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1 A Method for Measuring Co-authorship Relationships in MediaWiki Libby Veng-Sam Tang Department of Computer and Information Siene Faulty of Siene and Tehnology University of Maau Maau S.A.R., China Tel: Robert P. Biuk-Aghai Department of Computer and Information Siene Faulty of Siene and Tehnology University of Maau Maau S.A.R., China Tel: Simon Fong Department of Computer and Information Siene Faulty of Siene and Tehnology University of Maau Maau S.A.R., China Tel: ABSTRACT Collaborative writing through wikis has beome inreasingly popular in reent years. When users ontribute to a wiki artile they impliitly establish a o-authorship relationship. Disovering these relationships an be of value, for example in finding experts on a given topi. However, it is not trivial to determine the main o-authors for a given author among the potentially thousands who have ontributed to a given author s edit history. We have developed a method and algorithm for alulating a o-authorship degree for a given pair of authors. We have implemented this method as an extension for the MediaWiki system and demonstrate its performane whih is satisfatory in the majority of ases. This paper also presents a method of determining an expertise group for a hosen topi. Categories and Subjet Desriptors I.7.5 [Doument and Text Proessing]: Doument Capture doument analysis, H.3.1 [Information Storage and Retrieval]: Content Analysis and Indexing abstrating methods. General Terms Algorithms, Measurement, Experimentation. Keywords wiki, o-authorship, analysis. 1. INTRODUCTION Working ollaboratively in sholarly writing has been inreasing in the past few deades [5]. The rapid development of omputermediated ommuniation systems failitates and aelerates this working style around the world. Among the systems used for supporting ollaborative writing, wikis have gained popularity and widespread use within the past few years. Wiki systems enable people working in different loations to ommuniate and share their expertise easily. Authors with an interest and expertise in a speifi topi are enabled to ontribute to writing on that topi. When writing on publi wiki sites suh as Wikipedi however, o-authorship emerges as an impliit relationship from working on the same artile, rather than being planned from the outset as is the ase in traditional ollaborative writing. Coauthorship of a paper an be thought of as doumenting a ollaboration between two or more authors [14]. Consider the situation depited in Figure 1. The four irles represent authors b, and d, and the two boxes represent artiles x and y authored by them. The solid lines onneting authors to artiles indiate that the given author has ontributed to the given artile. As shown, authors a and have ontributed to both artiles x and y, whereas author b has only ontributed to artile x and author d has only ontributed to artile y. Thus there exists a o-authoring relationship among the authors of a given artile, suh as among the group of authors b and in the ase of artile x. However, as we show later, this o-authoring relationship is not equally strong among all members of suh a group. Therefore we analyze o-authorship relationships not on the group level but on the level of pairs of o-authors. In the example given there are five pairs of o-authors, i.e. a mutual oauthorship relationship exists for them, namely for the pairs ( b), ( ), ( d), (b, ) and (, d), represented by the dashed lines onneting authors. Out of these, the pairs ( b) and (b, ) are for o-authoring of artile x only, and the pairs ( d) and (, d) are for o-authoring of artile y only. However, the pair ( ) is for o-authoring both artiles x and y. If we wish to determine how strong the o-authoring ties are for the given o-author pairs, the pair ( ) should sore higher than the other pairs based on the fat that its authors are jointly involved in twie as many artiles. Artile x Artile y Permission to make digital or hard opies of all or part of this work for personal or lassroom use is granted without fee provided that opies are not made or distributed for profit or ommerial advantage and that opies bear this notie and the full itation on the first page. To opy otherwise, or republish, to post on servers or to redistribute to lists, requires prior speifi permission and/or a fee. WikiSym '08, September 8-10, Porto, Portugal. Copyright 2008 ACM /08/09...$5.00. a b d Figure 1. Co-authorship on two artiles x and y

2 A naïve alulation would thus assign twie as high a value for o-authorship for this pair of authors. However, an author may have ontributed to a given artile just one or maybe many times. If, say, authors a and b had ontributed to artile x numerous times, but author a had ontributed to artile y only one, and author had ontributed to both artiles x and y only one eah, the strength of the o-authorship relation should be muh greater for the pair of authors ( b) than for ( ). Other fators too should be taken into onsideration, suh as whether the oauthoring was onurrent or separated in time. Moreover, our disussion above was simplisti in assuming that the strength of a mutual o-authorship relationship for a given pair of authors i and j is idential in eah diretion, i.e. from i to j and from j to i. As explained later, this assumption is not true. In order to alulate the degree of o-authorship that takes all of the above fators into aount we propose a new method in this paper. Disovering o-authorship information an be useful in different areas. Signifiant o-authorship also implies o-expertise, and thus being able to disover the impliit