The identification and counting of small graph patterns, called network motifs, is a fundamental primitive in the analysis of networks, with application in various domains, from social networks to neuroscience. Several techniques have been designed to count the occurrences of motifs in static networks, with recent work focusing on the computational challenges provided by large networks. Modern networked datasets contain rich information, such as the time at which the events modeled by the networks edges happened, which can provide useful insights into the process modeled by the network. The analysis of motifs in temporal networks, called temporal motifs, is becoming an important component in the analysis of modern networked datasets. Several methods have been recently designed to count the number of instances of temporal motifs in temporal networks, which is even more challenging than its counterpart for static networks. Such methods are either exact, and not applicable to large networks, or approximate, but provide only weak guarantees on the estimates they produce and do not scale to very large networks. In this work we present an efficient and scalable algorithm to obtain rigorous approximations of the count of temporal motifs. Our algorithm is based on a simple but effective sampling approach, which renders our algorithm practical for very large datasets. Our extensive experimental evaluation shows that our algorithm provides estimates of temporal motif counts which are more accurate than the state-of-the-art sampling algorithms, with significantly lower running time than exact approaches, enabling the study of temporal motifs, of size larger than the ones considered in previous works, on billion edges networks.
翻译:小图案模式的识别和计算,称为网络图案,是分析从社交网络到神经科学等不同领域应用的网络的一个根本原始部分。一些技术的设计是为了计算静态网络中出现的情况,最近的工作重点是大型网络提供的计算挑战。现代网络数据集包含丰富的信息,例如网络边缘所模拟事件发生的时间,可以提供对网络模型所建过程的有用洞察。时间网络模型模型模型模型模型的分析,正在成为现代网络数据集分析中的一个重要组成部分。最近设计了几种方法来计算时间网络中出现的时间图案的数量,这些方法甚至比静态网络的对应数据更具挑战性。这些方法要么精确,对大型网络不适用,或者近似,但只能对它们生成的估计数提供薄弱的保证,而不能对非常大的网络规模进行保证。在这项工作中,我们对时间模型模型模型的精确度的精确度进行高效和可缩缩略的算,在对时间模型的精确度的计算中,我们的模型的精确度比实际模型的精确度的精确性计算要大。我们的算算法提供了一种简单的数据,而我们之前的精确的精确的算算算法则是我们之前的精确的精确的精确的精确的精确算法。我们的精确算法,我们的数据是用来进行一个简单的精确的精确的模型。我们的精确的精确的计算方法。我们的精确的精确的精确的算算法。我们的精确的精确的计算法是用来的。我们的精确的计算方法。我们的精确的计算方法。我们的精确的计算方法。我们的精确的精确的精确的精确的计算方法。