Community Detection Using Discrete Bat Algorithm

Transcription

1 IAENG Inernaonal Journal of Compuer Scence, 3:1, IJCS_3_1_5 Communy Deecon Usng Dscree Ba Algorhm Anpng Song, Mngbo L, ueha Dng, We Cao, Ke Pu Absrac Communy deecon s very mporan for undersandng he funcon of complex neworks. The radonal communy deecon algorhms such as specral cluserng and FN (Fas Newman algorhm end o fall no local opmum or canno denfy he number of communes. In hs paper, based on BA (Ba Algorhm, a new swarm nellgence opmzaon algorhm, we proposed DBA (Dscree Ba Algorhm for communy deecon. DBA can auomacally denfy he number of communes and easly search he global opmal soluon o overcome he shorcomngs of radonal algorhms. Compared wh radonal algorhms, expermenal resuls show ha DBA has hgher accuracy and effcency. We appled DBA o he communy deecon of bddng neworks and acheved good resuls, whch shows ha our algorhm has a srong praccal value. Index Terms complex nework, communy deecon, Ba Algorhm, bddng deecon C I. INTRODUCTION omplex neworks orgnaed n our lves. For example, he World Wde Web, socal neworks, elecrcy neworks, neural neworks and proen neracon neworks can all be seen as a complex nework. Sudy of complex neworks nvolvng physcs, mahemacs, bology and socology, has become one of he mos mporan nerdscplnary felds [1], []. Wh he n-deph sudy of complex neworks, scholars have found ha many complex neworks have a common naure: communy srucure. Lke he small world [3], scale-free [], he communy srucure of complex neworks s one of he mos popular and mporan properes of he opology. Communy deecon can be appled o he web mnng, socal nework analyss, semanc-analycs [3] and many felds of bology and has mporan sgnfcance n research. Grvan and Newman are poneers n he research of communy deecon algorhm. They proposed he Grvan- Newman (GN algorhm [5] n 1. GN algorhm Anpng Song s assocae professor wh he School of Compuer Engneerng and Scence, Shangha Unversy, Shangha, Chna (e-mal: apsong@shu.edu.cn. Mngbo L s wh he School of Compuer Engneerng and Scence, Shangha Unversy, Shangha, Chna (e-mal: lmb@shu.edu.cn. ueha Dng s wh he Hgh-Performance Compung Cener, Shangha Unversy, Shangha, Chna (e-mal: dngha@shu.edu.cn. We Cao s wh he School of Compuer Engneerng and Scence, Shangha Unversy, Shangha, Chna (e-mal: caowe@shu.edu.cn Ke Pu s wh he School of Compuer Engneerng and Scence, Shangha Unversy, Shangha, Chna (e-mal: Ths sudy s fnancally suppored by Naonal Naural Scence Foundaon of Chna (Gran No and (Gran No Ther suppor s grealy apprecaed. eravely compues he edge beweenness and removes he edge of maxmum beweenness. A herarchcal cluserng ree s bul by op-down approach. Because of he hgh compuaonal demands, GN algorhm s only suable for small neworks. Bu GN algorhm plays a very mporan role n he feld of communy deecon. Communy srucure was consdered as a ubquous propery of complex nework for he frs me, whch nspred n-deph sudy on hs ssue and se off a wave of research on communy deecon []. Maxmum flow communy (MFC algorhm [7] and GN algorhm are smlar n he way of cung nework. Theorecal bass of MFC algorhm s he Max Flow-Mn Cu heorem. MFC algorhm connuously removes Mn Cu edge, so nework s dvded no communes eravely. The prncpal dsadvanage of MFC algorhm s he hgh compuaonal demands makes. Fas Newman (FN [] algorhm was proposed by Newman n. I consdered communy deecon as a global opmzaon problem and he obecve funcon s Q funcon (modulary funcon. By local search sraegy, FN algorhm repeaedly ons communes ogeher n pars, choosng he on ha resul n he maxmum ΔQ a each sep, whch buld a herarchcal cluserng ree from he boom up. FN algorhm has a consderable advanage over GN algorhms n me complexy, bu he resul obaned by FN s a local opmum and lacks dversy. GA (Gumera-Amaral algorhm [9], based on smulaed annealng algorhm, was proposed by Gumera and Amaral n 5. The obecve funcon of GA algorhm s he same wh FN algorhm. However, GA algorhm s slow n convergence and sensve o parameers. Specral cluserng [1]-[1] ransforms communy deecon o he approxmae opmal soluon of consraned quadrac form, whch s src n mahemacal heory, bu does no auomacally recognze he number of communes. Basng on opmzaon mehod, Ronghua Shang e al proposed an mproved genec algorhm usng modulary [13]. Genec algorhm s very slow n convergence, because he muaon and crossover operaons are random. Many scholars ry o apply swarm nellgence algorhm n communy deecon. H Chang e al appled An Colony Opmzaon o communy deecon [1] wh he help of a new knd of heursc nformaon. Qng Ca e al appled parcle swarm opmzaon (PSO algorhm o he communy deecon of sgned nework [15] n 1, and have acheved good resuls. Ba Algorhm (BA, proposed by Yang n 1, s a new swarm nellgence algorhm [1]. The orgnal BA can only be used o solve he connuous opmzaon problem. In hs paper, we dscrezed he orgnal algorhm and proposed a novel dscree ba (Advance onlne publcaon: 9 February 1