relationship among authors in the wiki helps unover expertise groups whih an be of value when seeking experts in a given area. Based on our method for alulating the degree of o-authorship we have reated suh an appliation that determines a set of experts in a hosen area by searhing for signifiant o-authors on artiles within that area. Another appliation area is in automati doument lassifiation whih has been the subjet of reent researh in library information and siene [16]. Measurement of degree of o-authorship has the potential to be applied in this area to help ategorize douments, suh as unategorized artiles in a wiki system. A further appliation area is for reommender systems where artiles may be reommended to readers based on the o-authorship of an artile being urrently read. The remainder of this paper is organized as follows: Setion 2 reviews the related literature. Setion 3 briefly reviews ore onepts related to o-authorship. Setion 4 presents an analysis of wiki data used by us. Setion 5 then introdues the method and algorithm used in our method of alulating the degree of oauthorship. In Setion 6 we present a ase study of applying our method to the MediaWiki system, and in Setion 7 we evaluate our method in an expertise finder appliation. Finally, Setion 8 onludes this paper. 2. RELATED WORK In reent years, the researh problem of finding o-authorship has reeived muh attention. Most of the work in the literature fouses on analyzing o-authorship by means of graphial visualization and using network analysis. Biuk-Aghai [1] presented a olletion of display layouts for visualizing o-authorship networks in online Wikipedia. The visualizations display relationships between entities, between ategories, and between searh results, respetively. There are generally three shools of underlying tehniques that support visualizing o-authorship, suh as oauthorship network [3], [13], [14], [21], soial network [18], and small-world network [19]. These tehniques are based on the priniples of statistis, graph theory, psyhology and even a ombination of them. In partiular, Huang [7] used soial network algorithms to ompute the o-authorship information into a ustom-built InterRing visualizer for enabling users to understand the aademi ollaboration and knowledge domain of individuals from a omputer siene bibliography database. The purpose is to reate a Researh Quality Framework for assessing the researh quality of individuals and researh groups. Jdidia et al [8] enhaned the algorithm by using a soial evolving graph that iteratively prunes less important ars, together with a hierarhial lustering algorithm, on the artiles from IEEE Infoom onferene proeedings. They show that diret o-authors in the Infoom oauthorship network have a signifiant impat on the Program Committee board. Nasimento, Sander and Pound [12] takled a similar problem on artiles from the ACM SIGMOD ommunity, using soial networks instead. Another similar approah was adopted by Liu et al [10] where a weighted diretional network model is used in whih frequent ollaborations are given higher weight, for enabling users to analyze graphs of o-authorship via a visualization toolkit. Goldenberg and Moore [4] studied oauthorship analysis on medial publiations using Bayes-Net, laiming that it is relatively salable, robust to noise, and supports query results with probabilities. Nevertheless, the data-soure used in the experiments of the above-mentioned artiles mainly omes from DBLP, one of the largest aademi databases of artiles. The massive amount of data is downloaded to loal storage for off-line analysis. Online performane by the graphial visualization tehniques and network analysis was thus not of a onern. For instane, InterRing [7] is a visualizer that draws the results as widgets for visual inspetion in a web version. It may not be suitably integrated into an online interative system suh as a wiki. Likewise in [10] the authors implemented the first version as a web appliation built by Webdot visualization tool, the seond version as a standalone Java swing appliation based on TouhGraph. The other graph model implementations are offline/standalone analysis appliations, as a speialized tool for the users (or analysts) who speifially want to study the oauthorship for visually gaining some insights from the models. However, when working in an online setting suh as in a wiki system, the algorithm for extrating the related authors by oauthorships must be relatively fast. Calulating the degree of oauthorship is an add-on feature for a wiki where users expet to retrieve a list of o-authors ranked by their intensity of ollaboration with a partiular author of a partiular artile. While in suh an appliation senario there is no requirement for extensive graphial displays of relations among o-authors, ease of use and fast speed are of greater importane. In this situation, it is doubtful that graphis-intensive programs as doumented in most of the literature ould meet online response time requirements of general web users, whose tolerane threshold is around two seonds [11]. In this paper we present an alternative for the alulation of degree of o-authorship. 3. ARTICLES IN WIKI We briefly review some key onepts related to wikis. This is based on the popular wiki appliation MediaWiki whih we have hosen to apply our method to. However, the underlying onepts of our method are ommon in all wiki systems that maintain a revision history. The primary entities in a wiki system are: artiles, revisions and authors. The relationships between these entities are shown as an ER diagram in Figure 2. For eah artile there must be at least one

