生长网络模型的特征和异质性
Features and heterogeneities in growing network models
摘要：
从万维网到生物网络的许多复杂网络都考虑到了节点的异质性。一个节点的特征可以是一个离散的量，例如一个URL文档的分类，如个人页面，主题网站，新闻，博客，搜索引擎，社交网络等。或功能模块中基因的分类。此外，节点的特征可以是连续变量，诸如节点在嵌入空间中的位置。为了说明这些属性，在本文中，我们提供了一个泛化的增长网络模型的优先连接，包括异构功能的节点的效果。异质性的主要影响是每类节点的“有效适应度”的出现，决定了节点获得新链接的速度。度分布表现出类似于适应度模型的多尺度行为。只要链接是通过有效的优先连接来分配的，这个属性对于模型中的变化是鲁棒的。除了度分布之外，本文还给出了模型的其他相关性质的完整刻画。我们评估的聚类系数，并表明，它消失了大的网络规模，与巴拉巴西-阿尔伯特模型共享的属性。负度相关性也存在于所研究的一类模型中，以及特征之间的非平凡混合模式。因此，我们得出结论，小的聚类系数和dispersionative混合的结果，在一般的增长网络的优先连接机制。
英文摘要：
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as personal page, thematic website, news, blog, search engine, social network, ect. or the classification of a gene in a functional module. Moreover the feature of a node can be a continuous variable such as the position of a node in the embedding space. In order to account for these properties, in this paper we provide a generalization of growing network models with preferential attachment that includes the effect of heterogeneous features of the nodes. The main effect of heterogeneity is the emergence of an "effective fitness" for each class of nodes, determining the rate at which nodes acquire new links. The degree distribution exhibits a multiscaling behaviour analogous to the the fitness model. This property is robust with respect to variations in the model, as long as links are assigned through effective preferential attachment. Beyond the degree distribution, in this paper we give a full characterization of the other relevant properties of the model. We evaluate the clustering coefficient and show that it disappears for large network size, a property shared with the Barabási-Albert model. Negative degree correlations are also present in the studied class of models, along with non-trivial mixing patterns among features. We therefore conclude that both small clustering coefficients and disassortative mixing are outcomes of the preferential attachment mechanism in general growing networks.
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