The analysis of biological networks allows the understanding of many biological processes, including the structure, function, interaction and evolutionary relationships of their components. One of the most important concepts in biological network analysis is that of network motifs, which are patterns of interconnections that occur in a given network at a frequency higher than expected in a random network. In this work we are interested in searching and inferring network motifs in a class of biological networks that can be represented by vertex-colored graphs. We show the computational complexity for many problems related to colorful topological motifs and present efficient algorithms for special cases. A colorful motif can be represented by a graph in which each vertex has a different color. We also present a probabilistic strategy to detect highly frequent motifs in vertex-colored graphs. Experiments on real data sets show that our algorithms are very competitive both in efficiency and in quality of the solutions.

中文翻译：

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在顶点彩色图中搜索和推断多彩的拓扑图案

通过对生物网络的分析，可以了解许多生物过程，包括其组成部分的结构，功能，相互作用和进化关系。生物网络分析中最重要的概念之一是网络主题，它们是在给定网络中发生的互连模式，其频率高于随机网络中的预期频率。在这项工作中，我们感兴趣的是搜索和推断可以用顶点彩色图表示的一类生物网络中的网络主题。我们展示了与彩色拓扑图案相关的许多问题的计算复杂性，并针对特殊情况提出了有效的算法。彩色图案可以由其中每个顶点具有不同颜色的图形表示。我们还提出了一种概率策略，以检测顶点彩色图中的频繁出现的图案。在真实数据集上的实验表明，我们的算法在解决方案的效率和质量上都非常有竞争力。