Centrality has no single definition—it depends on the network, its dynamics, and context. This has led to a “zoo” of diverse centrality measures used to analyze complex networks.
Zoo of Centralities

This page provides a verified list of various metrics for nodes. While some, such as the clustering coefficient, are not centrality measures, they all quantify important properties of nodes within a network. Detailed descriptions will be available on their dedicated pages soon. If you have developed or contributed to a centrality measure that you believe should be included, please submit it through this form.

  1. k-betweenness centrality
  2. k-path centrality
  3. k-shell based on gravity centrality (KSGC)
  4. k-shell centrality
  5. k-shell hybrid method (ksh)
  6. k-shell iteration factor (KS-IF)
  7. k-shell Physarum centrality
  8. k-truss index
  9. m-reach centrality
  10. p-means centrality
  11. s-shell index
  12. X-degree centrality
  13. X-non-backtracking (X-NB) centrality
  14. Absorbing random-walk (ARW) centrality
  15. Access information
  16. Adaptive LeaderRank
  17. Adaptive omni-channel gravity centrality (AOGC)
  18. Adjusted Index of Centrality (AIC)
  19. Algebraic centrality
  20. All cycle betweenness (ACC) centrality
  21. All-around score
  22. Analytic Hierarchy Process (AHP) centrality
  23. ArticleRank
  24. Attentive betweenness centrality (ABC)
  25. Average shortest path centrality (AC)
  26. Balanced centrality (SWIPD)
  27. Betweenness centrality
  28. BG-index
  29. Biased random walk (BRW) centrality
  30. Bipartivity index
  31. Borda centrality
  32. Borgatti's effective size
  33. BottleNeck centrality
  34. BridgeRank
  35. Bridging capital
  36. Bridging centrality
  37. Bridging coefficient
  38. Bundle index
  39. Burt's constraint
  40. Cc-Burt centrality
  41. Centroid centrality
  42. Classified neighbors centrality
  43. Clique level
  44. Closeness centrality
  45. Closeness vitality
  46. Clustered local-degree (CLD)
  47. Clustering degree algorithm (CDA)
  48. ClusterRank centrality
  49. Coleman-Theil disorder index
  50. Collective influence
  51. Collective network entanglement (CNE)
  52. Comm Centrality
  53. Common out-neighbor (CON) score
  54. Communicability betweenness centrality
  55. Community centrality
  56. Community hub-bridge (CHB) measure
  57. Community-based centrality (CbC)
  58. Community-based mediator (CbM)
  59. Contribution centrality
  60. ControlRank
  61. Copeland centrality
  62. CoreHD
  63. Correlation centrality (CoC)
  64. Counting betweenness centrality (CBET)
  65. Cross-clique connectivity
  66. Cumulative Contact Probability (CCP)
  67. Current-flow betweenness centrality
  68. Current-flow closeness centrality
  69. Curvature index
  70. Decay centrality
  71. Decaying degree centrality (DDC)
  72. Degree and clustering coefficient (DCC) centrality
  73. Degree and clustering coefficient and location (DCL) centrality
  74. Degree and Importance of Lines (DIL)
  75. Degree and structural hole count (DSHC) method
  76. Degree centrality
  77. Degree mass
  78. DegreeDiscountIC
  79. DegreeDistance
  80. DegreePunishment
  81. Density centrality
  82. Density of the Maximum Neighborhood Component (DMNC)
  83. Diffusion centrality
  84. Diffusion degree
  85. DirichletRank
  86. Disassortativity and community structure (mDC) centrality
  87. Disassortativity of node (DoN)
  88. Distance entropy (DE)
  89. Distance-weighted fragmentation (DF)
  90. Diversity coefficient
  91. Diversity-strength centrality (DSC)
  92. Diversity-strength ranking (DSR)
  93. DK-based gravity model (DKGM)
  94. DomiRank centrality
  95. Dynamical importance
  96. Dynamical influence
  97. Dynamical spanning tree (DST) centrality
  98. Dynamics-sensitive (DS) centrality
  99. Eccentricity centrality