3 Artile Revision 1 M M Figure 2. Relationship between artile, revision and author revision, but it is possible for an artile to have many revisions. Eah revision has exatly one author. Eah author may have many revisions. Thus, there are one-to-many relationships between artile and revision, and between author and revision. 3.1 Artile Wiki systems may ontain many artiles. Eah artile has a title and may also have other attributes. Eah time an artile is modified, a new revision is reated. The latest revision onstitutes the urrent state of the artile. Different authors may modify the artile, thus beoming o-authors. Wiki systems additionally usually provide the onept of ategories for lassifying artiles, suh as in the MediaWiki system. 3.2 Revision Wiki systems maintain a history of an artile s revisions whih may be viewed and ompared. In most wiki systems revisions are immutable and the entire revision history is permanently maintained. Revisions have attributes suh as author, revision date and time, and other details. Revisions of an artile may be retrieved from its history and the details of a revision viewed. When a new revision of an artile is submitted, the submit time, user ID, and other revision information are stored. This revision history data is the main data used in our method. MediaWiki further distinguishes two types of revisions: minor edit and non-minor edit. An author modifying an artile in a MediaWiki system an indiate whether or not the edit is a minor one. Correting spelling, grammar or puntuation are examples of minor edits, whereas adding paragraphs of new text is an example of a non-minor edit. 3.3 Author Authors in a wiki are users who reate or modify artiles. A wiki system may allow anonymous users to author artiles, or may restrit this to registered users only. Registered users have a unique user ID so the user an be identified as the same author. Anonymous users an typially only be identified by the IP address of their omputer, and given that the same IP address may be assigned to different omputers at different times, and that a given omputer may be used by different users at different times, this identifiation effetively is useless in definitely identifying authors. For this reason, this paper mainly fouses on ontributions from registered users, but also onsiders the influene of anonymous users. If two registered authors in the wiki system are authors of the same artile, that is, they have at least one revision eah belonging to the same artile, then a o-authorship relationship exists between them and they are onsidered o-authors. This kind of relationship is measured in our method. 4. DATA ANALYSIS In developing our alulation method we used the popular wiki appliation MediaWiki and data from the well-known Wikipedia site. Wikipedia is a popular online enylopedia whih is written 1 Author ollaboratively by volunteers all around the world in more than 250 languages. General properties of the Wikipedia system and its user ommunity have been analyzed in [15]. Other researh has been done on analyzing artile quality in Wikipedia and found that the ooperative ontent prodution model of Wikipedia results in high artile quality [20]. The reasons why people ontribute effort to Wikipedia without any finanial return have been studied in [17], whih revealed a multi-faeted piture of motivations, inluding mainly feelings of satisfation in doing something useful, and enjoying sharing knowledge with others. Contributions to Wikipedia an also be ategorized by type, suh as adding new ontent, orreting grammatial and spelling mistakes, adding itations/referenes, and ategorizing artiles, et. This diversity of ontributions has resulted in the high quality of muh of Wikipedia ontent. Data dumps of Wikipedia databases are available for download. This enabled us to evaluate our method using atual data. The largest language editions of Wikipedi English, German and Frenh, now have more than 500,000 artiles eah. Their data sets are very large, measuring in the dozens of gigabytes, making the data diffiult to handle and requiring large omputing resoures. A too small language edition, however, would not ontain enough data to make a meaningful evaluation possible. We seleted the Wikipedia Simple English language edition, whih has a mediumsize data set. As of 27 April 2008 it ontained about 27,000 useful artiles. Artile, revision and author are the three main oneptual elements involved in our method. In MediaWiki, artile is alled page and eah page has a unique page ID 1. Also, eah revision has a unique revision ID. The revisions belonging to the same page eah ontain the same page ID. Eah registered user has a unique user name and is assigned a unique user ID. Data related to revisions involved in our method is shown in Table 1. Column REV_ID REV_PAGE REV_USER REV_USER_TEXT Table 1. Revision Desription A unique revision ID of a revision. The page ID of the revision belongs to. User ID of the modifier. User name of the modifier. REV_MINOR_EDIT 1 indiates this revision is only a minor edit and 0 indiates not. REV_TIMESTAMP The modify time of the revision. The data dump used by us is the one from 16 November It ontains 550,812 revision reords in the revision table, belonging to 57,441 pages. The pages are ategorized in different types by namespae. Useful artiles are those whih do not inlude user 1 More speifially, an artile is a page in one of the ontent namespaes, suh as main, that is not a rediret and ontains at least one internal link. See: Manual:Artile. In the remainder of this paper we use the two terms interhangeably when the ontext is the MediaWiki system.

