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arXiv 1009.3499cs.SIphysics.soc-ph
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现实网络的乘法属性图模型

Multiplicative Attribute Graph Model of Real-World Networks

Myunghwan Kim, Jure Leskovec

摘要:

大规模的真实世界的网络数据,如社会和信息网络是无处不在的。对这种社会和信息网络的研究试图找到模式,并通过易于处理的模型来解释它们的出现。在大多数网络中,尤其是在社交网络中,节点具有丰富的属性集(例如,与他们相关的年龄,性别。在这里,我们提出了一个模型,我们称之为乘法属性图(MAG),它自然地捕捉网络结构和节点属性之间的相互作用。我们考虑一个模型,其中每个节点都有一个与之相关联的分类潜在属性向量,一对节点之间的边的概率取决于单个属性-属性亲和力的乘积。该模型屈服于数学分析,我们得到阈值的连接和出现的巨型连接组件,并表明该模型产生的网络具有恒定的直径。通过对度分布的分析,我们发现MAG模型在一定条件下可以产生对数正态度分布或幂律度分布的网络。

英文摘要:

Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and especially in social networks, nodes have a rich set of attributes (e.g., age, gender) associated with them. Here we present a model that we refer to as the Multiplicative Attribute Graphs (MAG), which naturally captures the interactions between the network structure and the node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes then depends on the product of individual attribute-attribute affinities. The model yields itself to mathematical analysis and we derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to networks with a constant diameter. We analyze the degree distribution to show that MAG model can produce networks with either log-normal or power-law degree distributions depending on certain conditions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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