  100. Edge clustering coefficient (NC)
  101. Edge Percolated Component (EPC)
  102. Edge-disjoint k-path centrality
  103. Effective distance closeness centrality (EDCC)
  104. Effective distance gravity model (EffG)
  105. Effective gravity model (EGM)
  106. Effective Size (ES)
  107. Efficiency centrality (EffC)
  108. Egocentric betweenness centrality
  109. Eigentrust centrality
  110. Eigenvector centrality
  111. Electrical closeness centrality
  112. Endpoint betweenness centrality
  113. EnRenew
  114. Entropy and mutual information-based centrality (EMI)
  115. Entropy centrality
  116. Entropy variation (EnV)
  117. Entropy-based gravity model (EGM)
  118. Entropy-based influence disseminator (EbID)
  119. Entropy-based ranking measure (ERM)
  120. Entropy-Burt method (E-Burt)
  121. Even subgraph centrality
  122. Exogenous centrality
  123. Expected Force (ExF)
  124. Expected rank
  125. Extended h-index centrality (EHC)
  126. Extended k-shell hybrid method
  127. Extended cluster coefficient ranking measure (ECRM)
  128. Extended diversity-strength ranking (EDSR)
  129. Extended gravity centrality (EGC)
  130. Extended hybrid characteristic centrality (EHCC)
  131. Extended hybrid degree and k-shell method
  132. Extended hybrid degree and MDD method
  133. Extended improved k-shell hybrid method
  134. Extended local bridging centrality (ELBC)
  135. Extended local dimension (ELD)
  136. Extended mixed gravitational centrality (EMGC)
  137. Extended neighborhood coreness
  138. Extended RMD-weighted degree (EWD) centrality
  139. Extended weight degree centrality (EWDC)
  140. Fitness centrality
  141. Flow betweenness centrality
  142. Flow coefficient
  143. Fractional graph Fourier transform centrality (FrGFTC)
  144. Functional centrality
  145. Fusion gravity model (FGM)
  146. Fuzzy local dimension (FLD)
  147. Game centrality (GC)
  148. Gateway coefficient
  149. Generalized degree centrality
  150. Generalized gravity centrality (GGC)
  151. Generalized network dismantling (GND) method
  152. Generalized subgraph centrality (GSC)
  153. Geodesic k-path centrality
  154. Gil-Schmidt power index
  155. Global and local information (GLI) method
  156. Global and local structure (GLS) centrality
  157. Global importance of nodes (GIN)
  158. Global Structure Model (GSM)
  159. Godfather index
  160. Graph Fourier Transform Centrality (GFT-C)
  161. Graph regularization centrality (GRC)
  162. Graph-theoretic power index (GPI)
  163. Graphlet degree centrality (GDC)
  164. Gravity centrality
  165. Gravity model
  166. Gromov centrality
  167. h-index strength
  168. Harmonic centrality
  169. Heatmap centrality
  170. Hide information
  171. Hierarchical k-shell (HKS) centrality
  172. Hierarchical reduction by betweenness
  173. HITS (Hubs and Authorities)
  174. Hubbel centrality
  175. Hybrid centrality (HC)
  176. Hybrid centrality measure (X)
  177. Hybrid centrality measure (XmY)
  178. Hybrid centrality measure (XpY)
  179. Hybrid centrality measure (Y)
  180. Hybrid characteristic centrality (HCC)
  181. Hybrid degree and k-shell method
  182. Hybrid degree and MDD method
  183. Hybrid degree centrality
  184. Hybrid global structure model (H-GSM)
  185. Hybrid median centrality (HMC)
  186. HybridRank
  187. Immediate Effects Centrality (IEC)
  188. Improved k-shell algorithm (IKS)
  189. Improved k-shell decomposition (IKSD) method
  190. Improved k-shell hybrid method (IKH)
  191. Improved closeness centrality (ICC)
  192. Improved distance-based coloring method (IIS)
  193. Improved entropy-based centrality
  194. Improved Global Structure Model (IGSM)
  195. Improved iterative resource allocation (IIRA) method
  196. Improved neighbors’ k-core (INK)
  197. Improved node contraction (IIMC) centrality
