Centrality measures for simple graphs are well-defined and several main-memory algorithms exist for each. Simple graphs are not adequate for modeling complex data sets with multiple entities and relationships. Multilayer networks (MLNs) have been shown to be better suited, but there are very few algorithms for centrality computation directly on MLNs. They are converted (aggregated or collapsed) to simple graphs using Boolean AND or OR operators to compute centrality, which is not only inefficient but incurs a loss of structure and semantics. In this paper, we propose algorithms that compute closeness centrality on an MLN directly using a novel decoupling-based approach. Individual results of layers (or simple graphs) of an MLN are used and a composition function developed to compute the centrality for the MLN. The challenge is to do this accurately and efficiently. However, since these algorithms do not have complete information of the MLN, computing a global measure such as closeness centrality is a challenge. Hence, these algorithms rely on heuristics derived from intuition. The advantage is that this approach lends itself to parallelism and is more efficient compared to the traditional approach. We present two heuristics for composition and experimentally validate accuracy and efficiency on a large number of synthetic and real-world graphs with diverse characteristics.

翻译：简单图上的中心性度量定义明确，且每种度量均存在多种内存计算算法。然而，简单图难以对具有多重实体和关系的复杂数据集进行建模。尽管多层网络（MLNs）已被证明更适合此类建模，但直接针对MLNs进行中心性计算的算法却极为稀少。现有方法通常通过布尔AND或OR算子将MLNs转换（聚合或折叠）为简单图后再计算中心性，这不仅效率低下，还会导致结构与语义的损失。本文提出一种基于解耦的新方法，可直接在MLNs上计算紧密中心性。该方法利用MLN各层（即简单图）的个体结果，并构建组合函数来计算整个多层网络的中心性。其挑战在于需兼顾准确性与效率。由于此类算法不具备MLN的完整信息，计算全局度量（如紧密中心性）尤为困难，因此算法依赖基于直觉的启发式策略。该方法的优势在于天然支持并行化，且相较传统方法更具效率。我们提出两种组合启发式策略，并通过大量具有不同特征的合成图与真实图实验，验证了其准确性与效率。