4 Revision - All Revision - Reg. Author Revision - Anonymous Revision - All Revision - Reg. Author Revision - Anonymous Poly. (Revision - All) Poly. (Revision - Reg. Author) Poly. (Revision - Anonymous) Week No. Figure 3. Number of revisions by week (all, registered, and anonymous authors) pages, talk pages, help pages and page redirets. There are about 20,000 useful artiles in this data dump. However, we use all pages, not only useful artiles. About 82% of revisions are submitted by registered authors, the remaining 18% are from anonymous users. In total there are 5,401 registered authors. Of the revisions submitted by registered authors about 34% are nonminor edits. We alulated o-authorship degrees on a weekly basis from the beginning of the wiki data until the date of the data dump. There was no registered author before the 118 th week. The data for the last week, the 322 nd week, was not omplete and only had data of three days. Thus, the analysis only used the data from the 118 th week to the 321 st week, a total period of almost 4 years. Revision is the most important element in our method. The number of revisions over the analysis period is shown in Figure 3. As is shown, revisions by registered authors far outnumber those by anonymous users. At the last day of the data dump, there were only about 17.56% of revisions authored by anonymous users, thus about 4.5 times as many revisions were authored by registered authors than by anonymous users. Table 2. Average number of revisions per page Category of revision Rev./Artile % All % Non-minor edit % Minor edit % Submitted by registered author % Submitted by anonymous author % Over the analysis period, eah artile had an average of nearly 10 revisions. Table 2 shows the result of analyzing all data from the beginning to the last date in the data dump. Slightly over half of all revisions are non-minor edits. The differene between nonminor and minor edits is not signifiant, only about 9%. Over 4/5 of all revisions are submitted by registered authors. Moreover, the growth of numbers of revisions submitted by registered authors is Week No. Figure 4. Inrement of revisions by week (all, registered and anonymous authors) faster than those from anonymous users, as shown in Figure 4. The urve of registered authors is lose and similar to that of all revisions and we an infer that the growth of revisions by registered authors will follow the growth of all revisions, whih in this ase we observe follows an exponential growth path. 5. METHOD AND ALGORITHM We have developed an algorithm for alulating the degree of oauthorship of a pair of authors. The input parameters are the IDs of two registered authors and the output is the degree of oauthorship. Revision information of the entire wiki system is used in this algorithm. All neessary information mentioned in this setion an be retrieved from the revision table in MediaWiki. When an author submits a new revision, the required information is automatially reorded. 5.1 Method Our alulation of degree of o-authorship initially filters author and artile (page) data to eliminate authors and artiles that are irrelevant for our alulation. For a given author, we onsider other authors irrelevant as o-authors if they have only made minor edits on artiles to whih the given author has ontributed; and artiles as irrelevant if the given author has only made minor edits to these. This is to ensure that only signifiant o-authorship relationships are onsidered. For a given author the seletion of o-authors and artiles, and the subsequent alulation of oauthorship degree, is thus made as follows: 1. Obtain the set of all pages edited by author a

5 2. Eliminate the pages from the set of all pages for whih author a has only made minor edits 3. For eah remaining page, obtain the set of other authors 4. For eah set of other authors, eliminate those authors who have only made minor edits 5. For eah page s set of other authors, alulate a page degree 6. Calulate the o-authorship degree from all page degrees The alulation of steps 5 and 6 is explained in detail below. 5.2 Degree The output sought by our method is the degree of o-authorship. This is the result of the funtion d ( b) that maps from a given pair of authors ( b) to a real-numbered value indiating the strength of the o-authorship relationship for the given pair of authors. The larger the degree value, the stronger the relationship, and thus the higher the likelihood that if one author ontributes to an artile the other author will also ontribute to that artile. The range of d is the interval (0, ), i.e. {d: 0 < d < }. The funtion d is not symmetri, i.e. d ( b) is not neessarily equal to d (b, a). The reason for this is that the degree is affeted by the time fator, as explained below. 5.3 Co-Authorship Degree Our method alulates the degree of o-authorship d ( b) for the relationship from author a to o-author b. As b is a o-author of they have jointly authored at least one artile. The total number of jointly authored artiles is denoted as t, where {t: 1 t < }. The alulation of o-authorship degree is defined as: t d( b) = s p( b) (1) Page degree p is the degree of o-authorship of authors a and b on page i only (explained below). Thus, the total degree of oauthorship is the sum of all page degrees for authors a and b. A saling onstant s is used to tune the result to a range suitable for representation. In the ase of two authors a and b who have not o-authored any artile d ( b) = Page Degree Following the definition of 5.3, page degree p of page i for authors a and b is defined as: where p( b) min( n, n ) i= 1 min( m, m ) ia ib ia ib i = ( + k ) ni mi i Lia L L n i is the number of all non-minor edits