Interactive Visualization of Small World Graphs

2005 ◽  
Author(s):  
F. van Ham ◽  
J.J. van Wijk
Keyword(s):  
Interactive Visualization ◽  
Small World ◽  
Small World Graphs

Efficient and Robust WiFi Indoor Positioning Using Hierarchical Navigable Small World Graphs

2018 ◽  
Author(s):  
Max Willian Soares Lima ◽  
Horacio A. B. Fernandes de Oliveira ◽  
Eulanda Miranda dos Santos ◽  
Edleno Silva de Moura ◽  
Rafael Kohler Costa ◽  
...  
Keyword(s):  
Small World ◽  
Indoor Positioning ◽  
Small World Graphs

scholarly journals Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Géza Ódor ◽  
Jeffrey Kelling
Keyword(s):  
Control Parameter ◽  
Mean Field ◽  
Small World ◽  
Kuramoto Model ◽  
Crossover Point ◽  
Small World Graphs ◽  
Synchronization Phase ◽  
Experimental Values ◽  
The Kuramoto Model ◽  
Parameter Dependent

AbstractThe hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law–tailed synchronization durations, with τt ≃ 1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τt ≃ 1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1 < τt ≤ 2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

Centrality Based Visualization of Small World Graphs

2008 ◽  
Vol 27 (3) ◽  
pp. 975-982 ◽  
Author(s):  
F. van Ham ◽  
M. Wattenberg
Keyword(s):  
Small World ◽  
Small World Graphs

scholarly journals Small world graphs by iterated local edge formation

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
Ph. Blanchard ◽  
T. Krueger ◽  
A. Ruschhaupt
Keyword(s):  
Small World ◽  
Small World Graphs ◽  
Local Edge

scholarly journals On the connectivity and diameter of small-world networks

2007 ◽  
Vol 39 (4) ◽  
pp. 853-863 ◽  
Author(s):  
Ayalvadi Ganesh ◽  
Feng Xue
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Small World ◽  
Fixed Number ◽  
Total Degree ◽  
Small World Networks ◽  
Fixed Distance ◽  
Stochastic Point Process ◽  
Nearest Neighbours ◽  
Small World Graphs

We consider two different models of small-world graphs on nodes whose locations are modelled by a stochastic point process. In the first model each node is connected to a fixed number of its nearest neighbours, while in the second model each node is connected to all nodes located within some fixed distance. In both models, nodes are additionally connected via shortcuts to other nodes chosen uniformly at random. We obtain sufficient conditions for connectivity in the first model, and necessary conditions in the second model. Thereby, we show that connectivity is achieved at a smaller value of total degree (nearest neighbours plus shortcuts) in the first model. We also obtain bounds on the diameter of the graph in this model.

scholarly journals The neuromorphic Mosaic: re-configurable in-memory small-world graphs

2021 ◽  
Author(s):  
Thomas Dalgaty ◽  
Filippo Moro ◽  
Alessio De Pra ◽  
Giacomo Indiveri ◽  
Elisa Vianello ◽  
...  
Keyword(s):  
Graphical Models ◽  
Scale Up ◽  
Network Connectivity ◽  
Small World ◽  
Event Representation ◽  
Graph Theoretic ◽  
Software Models ◽  
Neuromorphic Hardware ◽  
Small World Graphs ◽  
Memristor Crossbars

Abstract Thanks to their non-volatile and multi-bit properties, memristors have been extensively used as synaptic weight elements in neuromorphic architectures. However, their use to define and re-program the network connectivity has been overlooked. Here, we propose, implement and experimentally demonstrate Mosaic, a neuromorphic architecture based on a systolic array of memristor crossbars. For the first time, we use distributed non-volatile memristors not only for computation, but also for routing (i.e., to define the network connectivity). Mosaic is particularly well-suited for the implementation of re-configurable small-world graphical models, with dense local and sparse global connectivity - found extensively in the brain. We mathematically show that, as the networks scale up, the Mosaic requires less memory than in conventional memristor approaches. We map a spiking recurrent neural network on the Mosaic to solve an Electrocardiogram (ECG) anomaly detection task. While the performance is either equivalent or better than software models, the advantage of the Mosaic was clearly seen in respective one and two orders of magnitude reduction in energy requirements, compared to a micro-controller and address-event representation-based processor. Mosaic promises to open up a new approach to designing neuromorphic hardware based on graph-theoretic principles with less memory and energy.

scholarly journals TECHNOLOGICAL MODEL AND SUSTAINABILITY ASSESSMENT METHODOLOGY OF THE MULTISERVICE COMMUNICATION NETWORK FUNCTIONING

T-Comm ◽  
2021 ◽  
Vol 15 (6) ◽  
pp. 70-74
Author(s):  
Viktor N. Kudelya ◽  
◽  
Valentine E. Gel ◽  
Valeriy V. Vovk ◽  
◽  
...  
Keyword(s):  
Communication Networks ◽  
Sustainability Assessment ◽  
Small World ◽  
Modern Development ◽  
Triple Play ◽  
Small World Graphs ◽  
The Stability ◽  
Audio Video ◽  
Technological Model

The modern development of multiservice communication networks (MÑN) is characterized by the desire of operators to provide users with an unlimited range of services with guaranteed quality of service (QoS). QoS is determined by the stability of the network’s functioning, that is, its ability to function without errors. The existing routing algorithms in modern networks focus the main load on the most productive sections, while the rest of the network is used quite poorly. This is confirmed by the results of studies [1,2], in which the structure of modern global communication networks is assigned to the class of small-world graphs. Obviously, that the increased connectivity of such networks determines high indicators of its stability, but at the same time, this route redundancy is poorly used by existing routing protocols to provide QoS when transmitting different traffic (triple-play: audio, video, and data) [3, 4]. There is also no work devoted to the analysis of the possibilities of sharing different routes (route parallelism) for the implementation of QoS enhancement mechanisms in the MÑN. This article discusses the technological concept of a network with route parallelism in communication networks built on the basis of the IP protocol family.

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