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Establish the expected number of induced motifs on unlabeled graphs through analytical models
Applied Network Science Pub Date : 2020-09-01 , DOI: 10.1007/s41109-020-00294-y
Emanuele Martorana , Giovanni Micale , Alfredo Ferro , Alfredo Pulvirenti

Complex networks are usually characterized by the presence of small and recurrent patterns of interactions between nodes, called network motifs. These small modules can help to elucidate the structure and the functioning of complex systems. Assessing the statistical significance of a pattern as a motif in a network G is a time consuming task which entails the computation of the expected number of occurrences of the pattern in an ensemble of random graphs preserving some features of G, such as the degree distribution. Recently, few models have been devised to analytically compute expectations of the number of non-induced occurrences of a motif. Less attention has been payed to the harder analysis of induced motifs. Here, we illustrate an analytical model to derive the mean number of occurrences of an induced motif in an unlabeled network with respect to a random graph model. A comprehensive experimental analysis shows the effectiveness of our approach for the computation of the expected number of induced motifs up to 10 nodes. Finally, the proposed method is helpful when running subgraph counting algorithms to get the number of occurrences of a topology become unfeasible.

中文翻译:

通过分析模型在未标记的图形上建立预期的诱导基序数

复杂的网络通常的特征是节点之间存在小而重复的交互模式,称为网络主题。这些小模块可以帮助阐明复杂系统的结构和功能。评估模式在网络G中作为主题的统计显着性是一项耗时的工作,需要计算在保留G的某些特征的一组随机图中,该模式的预期出现次数,例如度分布。最近,很少有人设计模型来分析计算对图案的非诱导出现次数的期望。较少的注意力集中在诱导图案的更难分析上。在这里,我们举例说明了一个分析模型,可以得出相对于随机图模型的未标记网络中诱导基序出现的平均次数。全面的实验分析表明,我们的方法可有效地计算多达10个节点的预期诱导图案数量。最后,所提出的方法在运行子图计数算法以使拓扑出现次数变得不可行时很有帮助。
更新日期:2020-09-01
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