2 IAENG Inernaonal Journal of Compuer Scence, 3:1, IJCS_3_1_5 algorhm (DBA o deec he communy srucure n complex nework. Expermenal resuls show ha compared wh several algorhms descrbed above, DBA has obvous advanages on he accuracy of communy paron and effcency. Then we appled DBA o he bddng neworks and acheved good resuls. The res of hs paper s organzed as follows. Secon II focuses on relaed work and BA algorhm; Secon III shows he dscrezaon of BA and he processes of DBA; Secon IV s expermen resuls n arfcal nework and real-word neworks; Secon V s he concluson and prospec. II. RELATED WORK A. The defnon of communy Communy srucure s an mporan feaure ha many complex neworks have n common, bu here s no src defnon ye. In leraure [17], communes are regarded as sub-graphs of nework whch have dense nra-lnks and sparse ner-lnks. In realy, he communes correspond o specfc feaure or arbue of a nework. For example, n a socal nework, a communy may represen a crcle of frends; n a leraure muual reference nework, a communy may represen a relevan scenfc feld. Thus, communy deecon s o dvde complex nework no several sub-graphs, he mahemacally descrpon s as follows: Gven a complex nework G (V, E, where V s he verces se, E s he edges se. To fnd a dvson C CC... 1 Ck, where C1 C... Ck V and C C,. A good dvson of C s o make nra edges of C as many as possble and edges beween C and C as few as possble. B. Modulary funcon Modulary funcon was proposed by Newman n [1], whch s currenly he mos wdely used evaluaon funcon of communy deecon. Gven a nework, assume ha he nework was dvded no k communes. Defne a k-order symmerc marx e, le e be one-half of he fracon of edges n he nework ha connec verces n communy o hose n communy. so ha he oal fracon of such edges s e e. The race Tre e s he oal fracon of edges ha fall whn communes. A dvson s good f he Tre s large. Bu he Tre canno be a good measure for communy deecon. If all verces are pu no a sngle communy, we wll ge maxmal value of 1, whch does no reflec any communy srucure of he nework. Thus, le a be he fracon of edges ha connecs o he communy, we defne he modulary funcon as follows: ( (1 Q e a Tre e Where ǁxǁ s he sum of all elemens n he marx x and a s he fracon of edges ha fall whn communes when all edges are conneced ogeher a random. Q s he dfference beween e and a. If he edges of a nework are conneced a random, hs means no communy srucure s formed, he value of Q approxmaely equal o. Maxmum Q s 1 and he acual suaon s n he range of.3 and.7. Q.3 ndcaes sgnfcan communy srucure n he nework. C. The fracon of verces denfed correcly If he communy srucure of a nework s known, we use FVIC (he fracon of verces denfed correcly [19] o evaluae he resul of communy deecon. We defne FVIC as follows: FVIC k maxc N ( Gven a nework, C s he correc communy dvson, ncludng k communes. C s he communy deecon resul. C C, fnd C C ha has he mos common verces wh C, denoed as maxc. Where N s he number of verces n he nework. The larger FVIC s, he closer he resul s o he correc dvson. D. Ba Algorhm BA was proposed by famous scholar Yang n 1. BA, whch combnes he feaures of PSO algorhm and smulaed annealng algorhm, s srong n convergence and global search capably. Basng on he echolocaon behavor of bas, BA smulaes he frequency, emsson raes and he loudness when bas forage. Bas change he wavelengh λ by adusng he pulse frequency f ( f. When he wavelengh concdes wh he sze of nsecs, bas are able o locae he arge. The poson and velocy updang rule of BA s smlar wh PSO algorhm. BA generaes a random soluon by a random flgh operaon o avod fallng no local opmum, whch s he defec of PSO. The local search operaon of BA s smlar o smulaed annealng algorhm, whch makes he BA algorhm converge more quckly. BA combnes he advanages of PSO algorhm and smulaed annealng algorhm, whch makes BA more ousandng. III. DISCRETE BAT ALGORITHM A. Defne of ba locaon and velocy The orgnal BA algorhm s used o solve connuous problem, bu communy deecon s a dscree problem. Therefore we propose he DBA for communy deecon. Frs, we defne he poson of ba. In he orgnal BA, f he soluon space s n-dmensonal, a poson s an n-dmensonal vecor. For communy deecon, we use he decmal code. The defnon of a poson s... 1 n, where n s he number of verces of he gven nework, s a decmal neger. For any and, means verex and verex are dvded no he same communy. Then we defne he ba velocy. The velocy of orgnal algorhm s he dfference beween he poson of he curren (Advance onlne publcaon: 9 February 1

