A is one of the important network parameters to describe clustering characteristics around a node in a network. It accounts for the number of cycles of length 3 (triangles) relative to the number of paths of length 2 in which this node participates as their inner node. In practice, the number of longer paths and cycles may be larger than the number of 2-paths and 3-cycles, thereby requiring its generalized version. In this paper, we aim at proposing the so-called - to characterize the node clustering tendency at level . We define it by counting the number of -cycles relative to the number of ()-paths containing a fixed inner node. In addition, we introduce the by considering the total number of all cycles relative to the total number of all paths consisting of this inner node. We formulate these generalized clustering coefficients for each of the following cases: undirected and unweighted networks, undirected but weighted networks, directed but unweighted networks, and directed and weighted networks. We then implement them for correlation- and conditional risk measure-based networks that represent conventional cryptocurrency markets and stablecoin markets. They can be viewed as new . The larger their values, the larger the tendency of risk transmission from one market to other subsequent markets forming longer cycles, and therefore the higher the systemic risk level. The systemic risk quantification is appropriate when they fulfill certain properties. In summary, the novelty of this study lies in the mathematical formulation of the generalized clustering coefficients and their computation for the cryptocoin networks with the purpose of appropriately managing systemic risk in the represented cryptocoin markets.

中文翻译：

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（无向）定向和（无）加权网络中聚类的广义系数：加密货币市场系统风险量化的应用


A是描述网络中节点周围聚类特征的重要网络参数之一。它说明了长度为 3（三角形）的循环数相对于该节点作为内部节点参与的长度为 2 的路径数。在实践中，较长路径和周期的数量可能大于2路径和3周期的数量，因此需要其通用版本。在本文中，我们旨在提出所谓的“在水平上表征节点聚类趋势”。我们通过计算相对于包含固定内部节点的 () 路径数量的 循环数量来定义它。此外，我们通过考虑所有循环的总数相对于由该内部节点组成的所有路径的总数来引入 。我们为以下每种情况制定这些广义聚类系数：无向和无权网络、无向但加权网络、有向但未加权网络以及有向和加权网络。然后，我们将它们应用于代表传统加密货币市场和稳定币市场的基于相关性和条件风险测量的网络。它们可以被视为新的。它们的值越大，表明风险从一个市场向其他后续市场传导并形成较长周期的倾向越大，系统性风险水平越高。当系统风险满足某些属性时，系统风险量化是合适的。总之，本研究的新颖性在于加密货币网络的广义聚类系数的数学公式及其计算，目的是适当管理所代表的加密货币市场中的系统性风险。