中文题名: | 基于电路网络的节点重要性研究 |
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学科代码: | 071101 |
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学生类型: | 硕士 |
学位: | 理学硕士 |
学位年度: | 2014 |
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研究方向: | 复杂网络 |
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提交日期: | 2014-06-20 |
答辩日期: | 2014-05-22 |
外文题名: | The research of node importance based on electrical-circuit network |
中文摘要: |
近些年来,复杂网络作为一门新兴的学科,为我们理解实际系统,如社会,生物系统,提供了一种新的工具和视角,有关复杂网络的研究方兴未艾。节点重要性衡量作为复杂网络结构研究的重要方向一直受到研究人员的关注,对网络中节点的重要性进行衡量的指标不断涌现。事实上,节点重要性研究也具有很强的理论和实用价值,例如对疾病传播的控制,在兴起的社交网络发挥的重要作用,在经济,生物,军事上的重要应用等。在复杂网络中,存在一些内部连接较稠密而外部连接较松散的顶点集合,这些顶点集被称作社团或者模块。社团结构作为网络的基本概念已经在很多领域得到了广泛的应用。研究者提出了许多算法对社团进行划分,这些方法的一个基本前提是网络中的节点都有比较明确的社团归属,也就是说网络能清晰的划分成几个社团,然而实际系统中有些节点可能分属于不同的社团,例如一个人可以出现在不同的朋友圈,这种社团重叠节点给原有的社团划分算法带来了比较大的困难。对这种社团之间的连接节点的探测与区分也一直没有得到很好的解决。本文在介绍了一些经典的节点重要性指标的基础上,提出了一种基于电路网络的理论电流重要性指标(C 指标),比较好的解决了社团之间重要节点的探测。在电路网络中,社团之间由于连接的稀疏,导致电阻较大,在跨社团的时候有大的电势差,所以连接社团的节点都具有较大的电流通过。因此,可以用电流中心性指标C 来对这些连接节点进行探测。更进一步,由这些节点与其邻边上电流分布的信息我们设计了偏差值指标D来进行衡量,用来对这些连接节点进行区分。方法的优势之一是在不需要知道社团结构信息的前提下能对无向网络进行有效的探测与区分,通过对模型的改进,将其推广到了有向网络。在人工和实际系统的应用验证了方法的有效性,这为理解和控制实际系统提供了一种很好的工具。
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外文摘要: |
network provides a new tool and perspective to understand real systems,such as social, biological systems. In recent years, the study of complex networks isin the ascendant. Researchers are paying more attention on nodes important,which is avital field of complex network structure. Thus, a large number of indices are developedto measure the important of nodes. In fact, the research of node important also hasa strong theoretical and practical meaning, such as the controlling of disease spreads,the study of social networks and other applications on biological network. This articlereviews several classic indices and provide a new method to measure the importanceof nodes based on electrical-circuit theory. This method can detect and distinguishthe nodes that connect communities. Although there are many effective algorithm todetect the community structure of network, a basic premise of methods is still missingto detect communities. The previous methods presume that the network can clearly bedivided into several parts, However, some nodes can belong to different communitiesat the same time in some real network, for example, a person can appear in a differentcircle of friends, the existence of overlapping nodes makes it hard to partition networks.The detection and distinguish nodes that connects communities also has not been solved. This article presents a current-flow centrality index (C index )based on the electrical-circuit network can gives a good solution to this question. The connection amongcommunities are sparse , so the resistance among communities are large, which causea large potential gap across communities. Therefore , one can use the current-flow Cto detect the important nodes that connect communities . Furthermore , Index D isdesigned to measure the imbalance of current on edges that connect nodes and theirneighbors. One advantage of this method is that it can detect and distinguish key nodes–without know the exact partitions of networks. Methods is extended to directed network. The application of artificial and real systems verifies the validity of the method , whichis provides a good tool to understand and control the actual system.
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参考文献总数: | 41 |
馆藏号: | 硕071101/1404 |
开放日期: | 2014-06-20 |