of page i n ia and n ib are the numbers of non-minor edits of page i by authors a and b, respetively m i is the number of all minor edits of page i m ia and m ib are the numbers of minor edits of page i by authors a and b, respetively ia ib (2) k is a minor edit onstant whih affets the weight of minor edits L ia and L ib are the editing periods of authors a and b on page i, respetively A detailed explanation of eah fator follows n, m: Number of all non-minor, minor edits These are the total numbers of all non-minor and minor edits (i.e. revisions), respetively. These numbers inlude both revisions authored by registered and anonymous authors of a given artile (i.e. page). Although o-authorship of anonymous authors is not measured, they are also authors of a given artile and therefore should be onsidered in the alulation of the page degree min(n a, n b ), min(m a, m b ): Minimum of nonminor, minor edits by authors a and b The numbers of edits made by authors a and b are also separated into non-minor and minor edits. For eah type (non-minor, minor) the smaller number of edits of that type among authors a and b is obtained. This is a measure of the extent of o-authorship of two authors on a given artile. The rationale is that we wish to get a measure of the extent to whih the two authors have atually oauthored, rather than individually authored, the given artile. Thus, if one author performed 100 edits on the artile and the other one only made 1 edit, the extent of ollaborative ontribution to authoring that artile would be onsiderably smaller than if eah had made 50 edits. We thus use the minimum of both values in our alulation min(n a, n b ) / n, min(m a, m b ) / m: Proportion of author ontribution in total This is the proportion of the extent of o-authoring of non-minor and minor edits by the two authors a and b in the given artile, over the total number of revisions of that type of that artile. It indiates the strength of o-authorship for these two authors relative to the ontributions of other authors of the same artile. This is to determine the signifiane of the two authors ontributions to the given artile. Thus if the two authors are the only ontributors to an artile and have eah made 100 edits, this ontribution is signifiantly greater than the ase where they eah made 100 edits but other authors ontributed 1000s of edits. The range of this ratio is the interval (0, 1], i.e. the upper bound is 1 if all revisions were submitted by these two authors only k: Minor edit onstant Non-minor edits are revisions onsidered to be more signifiant ontributions to quantity or quality of an artile whereas minor edits usually only make minor orretions suh as fixing spelling, puntuation and grammar. In determining o-authorship of an artile we onsider non-minor edits to be of greater importane than minor edits and therefore assign the minor edit a lower weight in the alulation of page degree. The minor edit onstant k an be set to a value in the interval [0, 1] to give minor edit oauthorship a value ranging from no weight at all to equal weight with non-minor edit o-authorship. We use a value of k = 0.05, i.e. minor edits have only 5% of the weight of non-minor edits, a value that appeared to us to be reasonable onsidering the low signifiane of edits labeled as minor in Wikipedia.

6 5.4.5 L: Authoring period of a given author For someone to be onsidered an author of an artile, we onsider not only the portion of their ontributions in terms of revisions made by them, but also the length of time over whih they have ontributed to an artile relative to the length of time this artile has been in existene. That is, if an author makes ontributions to an artile only during a short period it will be onsidered less than if that author had made ontributions over a longer period of time. The rationale is that a given author s influene on an artile exists only during the time period to whih they ontribute to it. In the ase of a singly authored work, the author is author of that work over its entire duration. However, in wikis where authoring is shared different authors may exert different influene over an artile by partiipating in or withdrawing from editing it. Therefore we onsider the authoring period as another important fator in alulating o-authorship degree for a given artile. An author s first non-minor edit on a page is onsidered the beginning of the authoring period, and the last non-minor edit of this author is onsidered as the end of the authoring period. Thus the authoring period is the time interval between these two bounding points, measured in number of days / : Proportion of intersetion of authoring period over first author s authoring period In onventional o-authoring, suh as on a book or journal artile, the authors are usually engaged in the authoring proess during more or less idential time periods. During this period the authors interat with eah other to disuss jointly authored ontent, and with eah other s writing by making revisions to it. In wikis, however, authors are not neessarily engaged in authoring during the same time periods, and it ould be that one author starts Case 1 Case 2 Case 3 Case 4 ontributing to an artile after another author has finished his ontributions to that artile. In this ase these authors thus do not interat with eah other (suh as through a wiki artile s disussion page) and have no mutual interation with eah other s writing (although one user may hange the other s writing, the onverse will not be true). Therefore, we onsider the intersetion of the authoring periods of two authors when alulating their degree of o-authorship: the longer the interseting period, the greater the degree of o-authorship as