Rank me thou shalln't Compare me

Saxena, Akrati; Malik, Vaibhav; Iyengar, S. R. S.

doi:10.48550/arxiv.1511.09050

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…In one of our previous works, we have validated this method on BA networks [49,50]. The proposed method estimates the rank with high accuracy for BA networks but does not give good results for real world networks, as they follow power law degree distribution with a droop head and a heavy tail.…”

Section: Using Power Law Degree Distribution (Pl Method)mentioning

confidence: 99%

Degree Ranking Using Local Information

Saxena¹,

Gera²,

Iyengar³

2017

Preprint

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Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties of the network. In the present work, we estimate degree rank of a node without having the entire network. The proposed methods are based on the power law degree distribution characteristic or sampling techniques. The proposed methods are simulated on synthetic networks, as well as on real world social networks. The efficiency of the proposed methods is evaluated using absolute and weighted error functions. Results show that the degree rank of a node can be estimated with high accuracy using only 1% samples of the network size. The accuracy of the estimation decreases from high ranked to low ranked nodes. We further extend the proposed methods for random networks and validate their efficiency on synthetic random networks, that are generated using Erdős-Rényi model. Results show that the proposed methods can be efficiently used for random networks as well.

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Section: Using Power Law Degree Distribution (Pl Method)mentioning

confidence: 99%

Degree Ranking Using Local Information

Saxena¹,

Gera²,

Iyengar³

2017

Preprint

Self Cite

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“…In our previous works, we proposed methods to estimate the degree rank of a node using its local information. First, we proposed a method based on the power law degree distribution of scale-free networks and it computes the degree rank of a node in O(1) time [31,32]. We further compute the variance in the rank estimation using power law degree distribution [33].…”

Section: Related Workmentioning

confidence: 99%

Fast Estimation of Closeness Centrality Ranking

Saxena

Gera

Iyengar

2017

Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2017

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Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is O(n · m + n), where n represents total number of nodes, and m represents total number of edges in the network. In the present work, we propose a heuristic method to fast estimate the closeness rank of a node in O(α · m) time complexity, where α = 3. We also propose an extended improved method using uniform sampling technique. This method better estimates the rank and it has the time complexity O(α · m), where α ≈ 10 − 100. This is an excellent improvement over the classical centrality ranking method. The efficiency of the 1 proposed methods is verified on real world scale-free social networks using absolute and weighted error functions.

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“…The probability f (j) of a node having degree j is given as f (j) = cj −γ , where c and γ are constants for a network. Once we estimate the equation of the degree distribution, the number of nodes of each degree can be computed using the equation [73]. The total number of nodes having degree j can be computed as n j = n • f (j), where n j represents total number of nodes having degree j in network G. The degree rank of a node u can be computed by adding the number of nodes having degree greater than the degree of node u plus 1.…”

Section: Degree Rank Estimation Using Power Law Degree Distribution (...mentioning

confidence: 99%

Global Rank Estimation

Saxena,

Iyengar

2017

Preprint

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In real world complex networks, the importance of a node depends on two important parameters: 1. characteristics of the node, and 2. the context of the given application. The current literature contains several centrality measures that have been defined to measure the importance of a node based on the given application requirements. These centrality measures assign a centrality value to each node that denotes its importance index. But in real life applications, we are more interested in the relative importance of the node that can be measured using its centrality rank based on the given centrality measure. To compute the centrality rank of a node, we need to compute the centrality value of all the nodes and compare them to get the rank. This process requires the entire network. So, it is not feasible for real-life applications due to the large size and dynamic nature of real world networks.In the present project, we aim to propose fast and efficient methods to estimate the global centrality rank of a node without computing the centrality value of all nodes. These methods can be further extended to estimate the rank without having the entire network. The proposed methods use the structural behavior of centrality measures, sampling techniques, or the machine learning models. In this work, we also discuss how to apply these methods for degree and closeness centrality rank estimation.

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Rank me thou shalln't Compare me

Cited by 3 publications

References 21 publications

Degree Ranking Using Local Information

Degree Ranking Using Local Information

Fast Estimation of Closeness Centrality Ranking

Global Rank Estimation

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