Tight Bounds for the Probability of Connectivity in Random K-out Graphs

2021 ◽  
Author(s):  
Mansi Sood ◽  
Osman Yagan
Keyword(s):  
Probability Of Connectivity

scholarly journals On the Isolated Vertices and Connectivity in Random Intersection Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Random Graphs ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Random Intersection Graph ◽  
Probability Of Connectivity ◽  
Asymptotic Probability

We study isolated vertices and connectivity in the random intersection graph . A Poisson convergence for the number of isolated vertices is determined at the threshold for absence of isolated vertices, which is equivalent to the threshold for connectivity. When and , we give the asymptotic probability of connectivity at the threshold for connectivity. Analogous results are well known in Erdős-Rényi random graphs.

scholarly journals Analysis of the probability of connectivity of a telecommunications network based on the reduction of several non-connectivity events to a union of independent events

2021 ◽  
pp. 53-63
Author(s):  
Aleksandr Batenkov ◽  
Kirill Batenkov ◽  
Aleksandr Fokin
Keyword(s):  
Network Connectivity ◽  
Telecommunication Networks ◽  
Huge Number ◽  
Connectivity Probability ◽  
Independent Events ◽  
Telecommunications Network ◽  
Probability Of Connectivity ◽  
Analytical Relations ◽  
Sums Of Products ◽  
Routine Procedures

Introduction: For large and structurally complex telecommunication networks, calculating the connectivity probability turns out to be a very cumbersome and time-consuming process due to the huge number of elements in the resulting expression. The most expedient way out of this situation is a method based on the representation of a network connectivity event in the form of sums of products of incompatible events. However, this method also requires performing additional operations on sets in some cases. Purpose: To eliminate the main disadvantages of the method using multi-variable inversion. Results: It is shown that the connectivity event of a graph should be interpreted as a union of connectivity events of all its subgraphs, which leads to the validity of the expression for the connectivity event of the network in the form of a union of connectivity events of typical subgraphs (path, backbone, and in general, a multi-pole tree) of the original random graph. An iterative procedure is proposed for bringing a given number of connectivity events to the union of independent events by sequentially adding subgraph disjoint events. The possibility of eliminating repetitive routine procedures inherent in methods using multi-variable inversion is proved by considering not the union of connectivity events (incoherence) degenerating into the sum of incompatible products, but the intersection of opposite events, which also leads to a similar sum. However, to obtain this sum, there is no need to perform a multi-variable inversion for each of the terms over all those previously analyzed. Practical relevance: The obtained analytical relations can be applied in the analysis of reliability, survivability or stability of complex telecommunications networks.

scholarly journals SACA: Self-Aware Communication Architecture for IoT Using Mobile Fog Servers

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Vishal Sharma ◽  
Jae Deok Lim ◽  
Jeong Nyeo Kim ◽  
Ilsun You
Keyword(s):  
Network Reliability ◽  
Packet Losses ◽  
State Dependency ◽  
Communication Architecture ◽  
Storage And Retrieval ◽  
Aerial Vehicle ◽  
Network Simulations ◽  
Probability Of Connectivity ◽  
Increasing Demand ◽  
Iot Devices

Internet of things (IoT) aims at bringing together large business enterprise solutions and architectures for handling the huge amount of data generated by millions of devices. For this aim, IoT is necessary to connect various devices and provide a common platform for storage and retrieval of information without fail. However, the success of IoT depends on the novelty of network and its capability in sustaining the increasing demand by users. In this paper, a self-aware communication architecture (SACA) is proposed for sustainable networking over IoT devices. The proposed approach employs the concept of mobile fog servers which make relay using the train and unmanned aerial vehicle (UAV) networks. The problem is presented based on Wald’s maximum model, which is resolved by the application of a distributed node management (DNM) system and state dependency formulations. The proposed approach is capable of providing prolonged connectivity by increasing the network reliability and sustainability even in the case of failures. The effectiveness of the proposed approach is demonstrated through numerical and network simulations in terms of significant gains attained with lesser delay and fewer packet losses. The proposed approach is also evaluated against Sybil, wormhole, and DDoS attacks for analyzing its sustainability and probability of connectivity in unfavorable conditions.

Multi-institutional evaluation of deep brain stimulation targeting using probabilistic connectivity-based thalamic segmentation

2011 ◽  
Vol 115 (5) ◽  
pp. 995-1004 ◽  
Author(s):  
Nader Pouratian ◽  
Zhong Zheng ◽  
Ausaf A. Bari ◽  
Eric Behnke ◽  
W. Jeff Elias ◽  
...  
Keyword(s):  
Deep Brain Stimulation ◽  
Brain Stimulation ◽  
Premotor Cortex ◽  
Patient Specific ◽  
University Of Virginia ◽  
School Of Medicine ◽  
Connectivity Patterns ◽  
Probability Of Connectivity ◽  
Thalamic Region ◽  
Deep Brain