the authors would have been involved in joint authoring during at least part of that artile s overall authoring period. The alulation of determines the length of the joint authoring period. There are five different ases of intersetion, as shown in Figure 5: two ases where the intersetion is equal to one of the two authoring periods (ases 1 and 2), two ases where the intersetion is shorter than both of the two authoring periods (ases 3 and 4), and one ase where the two authoring periods do not overlap, divided into two sub-ases (5a and 5b). Time is shown along the horizontal dimension, and the authoring periods of authors a and b is represented by the two parallel lines, that of above that of. In ases 1 through 4, the authoring periods and overlap. This overlapping period is the ommon authoring period and is denoted as, shown as the shaded area. The value of is an integer and is ounted in days. For ases 1 through 4 this value is greater zero. In ase 5, there is no intersetion between two authors. However, non-overlapping periods of authoring should not be entirely disregarded, but should be onsidered with a redued weight. Therefore we use the absolute value of, whih in ase 5 is the distane between the end point of the earlier authoring period and the start point of the later authoring period, to alulate as 1 / 0.5. Thus a longer distane results in a smaller intersetion value. The value of for > 0 is, and for < 0 it is in the interval (0, 1]. Finally, the intersetion value is divided by. The resulting value indiates the proportion of a s authoring period that both a and b were working on the artile. This part of the alulation results in a different page degree value for authors a and b, i.e. usually p( b) i p(b, a) i as the denominator value is different based on author. For instane if author a had been involved in an artile for one year, and author b for only one day, then author b would only be a very insignifiant o-author to but author a would be a very signifiant o-author to b. The value of / is in the interval (0, 1]. Case 5a Case 5b Figure 5. The five ases of 5.5 Boundary The upper bound for the page degree p( b) i is given when all ontributions to a page are made by authors a and b only, in equal proportions both for minor and non-minor edits, and with idential authoring periods. That is, referring to equation (2), when n ia = n ib, n ia + n ib = n, m ia = m ib, m ia + m ib = m, L ia = L ib. Thus p( b) i will be: p( b) where k is the minor edit onstant. i k = ( + k ) 1= Therefore, referring to equation (1), the upper bound of oauthorship degree d( b) is given when all page degrees are at the upper bound, that is:

7 t 1+ k s t (1+ k) d( b) = s = 2 2 i= 1 where s is the saling fator and t is the number of pages oauthored. The values of s and k an be adjusted as desired. Thus, the upper bound of the o-authorship degree is determined by the value of t, i.e. how many pages were o-authored, whih in turn is bounded by the number of pages in the system. Thus, as stated above, the range of d is the interval (0, ). 5.6 Complexity To evaluate the omplexity of our algorithm, we firstly outline the overall steps of determining the degree of o-authorship for a given author: 1 FOR eah o-author in the author s o-author list 2 FOR eah o-authored page authored by the given author and o-author 3 CALCULATE the page degree for the urrent page of the given author and o-author 4 ACCUMULATE the page degree as o-author degree END FOR 5 STORE the o-author degree of the o-author END FOR There are five operations, among whih operations 4 and 5 an be negleted sine they are simple operations. The proessing time of operation 3 approximates to onstant. Refer to equation (2) above for alulating the page degree, k is a onstant and the parameters m and n are the total number of revisions of the speified page under different onditions. Thus, the number of revisions of the speified page does not signifiantly affet the proessing time for finding m and n in the proess, and similarly for the time fator L. Therefore, the proessing time for alulating the page degree is quite stable and only minimally influened by the number of revisions. The remaining operations are the two loops whih depend on the number of o-authors n and the number of oauthored pages mi of a given pair of authors. They are the main fators that affet the proessing time signifiantly. As the proessing time of finding the page degree approximates to onstant, the proessing time needed for the algorithm an be simplified as follows: n PT( d( b )) = n mi PT( p( b ) ) i i j i= 1 i= 1 j= 1 i= 1 j= 1 where PT( ) is a funtion whih returns the proessing time a is the given author b i is o-author i of the given author a n mi C Figure 6. Speial page list with the Co-Authors extension. Assuming an average ase of the number of o-authors n that is lose to the number of o-authored pages mi, our algorithm thus has quadrati omplexity, i.e. O(n 2 ). 6. CASE STUDY We have implemented our method and algorithm on the MediaWiki system and using data from Wikipedia. 