Granovetter's weak ties theory is a very important sociological theory according to which a correlation between edge weight and the network's topology should exist. More specifically, the neighbourhood overlap of two nodes connected by an edge should be positively correlated with edge weight (tie strength). However, some real social networks exhibit a negative correlation - the most prominent example is the scientific collaboration network, for which overlap decreases with edge weight. It has been demonstrated that the aforementioned inconsistency with Granovetter's theory can be alleviated in the scientific collaboration network through the use of asymmetric measures. In this paper, we explain that while asymmetric measures are often necessary to describe complex networks and to confirm Granovetter's theory, their interpretation is not simple, and there are pitfalls that one must be wary of. The definitions of asymmetric weights and overlaps introduce structural correlations that must be filtered out. We show that correlation profiles can be used to overcome this problem. Using this technique, not only do we confirm Granovetter's theory in various real and artificial social networks, but we also show that Granovetter-like weight-topology correlations are present in other complex networks (e.g. metabolic and neural networks). Our results suggest that Granovetter's theory is a sociological manifestation of more general principles governing various types of complex networks.

翻译：格兰诺维特的弱连边理论是社会学中的重要理论，该理论认为边权重与网络拓扑结构之间存在关联。具体而言，由边连接的两个节点的邻域重叠程度应与边权重（连边强度）呈正相关。然而，部分真实社交网络却呈现负相关——最典型的例子是科研合作网络，其重叠度随边权重增加而降低。已有研究表明，在科研合作网络中采用非对称度量可以缓解上述与格兰诺维特理论的不一致性。本文阐释了尽管非对称度量通常是描述复杂网络并验证格兰诺维特理论的必要工具，但其解释并不简单，且存在需要警惕的陷阱。非对称权重与重叠度的定义会引入必须滤除的结构相关性。我们证明相关性剖面可有效解决该问题。通过这一技术，我们不仅验证了格兰诺维特理论在多种真实与人工社交网络中的有效性，还揭示了类格兰诺维特的权重-拓扑相关性同样存在于其他复杂网络（如代谢网络与神经网络）中。研究结果表明，格兰诺维特理论是支配各类复杂网络的一般性原理在社会学层面的具体体现。