Object Due to the lack of internal anatomical detail with traditional MR imaging, preoperative stereotactic planning for the treatment of tremor usually relies on indirect targeting based on atlas-derived coordinates. The object of this study was to preliminarily investigate the role of probabilistic tractography–based thalamic segmentation for deep brain stimulation (DBS) targeting for the treatment of tremor. Methods Six patients undergoing bilateral implantation of DBS electrodes in the thalamus for the treatment of upper-extremity tremor were studied. All patients underwent stereotactic surgical implantation using traditional methods (based on indirect targeting methodologies and intraoperative macrostimulation findings) that were programmed for optimal efficacy, independent of tractography-based segmentations described in this report. Connectivity-based thalamic segmentations were derived by identifying with which of 7 cortical target regions each thalamic voxel had the highest probability of connectivity. The authors retrospectively analyzed the location of the optimal contact for treatment of tremor with connectivity-based thalamic segmentations. Findings from one institution (David Geffen School of Medicine at UCLA) were validated with results from 4 patients at another institution (University of Virginia Health System). Results Of 12 electrodes implanted using traditional methodologies, all but one resulted in efficacious tremor control. Connectivity-based thalamic segmentation consistently revealed discrete thalamic regions having unique connectivity patterns with distinct cortical regions. Although the authors initially hypothesized that the most efficacious DBS contact for controlling tremor would colocalize with the thalamic region most highly connected with the primary motor cortex, they instead found it to highly colocalize with those thalamic voxels demonstrating a high probability of connectivity with premotor cortex (center-to-center distance: 0.36 ± 0.55 mm). In contrast to the high degree of colocalization with optimal stimulation site, the precise localization of the premotor cortex–defined thalamic region relative to the anterior and posterior commissures was highly variable. Having defined a connectivity-based target for thalamic stimulation in a cohort of patients at David Geffen School of Medicine at UCLA, the authors validated findings in 4 patients (5 electrodes) who underwent surgery at a different institution (University of Virginia Health System) by a different surgeon. Conclusions This report identifies and provides preliminary external validation of a novel means of targeting a patient-specific therapeutic thalamic target for the treatment of tremor based on individualized analysis of thalamic connectivity patterns. This novel thalamic targeting approach is based on identifying the thalamic region with the highest probability of connectivity with premotor and supplementary motor cortices. This approach may prove to be advantageous over traditional preoperative methods of indirect targeting, providing patient-specific targets that could improve the precision, efficacy, and efficiency of deep brain stimulation surgery. Prospective evaluation and development of methodologies to make these analyses more widely available to neurosurgeons are likely warranted.

scholarly journals The probability of connectivity in a hyperbolic model of complex networks

2016 ◽  
Vol 49 (1) ◽  
pp. 65-94 ◽  
Author(s):  
Michel Bode ◽  
Nikolaos Fountoulakis ◽  
Tobias Müller
Keyword(s):  
Complex Networks ◽  
Hyperbolic Model ◽  
Probability Of Connectivity

scholarly journals The Review of Ecological Network Indicators in Graph Theory Context: 2014-2019

2021 ◽  
Author(s):  
Hassan Darabi ◽  
Rastgar Hashemi ◽  
Faroq Lotfi
Keyword(s):  
Graph Theory ◽  
Network Analysis ◽  
Ecological Networks ◽  
Ecological Studies ◽  
Ecological Network ◽  
Integral Index ◽  
Screening Process ◽  
Ecological Network Analysis ◽  
Increasing Trend ◽  
Probability Of Connectivity

Abstract Ecological Network Analysis (ENA) capability has led to develop a set of indicators. Ecological Network Indicators (ENIs) investigates a range of subject in different context “e.g. Graph theory”, which is the origin of variety of questions such as following: What is the geographical distribution of studies and their relationship with each other? On what fields these studies are focused? What graph-based index or indexes have been used in the studies of ecological networks? What are the most widely used indexes in ecological studies? Accordingly, this study is to investigate the related literature between 2014 and 2019 in the framework of graph theory. To answer the mentioned question, we conducted systematic literature review. To find as many potentially eligible articles as possible, the search was performed multiple times using diverse related keywords. We identified 456 related records. After the screening process, 114 articles were left as the basis of further analysis. The results indicate that ENA applied mainly in China, USA, France. ENIs is studied more frequently among plants and mammals. We identified about 58 ENIs. But the Probability of Connectivity (PC), Integral index of connectivity (IIC) have been consistently used in most studies. Also, these two indices are used in combination with others ENIs. The outcomes show researchers introduce new indexes every year. The increasing trend of introducing new indicators shows the usability and applicability ENIs. But so far, PC, IIC, and LCP seem to be the most credible graph-based indexes for use in ecological network research. The overall results imply that graph theory as base of ecological network is developing, presents new indicators and opening new dimensions in the study and analysis of connections and communications in ecological networks. It has adequate flexibility to answer questions that may arise in the future in the field of ecological network analysis.

scholarly journals PROBABILITY OF THE UTILITY NETWORKS DOUBLE-RING STRUCTURES’ CONNECTIVITY FOR SITES WITH VARIOUS RELIABILITY

2018 ◽  
Vol 1 (50) ◽  
pp. 270-277
Author(s):  
V. H. Usenko ◽  
О. А. Kodak
Keyword(s):  
Network Structure ◽  
Analytical Description ◽  
Network Structures ◽  
Structural Redundancy ◽  
Double Ring ◽  
Connectivity Probability ◽  
Study Results ◽  
Ring Structures ◽  
Probability Of Connectivity ◽  
Structural Parts

The analytical description study results on probability of connectivity for the structures used to model the reliability of various complicated systems are presented. Expressions are formed to calculate the connectivity probability of systems that have structural redundancy. The characteristic components of the formulas are distinguished and they are systematized according to their increasing complexity and the number of elements. The features of the equations’ structure permitting to conveniently formulate the probability of the structures connectivity in the process of their construction and transformations are determined. The examples show the formation of formulas and their structural parts at various levels of complexity. The use of the ratio value of the network structure element’s unreliability and its reliability is justified, thus reducing the awkwardness of exact expressions for the connectivity probability of network structures and substantially improves the compactness and convenience of using the equations.

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