The connectivity of a graph on uniform points on [0,1]d

Appel, Martin J. B.; Russo, Ralph P.

doi:10.1016/s0167-7152(02)00233-x

Cited by 71 publications

(76 citation statements)

References 8 publications

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“…Here we propose to use the connectivity distance as defined by Appel and Russo (2002), and Penrose (1999) to determine the bin length along one dimension. We use a function of connectivity distance along a single dimension.…”

Section: Proposed Methods Of Bin Length Estimationmentioning

confidence: 99%

A new estimate of mutual information based measure of dependence between two variables: properties and fast implementation

Jain

Murthy

2015

Int. J. Mach. Learn. & Cyber.

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This article proposes a new method to estimate an existing mutual information based dependence measure using histogram density estimates. Finding a suitable bin length for histogram is an open problem. We propose a new way of computing the bin length for histogram using a function of maximum separation between points. The chosen bin length leads to consistent density estimates for histogram method. The values of density thus obtained are used to calculate an estimate of an existing dependence measure. The proposed estimate is named as MIDI (Mutual Information based Dependence Index). Some important properties of MIDI have also been stated.The performance of the proposed method has been compared to generally accepted measures like distance correlation (dcor), Maximal Information Coefficient (MINE) in terms of accuracy and computational complexity with the help of several artificial data sets with different amounts of noise. The proposed method is able to detect many types of relationships between variables, without making any assumption about the functional form of the relationship. The power statistics of proposed method illustrate their effectiveness in detecting non linear relationship. Thus, it is able to achieve generality without a high rate of false positive cases. MIDI is found to work better on a real life data set than competing methods. The proposed method is found to overcome some of the limitations which occur with dcor and MINE. Computationally, MIDI is found to be better than dcor and MINE, in terms of time and memory, making it suitable for large data sets.

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Section: Proposed Methods Of Bin Length Estimationmentioning

confidence: 99%

A new estimate of mutual information based measure of dependence between two variables: properties and fast implementation

Jain

Murthy

2015

Int. J. Mach. Learn. & Cyber.

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“…Using these values for distance parameters, the average node degrees for all generated networks were the same; this in turn kept the update time constant because, according to Algorithm 1, we only update rates for the node that makes the transition and that node's neighbors. For N 1 , we selected r c1 = 2 log(N 1 )/(πN 1 ), in order to guarantee connectivity of generated RG networks [10].…”

Section: Simulation Run-time Of Large Networkmentioning

confidence: 99%

GEMFsim: A stochastic simulator for the generalized epidemic modeling framework

Sahneh

Vajdi

Shakeri

et al. 2017

Journal of Computational Science

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Abstract-The recently proposed generalized epidemic modeling framework (GEMF) [1] lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article builds an algorithm for exact, continuous-time numerical simulation of GEMF-based processes. Moreover the implementation of this algorithm, GEMFsim, is available in popular scientific programming platforms such as MATLAB, R, Python, and C; GEMFsim facilitates simulating stochastic spreading models that fit in GEMF framework. Using these simulations one can examine the accuracy of mean-field-type approximations that are commonly used for analytical study of spreading processes on complex networks.

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“…, n, that are distributed over D according to a common spatial distribution. 3 Two vertices i and j then have an undirected edge between them if…”

Section: Random Geometric Graphsmentioning

confidence: 99%

“…Some of these random graph models include the famous Erdös-Rényi random graphs [10], random intersection graphs [8], random graphs with hidden variables [9,12], random threshold graphs [35], and random geometric graphs [3,39], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

A New Random Graph Model with Self-Optimizing Nodes: Connectivity and Diameter

Kabkab

2015

Internet Mathematics

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We introduce a new random graph model. In our model, n, n ≥ 2, vertices choose a subset of potential edges by considering the (estimated) benefits or utilities of the edges. More precisely, each vertex selects k, k ≥ 1, incident edges it wishes to set up, and an undirected edge between two vertices is present in the graph if and only if both of the end vertices choose the edge. First, we examine the scaling law of the smallest k needed for graph connectivity with increasing n and prove that it is (log(n)). Second, we study the diameter of the random graph and demonstrate that, under certain conditions on k, the diameter is close to log(n)/ log(log(n)) with high probability. In addition, as a byproduct of our findings, we show that, for all sufficiently large n, if k > β log(n), where β ≈ 2.4626, there exists a connected Erdös-Rényi random graph that is embedded in our random graph, with high probability.

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The connectivity of a graph on uniform points on [0,1]d

Cited by 71 publications

References 8 publications

A new estimate of mutual information based measure of dependence between two variables: properties and fast implementation

A new estimate of mutual information based measure of dependence between two variables: properties and fast implementation

GEMFsim: A stochastic simulator for the generalized epidemic modeling framework

A New Random Graph Model with Self-Optimizing Nodes: Connectivity and Diameter

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