  198. Improved WVoteRank centrality
  199. Independent set (IS) method
  200. Index of CENTRality (Icentr)
  201. INF centrality
  202. Infection number
  203. Influence capability (IC)
  204. Information distance index (IDI)
  205. Integral k-shell centrality
  206. Integration centrality
  207. Interdependence centrality
  208. Intra-module degree (IMD)
  209. Inward accessibility
  210. Isolating centrality (ISC)
  211. Iterative resource allocation (IRA) method
  212. Katz centrality
  213. KDEC method
  214. KED method
  215. Laplacian centrality
  216. Laplacian gravity centrality
  217. LeaderRank
  218. Length-scaled betweenness centrality (LSBC)
  219. Leverage centrality
  220. Lhc index
  221. Lin's index
  222. Linearly scaled betweenness centrality
  223. LineRank
  224. Link influence entropy (LInE) centrality
  225. Load centrality
  226. Lobby index
  227. Local and global centrality (LGC)
  228. Local clustering coefficient
  229. Local degree dimension (LDD)
  230. Local dimension (LD)
  231. Local entropy (LE) centrality
  232. Local fuzzy information centrality (LFIC)
  233. Local gravity model
  234. Local H-index
  235. Local information dimensionality (LID)
  236. Local neighbor contribution (LNC) centrality
  237. Local reaching centrality
  238. Local relative change of average shortest path (LRASP) centrality
  239. Local structural centrality (LSC)
  240. Local volume dimension (LVD)
  241. Localized bridging centrality (LBC)
  242. LocalRank centrality
  243. Long-Range Interaction Centrality (LRIC)
  244. M-centrality
  245. Malatya centrality
  246. Map equation centrality
  247. Mapping entropy (ME) centrality
  248. Mapping entropy betweenness (MEB) centrality
  249. Markov centrality
  250. Markov entropy centrality
  251. Maximal Clique Centrality (MCC)
  252. Maximum Neighborhood Component (MNC)
  253. Mediative effects centrality (MEC)
  254. Message-passing approach
  255. Meta-centrality
  256. Mixed core, degree and entropy (MCDE) method
  257. Mixed core, degree and weighted entropy (MCDWE) method
  258. Mixed core, semi-local degree and entropy (MCSDE) method
  259. Mixed core, semi-local degree and weighted entropy (MCSDWE) method
  260. Mixed degree decomposition (MDD)
  261. Mixed gravitational centrality
  262. Modified Expected Force (ExF^M)
  263. Modified local centrality (MLC)
  264. ModuLand centrality
  265. Modularity centrality
  266. Modularity density centrality
  267. Modularity vitality
  268. Multi-attribute ranking method based on information entropy (MABIE)
  269. Multi-characteristics gravity model (MCGM)
  270. Multi-criteria influence maximization (MCIM) method
  271. Multi-local dimension (MLD) centrality
  272. Multiple local attributes weighted centrality (LWC)
  273. Mutual information centrality
  274. NCVoteRank
  275. Neighbor distance centrality
  276. Neighborhood centrality
  277. Neighborhood connectivity
  278. Neighborhood core diversity centrality (Cncd)
  279. Neighborhood density (ND)
  280. Neighborhood structure-based centrality (NSC)
  281. Network global structure-based centrality (NGSC)
  282. New Evidential Centrality (NEC)
  283. Nieminen's closeness centrality
  284. NL centrality
  285. Node and neighbor layer information (NINL) centrality
  286. Node contraction (IMC) centrality
  287. Node importance contribution correlation matrix (NICCM) method
  288. Node importance contribution matrix (NICM) method
  289. Node importance evaluation matrix (NIEM) method
  290. Node information dimension (NID)
  291. Node local centrality (NLC)
  292. Non-backtracking centrality
  293. Normalized local centrality (NLC)
  294. Normalized wide network ranking (NWRank)
  295. Odd subgraph centrality
  296. Outward accessibility
  297. PageRank
  298. Pairwise disconnectivity centrality
