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首页> 外文会议>IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining >Random Preferential Attachment Hypergraph
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Random Preferential Attachment Hypergraph

机译：随机优先依附超图

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In the future, analysis of social networks will conceivably move from graphs to hypergraphs. However, theory has not yet caught up with this type of data organizational structure. By introducing and analyzing a general model of preferential attachment hypergraphs, this paper makes a step towards narrowing this gap. We consider a random preferential attachment model H(p,Y) for network evolution that allows arrivals of both nodes and hyperedges of random size. At each time step t, two possible events may occur: (1) [vertex arrival event:] with probability p > 0 a new vertex arrives and a new hyperedge of size yt, containing the new vertex and Yt-1 existing vertices, is added to the hypergraph; or (2) [hyperedge arrival event:] with probability 1-p, a new hyperedge of size Yt, containing Yt existing vertices, is added to the hypergraph. In both cases, the involved existing vertices are chosen independently at random according to the preferential attachment rule, i.e., with probability proportional to their degree, where the degree of a vertex is the number of edges containing it. Assuming general restrictions on the distribution of Yt, we prove that the H(p,Y) model generates power law networks, i.e., the expected fraction of nodes with degree $k$ is proportional to $k$−1-Γ, where $Gamma=limolimits_{tightarrowinfty}rac{Sigma^{t-1}_{i=0}mathbb{E}[Y_{i}]}{t(mathbb{E}[Y_{t}]-ho)}in(0, infty)$. This extends the special case of preferential attachment graphs, where $Y_{t}= 2$ for every t, yielding Γ = 2/ (2- p). Therefore, our results show that the exponent of the degree distribution is sensitive to whether one considers the structure of a social network to be a hypergraph or a graph. We discuss, and provide examples for, the implications of these considerations.
机译：将来，可以想象社交网络的分析将从图到超图。但是，理论尚未赶上这种类型的数据组织结构。通过介绍和分析偏好依附性超图的通用模型，本文朝着缩小这一差距迈出了一步。我们考虑用于网络演化的随机优先附着模型H（p，Y），该模型允许节点的到达以及随机大小的超边缘。在每个时间步长t处，可能发生两个可能的事件：（1）[顶点到达事件：]概率p> 0时，出现了一个新的顶点，并且出现了一个大小为y的新超边 t ，包含新的顶点和Y t 将-1个现有顶点添加到超图中;或（2）[超边缘到达事件：]的概率为1-p，即大小为Y的新超边缘 t ，包含Y t 现有顶点被添加到超图中。在这两种情况下，所涉及的现有顶点都是根据优先依附规则独立地随机选择的，即概率与它们的程度成正比，其中顶点的程度是包含它的边的数量。假设对Y的分配有一般限制 t ，我们证明了H（p，Y）模型会生成幂律网络，即具有度数的节点的期望分数 $ k $ 与...成正比 $ k $ −1-Γ ， 在哪里 $ \ Gamma = \ lim \ nolimits_ {t \ rightarrow \ infty} \ frac {\ Sigma ^ {t-1} _ {i = 0} \ mathbb {E} [Y_ {i}]} {t（\ mathbb {E} [Y_ {t} ]-\ rho）} \ in（0，\ infty）$ 。这扩展了优先附件图的特殊情况，其中 $ Y_ {t} = 2 $ 对于每t，得出Γ= 2 /（2- p）。因此，我们的结果表明，度分布的指数对于是否将社交网络的结构视为超图或图是敏感的。我们讨论了这些注意事项并提供了示例。

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