-
Complex networks serve as indispensable instruments for characterizing and understanding intricate real-world systems. Recently, researchers have delved into the realm of higher-order networks, seeking to delineate interactions within these networks with greater precision or analyze traditional pairwise networks from a higher-dimensional perspective. This effort has unearthed some new phenomena different from those observed in the traditional pairwise networks. However, despite the importance of higher-order networks, research in this area is still in its infancy. In addition, the complexity of higher-order interactions and the lack of standardized definitions for structure-based statistical indicators, also pose challenges to the investigation of higher-order networks. In recognition of these challenges, this paper presents a comprehensive survey of commonly employed statistics and their underlying physical significance in two prevalent types of higher-order networks: hypergraphs and simplicial complex networks. This paper not only outlines the specific calculation methods and application scenarios of these statistical indicators, but also provides a glimpse into future research trends. This comprehensive overview serves as a valuable resource for beginners or cross-disciplinary researchers interested in higher-order networks, enabling them to swiftly grasp the fundamental statistics pertaining to these advanced structures. By promoting a deeper understanding of higher-order networks, this paper facilitates quantitative analysis of their structural characteristics and provides guidance for researchers who aim to develop new statistical methods for higher-order networks.
-
Keywords:
- higher-order network/
- hypergraph/
- simplicial network/
- statistics
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] -
指标类型 指标名称 度相关指标 度、超度、超边度、余平均度 聚集系数 节点的聚集系数、网络的聚集系数 距离相关指标 路径长度、超节点之间的距离 密度相关指标 超边密度、超图密度 曲率相关指标 Forman-Ricci曲率、Ollivier-Ricci曲率 中心性指标 度中心性、核心度中心性、接近中心性、
介数中心性、特征向量中心性熵相关指标 超图熵、超图的香农熵、加权超图的超图熵 
DownLoad:
CSV
指标类型 指标名称 度相关指标 上邻接度、下邻接度、度、上p邻接度、下p邻接度、严格上p邻接度、严格下p邻接度、
上$(h, p)$邻接度、下$(h, p)$邻接度、p邻接度、最大p邻接度、最大单纯形度路径和距离相关指标 $s_k$游走、p游走、最短路径长度、离心率、直径 中心性指标 度中心性、特征向量中心性、Katz中心性、接近中心性、介数中心性 聚集系数 聚集系数 拓扑不变量 贝蒂数、欧拉示性数 DownLoad:
CSV
-
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109]
DownLoad:
Catalog
Metrics
- Abstract views:1960
- PDF Downloads:226
- Cited By:0