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Detection of Central Nodes in Social Networks

Mahyar, Hamid Reza | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50771 (52)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Movaghar, Ali; Rabiee, Hamid Reza
  7. Abstract:
  8. In analyzing the structural organization of many real-world networks, identifying important nodes has been a fundamental problem. The network centrality concept deals with the assessment of the relative importance of network nodes based on specific criteria. Central nodes can play significant roles on the spread of influence and idea in social networks, the user activity in mobile phone networks, the contagion process in biological networks, and the bottlenecks in communication networks. High computational cost and the requirement of full knowledge about the network topology are the most significant obstacles for applying the general concept of network centrality to large real-world social networks. To this end, a prevalent approach for this interesting task is to use network sampling-based methods, which have three major shortcomings: (1) They induce two sources of error; sampling (collection) error and identification (compression) error. (2) Sampling with complete rate and then removing the least significant centrality coefficients leads to loss of system resources and to impose high overhead. (3) Proposing algorithms with the capability of sampling with complete rate and direct measurement of network nodes can be difficult, costly and sometimes impossible because of massive scale, distributed management, and access limitations of real-world networks. In this thesis, we propose two methods to efficiently and accurately detect central nodes in networks, using compressive sensing which is a well-known paradigm in sparse signal recovery. In the first approach, we construct the measurement matrix in a column-wise fashion and theoretically show that by using only O(k log( n )) indirect end-to-end measure- k ments in this method, one can recover top-k central nodes in a network with n nodes, even though the measurements have to follow network topological constraints. Furthermore, we show that the computationally efficient l1-minimization can provide recovery guarantees to infer such central nodes from the constructed measurement matrix with this number of measurements. In the second approach, we construct the measurement matrix in a row-wise manner to be tailored for sparse recovery of every notion of centrality for which there exists a highly correlated and efficiently computable local metric over nodes. We then apply this method for the community detection problem which has been of great importance in sociology, biology, and computer science. This problem is very important because one of the most relevant characteristics of social networks is community structure. After that, we extend the problem into weighted networks. The links in many real-world networks are not only binary entities, either present or not, but have been associated given weights that record their strengths relative to one another. Such models are generally described in terms of weighted networks. Finally, we experimentally evaluate the performance of the proposed methods by extensive simulations under various configurations over several synthetic and real-world networks
  9. Keywords:
  10. Social Networks ; Clustering Coefficient ; Sparse Recovery ; Compressive Sensing ; Network Centrality ; Complex Network ; Betweenness Centrality

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