million nodes) with ground truth information. Ideas and concepts from game theory are applied towards graph clustering to formulate a new proposed algorithm, Game Theoretical Approach for Clustering (GTAC). This theoretical framework is shown to be a generalization of both the Label Propagation and Louvain methods, offering an additional means of derivation and analysis. GTAC introduces a tuning parameter which allows variable algorithm performance in accordance with application needs. Experimentation shows that these GTAC algorithms offer scalability and tunability towards big data applications.

Game Theoretical Approach for Non-Overlapping Community Detection

https://digital.csic.es/bitstream/10261/247551/1/graphs_networks.pdf

Hubs-biased resistance distances on graphs and networks

https://www-verimag.imag.fr/~devismes/WWW/rapports/deg_biased.pdf

Comparison of mean hitting times for a degree-biased random walk

A tabu random walk on a graph is a partially self-avoiding random walk which uses a bounded memory to avoid cycles. This memory is called a tabu list and contains vertices already visited by the walker. The size of the tabu list being bounded, the way vertices are inserted and removed from the list, called here an update rule, has an important impact on the performance of the walk, namely the mean hitting time between two given vertices.

We define a large class of tabu random walks, characterized by their update rules. We enunciate a necessary and sufficient condition on these update rules that ensures the finiteness of the mean hitting time of their associated walk on every finite and connected graph. According to the memory allocated to the tabu list, we characterize the update rules which yield smallest mean hitting times on a large class of graphs. Finally, we compare the performances of three collections of classical update rules according to the size of their associated tabu list.

/pdf/analysis-of-random-walks-using-tabu-lists-1k8239plb2.pdf

Analysis of random walks using tabu lists

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Comparison of mean hitting times for a degree-biased random walk

Analysis of random walks using tabu lists