6.1 Implementation of the Algorithm We implemented our algorithm in PHP ode as a MediaWiki extension, together with MySQL stored proedures. Extensions are self-ontained piees of PHP ode that add new features or enhane funtionality of the main MediaWiki ore and that an be easily integrated in MediaWiki. Extensions are divided in different ategories. The one we developed belongs to the Speial page ategory whih is about adding new reporting and administrative apabilities. All speial pages enabled in MediaWiki are listed by liking the link Speial pages in the toolbox setion of the left menu in MediaWiki. A list of speial pages inluding our extension is shown in Figure 6. With our extension a MediaWiki user an disover the list of o-authors of a speified author by entering a username and desired sort order as shown in Figure 7. The o-authoring degrees are alulated for all o-authors aording to our method as desribed in the previous setion. The resulting o-author list displays username and o-authorship degree as shown in Figure 8. A bar whose length is proportional to the degree is inluded as a simple visualization to failitate the omparison of o-authors. Moreover, for eah listed o-author, a link (o-authors) is inluded after d( ) is the degree of o-authorship of a and b i p( ) j is the page degree of page j o-authored by a and b i C is a onstant proessing time needed for finding the page degree n is number of o-authors of a mi is number of o-authored pages by a and b i,, it is variant for eah o-author pair i Figure 7. Author searh in the o-authors page

8 we expet performane of a real-time o-authorship alulation to be unaeptable. In suh ases an offline pre-alulation performed periodially in bath mode would be more appropriate. Figure 8. List of o-authors of a seleted author their username to allow a searh for that o-author s o-authors. Having implemented the algorithm we validated the results produed by our implementation by omparing them with manually alulated results. As the data volume involved tends to be very large, making it unwieldy for manual alulation, we hose several authors with a small number of pages, revisions and o-authors. The manually alulated results were idential to those produed by our implementation, leading us to believe that the results are valid also in the ase of larger data volumes. 6.2 Performane Our implementation was deployed on a Windows PC with a 3 GHz Intel Pentium 4 CPU, and 2 GB RAM. The Simple English Wikipedia database we used had 550,812 revision reords. Through several rounds of trials and optimization we improved the performane so that it now is within an aeptable range for most user reords. A previous study found that a waiting time of 2 seonds was tolerable for web appliations [11]. Taking this as our primary performane target, we also set a seondary performane target of 10 seonds as the maximum aeptable waiting time. We then determined the distribution of the o-author alulation time relative to these two performane targets on our trial database, whih is shown in Table 3. Table 3. Distribution of alulation time t t 2 se. 2 se. < t 10 se. t > 10 se. 92% 7% 1% Given the quadrati omplexity of our algorithm, an implementation whih alulates the degree of o-authorship in real time, suh as ours, is only suited for wiki databases of moderate size. In the ase of the Simple English Wikipedia database that we used there were about 5,400 registered authors and about 27,000 pages, and we ahieved an aeptable real-time performane. However, in the ase of muh larger databases, suh as the standard English Wikipedia one, whih had about 2.5 million pages and 7.5 million registered authors as of July 2008, 7. EVALUATION The MediaWiki system and its extensions do not urrently have a funtion to show o-authors of a given author. The ase study introdued above demonstrates how to apply our method pratially in the MediaWiki system. The appliability of our method is not limited to the MediaWiki system, however. Besides other wiki and o-authoring systems it an also be used in visualization systems suh as WikiVis [1] whih disovers impliit relationships among artiles in Wikipedia. WikiVis is based on a simple notion of o-authorship between artiles. By using our method, it will be possible to determine the strength of the relationship among Wikipedia artiles more aurately. In other related work [2], the o-revision network of an artile was used to find the similarity of pages and the onept of a o-author network was introdued. Again, our method will be able to ontribute by allowing a more aurate alulation. Another appliation of o-authorship is in finding expertise groups. When searhing for experts on a ertain topi, a searh for o-authors of an artile on the hosen topi an provide a good starting point. We outline below the proess of finding expertise groups, as illustrated in Figure 9. The steps are: 1. Selet a page or ategory losely related to the required area of expertise. 2. Find the main authors of the page or ategory. 3. Find the lose o-authors of those main authors, i.e. with strong degree of o-authorship. 4. Apply rules to inlude seleted o-authors in the group of main authors. 5. The resulting group of authors forms the expertise group of the seleted page or ategory. 7.1 Main authors of page/ategory Initially we define the main author of a page as the author who Close o-authors Main Authors in seleted ategory Expertise group Expert hooser Figure 9. Finding the expertise group

9 Seleted ategory Main authors of eah page Main authors of ategory Figure 10. Finding the main authors of a ategory has made a number of revisions that onstitute a signifiant portion of all revisions. For instane, we may define that any author who has made 10% or more of all revisions is a main author of the given page. Alternatively we may define that the top n ontributors of a page are the main authors of that page. Following the seletion of main authors of a page, we an define a similar rule for the ategory. That is, a user who is among the main authors of a signifiant portion of all pages belonging to that ategory is defined to be a main author of that ategory. For instane, a user who is main author of 10% or more of all pages of a ategory is a main author of that ategory, or again an alternative seletion ould be to selet the top n among the main authors of pages in that ategory, i.e. those users who are main authors of the largest number of pages of that ategory. The onept is represented in Figure Close o-authors of main authors The lose o-authors of main authors an be found using the method defined in this paper, namely by alulating the degree of o-authorship between them. Then, only the o-authors who fulfill a defined ondition (suh as degree of o-authorship > x, or top n o-authors) are onsidered as lose o-authors, i.e. having strong ties of o-authorship with the main author. 