Analysing and modelling editors’ behavior of different languages in Wikimedia projects

Anita Chandra, Department of Computer Science and Engineering, IIT Patna Email: [email protected]

I.INTRODUCTIONAND MOTIVATION After Solving previous ordinary differential Eq., at initial In this research work, we compare behaviors of editors in condition ka(t0) = 0. We get, different languages in Wikimedia projects. We consider 12 r r −(1+ r ) p(k) = (k0) s (k + k0) s Wiki datasets which include 4 different projects of Wikimedia s namely Wikipedia, Wikibook, Wikinews, and Wiktionary in Where, r = (c + wγe)(c + wγi), s = mc + mwγi + nc + different languages. Here, we report similarities and differ- nwγe, k0 = (mγec+mwγeγi +nγic+nwγeγi)/s, c = m+n. ences in editing behaviors of english, french and german The results given in Fig 1 show good agreement between editors for Wikibook and Wiktionary only. Because of the data and model with fitted parameters (estimated all the multilingual nature of Wikis, millions of editors contribute parameters of model i.e, m, n, w, γe and γi from datasets) for from all across the continents who have diverse cultures Wikibook (en,fr) and Wiktionary (en,fr,de). From the Fig 1a and backgrounds. Consequently, this provides a scope of and 1b, we observe that γi < γe in Wikibook (E) which comparison among editors of different languages which also means old English editors edit popular or well known books sheds light on multilingual and multicultural editors’ behav- than new editors while in Wikibook (F) editing behaviors ior. Here, we attempt to show that the differences observed of french editors are opposite. From Fig 1c, 1d and 1e we in the physical world, also exist in the virtual world. have γi > γe in every language of Wiktionary, that means new english, french and german editors always prefer to edit II.PRELIMINARY RESULTS popular dictionary words while old editors edit less known Wiki data are represented as bipartite network, where words. Hence we observe different editing behaviors in new two disjoint sets are editors and edited objects (arti- and old English and french editors of Wikibook while their cles/books/news/words) and links exist when an editor edits patterns are similar in case of Wiktionary. an article (excluding bot edits). We have given a growth model of evolution of Wiki networks. Since our interest lies 100 100 Data Data -1 in editors’ behavior, we have therefore given the evolution of 10 Model 10-1 Model degree distribution of articles. 10-2 -2

k k 10 p p -3 Model description: The wiki network is represented as 10 γe=30.89, γi=13.89 -3 10 γe=26.8, γi=50.9 triplet G = E, A, Ea , where E and A are two disjoint 10-4 10-4 sets of editors and articles respectively and Ea ⊆ E × A 100 101 102 103 104 105 100 101 102 103 104 is set of edits to articles. Initially, we have e0 editors in E, Degree (k) Degree (k) a articles in A and e edits in E . Let an article a ∈ A 0 a0 a (a) Wikibook (en) (b) Wikibook (fr) such that ka is degree of an article a. Network evolves as, 100 10-1 at each time step, one editor and ‘w’ articles are added and Data Data -1 Model Model edges arrive only from the editors set. Here, we assume that 10 10-2 -2 γ =29.76, γ =38.73 k 10 e i k -3 the arrival of next new editor specifies the next time step. p p 10 γe=40.1, γi=75.3 10-3 Thus, in subsequent time step, a new editor becomes an old -4 10 one. The parameters m and n denote the number of external 10-4 edges brought by a new editor and number of internal edges 100 101 102 103 104 105 100 101 102 103 104 from all old editors respectively. These edges are attached Degree (k) Degree (k) to articles with a combination of preferential and random (c) Wiktionary (en) (d) Wiktionary (fr) 100 mechanism. We have introduced two different randomness Data -1 Model parameters γe and γi for new and old editors respectively. 10 10-2

Attachment kernel for an edge is given as, k

p -3 10 γe=39.9, γi=68.6 Attachment kernel: Let Ae(ka,t) denotes the attachment -4 probability of an incoming edge to an article a at time t 10 -5 where the degree of that article is k . Then A(k ) is the 10 a,t e a,t 100 101 102 103 104 attachment kernel and given as: Degree (k)

ka,t + γ (e) Wiktionary (de) Ae(ka,t) = Pa0+wt a=1 (ka,t + γ) Fig. 1: (a),(b)- Books degree distributions plots for Wikibook From the description of model, change in degree of an (en, fr) from data and model. (c),(d),(e) - Words degree article a is modelled as, distributions plots for Wkitionay (en, fr, de) from data and model. X -axis shows the degree (k) and Y-axis depicts the dka ka + γe ka + γi = m + n probability of having a book and word with degree k (pk). dt Pa0+wt Pa0+wt a=1 ka + γe a=1 ka + γi