Mrowinski Maciej J, Orzechowski Kamil P, Fronczak Agata, Fronczak Piotr
Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland.
Sci Rep. 2024 Apr 3;14(1):7811. doi: 10.1038/s41598-024-58357-4.
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.
格兰诺维特的弱关系理论是一个非常重要的社会学理论，据此，边权重与网络拓扑结构之间应该存在相关性。更具体地说，由一条边连接的两个节点的邻域重叠应该与边权重（关系强度）呈正相关。然而，一些真实的社会网络呈现出负相关——最突出的例子是科学合作网络，其重叠随着边权重的增加而减少。已经证明，通过使用非对称度量，上述与格兰诺维特理论的不一致在科学合作网络中可以得到缓解。在本文中，我们解释了虽然非对称度量通常对于描述复杂网络和证实格兰诺维特理论是必要的，但其解释并不简单，并且存在一些必须警惕的陷阱。非对称权重和重叠的定义引入了必须被过滤掉的结构相关性。我们表明相关轮廓可用于克服这个问题。使用这种技术，我们不仅在各种真实和人工社会网络中证实了格兰诺维特理论，而且还表明类似格兰诺维特的权重 - 拓扑相关性存在于其他复杂网络（例如代谢网络和神经网络）中。我们的结果表明，格兰诺维特理论是支配各种类型复杂网络的更一般原则的社会学表现。