7.3 Expert seletion Expert seletion aims to determine the members of the expertise group. The main author group and the groups of lose o-authors are analyzed and members hosen aording to ertain defined rules. For instane, a member of the main authors group who is also a member of at least n of the other main authors groups of lose o-authors is onsidered a member of the expertise group. Authors who are not main authors but are members of at least m main authors groups of lose o-author groups may likewise be onsidered members of the expertise group. This proess is illustrated in Figure Example We give a demonstration of the expertise group seletion proess, again for the Simple English Wikipedia data mentioned earlier and hoosing the ategory Musi as an example. The first step is finding the main authors in this ategory. We implemented a Figure 11. The implemented speial page Main Authors. MediaWiki extension for finding the main authors of a speified ategory. The extension is similar to the o-author extension implemented before. A searh funtion whih aepts a ategory name, ordering and reord limit of the result is provided as a speial page, as shown in Figure 11. The result is a list of main authors with a page number indiating for how many pages in the given ategory the shown author is a main author. We used the riteria of registered users who have made at least 10% of all revisions for seleting the main authors. Likewise, for the ategory we defined that an author who is a main author of at least 10% of all pages of that ategory is also a main author of that ategory. System administrators and bots are not ounted in this seletion beause their modifiations are assumed as non-ontent related. In the example of the Musi ategory there are 126 pages with a total of 1,483 revisions. Out of these, 251 revisions were submitted by anonymous users and 705 revisions by administrators and bots, and are thus not inluded. The remaining 527 revisions were submitted by 124 distint registered authors. Table 4 shows the main author list returned for this ategory. Table 4. Main author list of ategory Musi Author Main author of number of pages % of total Hikitsurisan % Zephyrad % These two ategory main authors are initially seleted as members of the expertise group. Subsequently we look for the members of the expertise group among the lose o-authors of these main authors. We deided to use a degree of o-authorship of at least 0.1 to define a lose o-author, and a riterion of the same author being a lose o-author of at least two ategory main authors to selet expertise group members. In this example, there are 28 oauthors of main author Hikitsurisan, and 10 o-authors of main author Zephyrad with degree 0.1, i.e. their lose o-authors. Of these, three are o-authors of both of these two main authors. Therefore, the expertise group of the ategory Musi onsists of its two main authors and these three lose o-authors. We have demonstrated how to determine an expertise group of a given artile ategory in MediaWiki-based systems. Are members of this expertise group really experts in the seleted ategory? This question begs further researh. However, we are onfident that our method provides a good starting point in this diretion.

10 8. CONCLUSIONS Wikis have gained inreasing importane and use throughout the world. Through their use, impliit groups of expertise are established around different topis. However, as these relationships are diffiult to disern, data analysis tehniques are used for disovering them. In this paper we have presented a new method for alulating the degree of o-authorship for a given pair of authors. This method is more aurate than any other existing methods that analyze o-authorship, and has satisfatory performane that makes it suitable for online use. Besides use in the MediaWiki system, it has the potential to be integrated in other ollaborative writing systems that maintain a omplete edit history. For instane, a wiki in a large organization an reveal expertise groups that are not expliitly reorded or known. Our method also has the potential to be integrated in visualization systems that display relationships of wiki entities. Future work will better haraterize revisions. In the urrent algorithm we only distinguish between minor and non-minor edits (whih are expliitly labeled as suh by the author). Our next step is to analyze revisions made to be able to distinguish, for example, between new additions of text, spelling/grammar orretion, editing to bring an artile in line with style guides, and other types of edits. A different weight an then be assigned to eah type and used in the alulation of o-authorship to produe a more aurate result, rather than using a fixed ratio as with the minor edit onstant in our urrent algorithm. 9. ACKNOWLEDGMENTS The finanial support from the University of Maau Researh Committee is gratefully aknowledged. 10. REFERENCES [1] Biuk-Aghai, R. P Visualizing Co-Authorship Networks in Online Wikipedia. Communiations and Information Tehnologies, ISCIT '06 (Bangkok, Thailand, September 2006), [2] Brandes, U. and Lerner, J Revision and o-revision in Wikipedia. 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