  299. Participation coefficient
  300. Partition-based spreaders identification (PBSI) method
  301. Path-transfer centrality
  302. PathRank
  303. Percolation centrality
  304. Physarum centrality
  305. PhysarumSpreader
  306. Pivotal index
  307. Principal component centrality (PCC)
  308. Probabilistic-jumping random walk (PJRW) centrality
  309. ProfitLeader
  310. Proximal betweenness centrality
  311. Quantum Jensen-Shannon Divergence (QJSD) centrality
  312. Quasi-Laplacian centrality (QC)
  313. Radiality centrality
  314. Random walk accessibility (RWA)
  315. Random walk centrality (RWC)
  316. Random walk decay (RWD) centrality
  317. Random walk-based gravity (RWG) centrality
  318. Randomized shortest paths (RSP) betweenness centrality
  319. Randomized shortest paths (RSP) net betweenness centrality
  320. Rank centrality
  321. Ranking-betweenness centrality
  322. Rapid identifying method (RIM)
  323. Redundancy measure
  324. Relative entropy
  325. Relative local-global importance (RLGI) measure
  326. Renewed coreness centrality
  327. Residual closeness centrality
  328. Resilience centrality
  329. Resistance curvature
  330. Resolvent betweenness (RB) centrality
  331. Resolvent centrality
  332. Return Random Walk Gravity (RRWG) centrality
  333. RMD-weighted degree (WD) centrality
  334. Routing betweenness centrality (RBC)
  335. Rumor centrality
  336. Second-order centrality
  337. Seeley’s index
  338. Semi-global triangular centrality
  339. Semi-local degree and clustering coefficient (SLDCC)
  340. Semi-local iterative algorithm (semi-IA)
  341. Semi-local ranking centrality (SLC)
  342. Shapley value
  343. Shapley value based information delimiters (SVID)
  344. Shell clustering coefficient (SCC)
  345. Short-Range Interaction Centrality (SRIC)
  346. Shortest cycle closeness (SCC) centrality
  347. Silent node rank (SNR)
  348. Similarity-based PageRank
  349. Simulations-based LRIC (LRIC-sim) index
  350. SingleDiscount
  351. Spanning tree centrality (STC)
  352. SpectralRank (SR)
  353. Spreading probability (SP) centrality
  354. Spreading strength
  355. Stochastic Approach for Link Structure Analysis (SALSA)
  356. Stress centrality
  357. Subgraph centrality
  358. Super mediator degree (SMD)
  359. Support
  360. Synthesize centrality (SC)
  361. Third Laplacian energy centrality (LC)
  362. Topological centrality (TC)
  363. Topological coefficient
  364. TOPSIS centrality
  365. TOPSIS-RE centrality
  366. Total centrality
  367. Total communicability centrality (TCC)
  368. Total effects centrality (TEC)
  369. Transportation centrality (TC)
  370. Trophic level centrality
  371. Truncated curvature index
  372. Trust-PageRank
  373. Two-step framework (IF) centrality
  374. Two-way random walk betweenness (2RW) centrality
  375. Vertex Entanglement (VE)
  376. Vertex-disjoint k-path
  377. ViralRank
  378. VMM algorithm
  379. Volume centrality
  380. VoteRank centrality
  381. VoteRank^++ centrality
  382. Weight degree centrality (WDC, Liu)
  383. Weight neighborhood centrality
  384. Weighted h-index
  385. Weighted k-shell decomposition (Wks) centrality
  386. Weighted k-shell degree neighborhood (Wksd)
  387. Weighted k-shell degree neighborhood (WKSDN)
  388. Weighted k-short node-disjoint paths (WKPaths) centrality
  389. Weighted community betweenness (WCB) centrality
  390. Weighted formal concept analysis (WFCA)
  391. Weighted gravity model (WGravity)
  392. Weighted LeaderRank
  393. Weighted TOPSIS (w-TOPSIS) centrality
  394. Weighted volume centrality
  395. Wide ranking (WRank)
  396. WVoteRank
  397. Zeta vector centrality
  398. δ-betweenness centrality
  399. δ-closeness centrality
  400. ε-betweenness centrality
  401. θ-Centrality
  402. μ-Power Community Index (μ-PCI)