3 IAENG Inernaonal Journal of Compuer Scence, 3:1, IJCS_3_1_5 ndvdual and he curren bes ndvdual. Bu for dscree code, we canno ge he dfference drecly by subracon. Therefore, we propose a new velocy formula, he operaon beween he curren ndvdual and he curren bes ndvdual becomes OR. In fac, ba wll adus s velocy by learnng from he curren bes. The learnng process s acually a comparson beween he posons. So he OR operaon acually reflecs he dfference beween wo nework dvsons, as a ba on behalf of a nework dvson. If, where s he curren bes ndvdual, hen ; If, hen 1. I can be seen ha OR well reflecs he dfference beween he curren ndvdual and he curren bes ndvdual. The curren ndvdual wll adus self by learnng from he curren bes ndvdual. B. Dscree formula The poson and velocy updae formula of DBA algorhm are defned as follows: Pulse frequency formula: f f ( f f (3 mn max mn Where β s a random number, <β <1, fmax s maxmum frequency, fmn s mnmum frequency. The velocy a sep s gven by: V V ( f ( 1 V d Sg( V 1/(1 exp( V (5 1 f rand( Sg( V f rand( Sg( V Where Sg s he sgmod funcon. Sg mapped he velocy o he range (, 1. rand( generaes a random number n he range of (, 1. We can ge he dscree velocyv by he above formula. Then we wll calculae he new poson of he ba. In he orgnal algorhm, we can ge he new poson vecor by addng he poson of he prevous generaon o he curren velocy vecor, bu no for dscree ssues. In hs regard, we proposed a new poson updae funcon. For he curren poson... 1 n : d fvd f Vd 1, rand( r new f Vd 1, rand( r Where r s curren emsson rae, ( (7 new s he new poson of afer adusmen, he adusng mehod s descrbed as follows: For each verex v, <<n, fvd 1, hen calculae: Connec f ( v, C C C, k ( Where 1 V s he new velocy, V s he velocy of he prevous generaon, s he curren poson, s he curren bes poson, f s he curren frequency, s OR. Velocy dscree formula: Where C CC... 1 Ck s a communy deecon resul; k s he number of communes. f ( calculaes he edges beween verex v and C, k. If communy Cmax ( Cmax C corresponds o he max TABLE I THE PSEUDO-CODE OF DBA The pseudo-code of DBA Inpu: adacency marx of complex neworks, populaon and oher parameers Oupu : communes 1 Inalze he populaon m, he max and mn pulse frequency f max and f mn, max emsson raes r, max loudness A, frequency ncrease facor γ, sound aenuaon coeffcen α, he max number of eraons sep Inalze he poson and velocy of each ba randomly, calculae he fness of each ba, selec he curren bes 3 whle (<sep Updae he curren velocy, poson and fness of each ba 5 f ( rand( r Generae a local soluon local for he curren ba by local search 7 f ( f ( local f( Replace he curren soluon wh local 9 Generae a new random soluon new 1 f ( rand( A & f ( new f ( 11 Accep he new soluons new, updae A and r 1 Ge he curren bes by rank all bas 13 end whle 1 Decode he opmal soluon s and oupu he communes. (Advance onlne publcaon: 9 February 1

4 IAENG Inernaonal Journal of Compuer Scence, 3:1, IJCS_3_1_5 Connec, adus v o C max wh a ceran probably. C. Local search The local search sraegy of DBA s smlar o he smulaed annealng algorhm. Advanage of local search s ha can easly search for he opmal soluon and accelerae he convergence. The mehod s oulned below. Gven a soluon C CC... 1 Ck, C C, calculae he Connec of verex v and communy C, see equaon (, where v C. For he verex v mn correspondng o he mnmum Connec, calculae s Connec wh all oher communes C, where C C and. Fnally, we adus verex v mn o C max, where v mn and C max have he maxmum Connec. D. Work flow of DBA We use a decmal code n hs paper. If wo verces have he same code, hey are dvded no he same communy. In he nalzaon, we generae each code randomly. However, hs wll dvde some unconneced verces no he same communy, whch s obvously of no sense. Therefore, we es each code n he nalzaon, so as o avod nonsense nalzaon. The obecve funcon of DBA s he Q funcon. We use wo ermnaon condons. Frs, manually se he number of eraons; second, f he Q funcon value of he opmal soluon remans unchanged for 1 eraons, he algorhm sops. Table I shows he pseudo-code of DBA. IV. EPERIMENTS AND RESULTS In hs paper, expermens were performed n deskop compuer wh he operang sysem Wndows7, CPU 3-3, clocked 3.GHz, memory G. Our algorhm was coded n Java, JDK1.7. Complng envronmen s MyEclpse. We appled DBA o arfcal nework, real-word neworks and bddng neworks. The dfference beween arfcal nework and real-word nework s ha he communy srucure of he former s known n advance. A. Arfcal nework Frs, we used a symmercal nework wh known communy srucure proposed by Grvan and Newman n he paper [5] o valdae he performances of DBA. The nework generaed by compuer, consruced wh 1 verces, s dvded no four communes n average. The edges are randomly generaed by a fxed probably p n and p ou. Where p n s he possbly ha boh verces of an edge belong o he same communy, and pou for dfferen communes, pn pou. The probables were chosen so as o keep he average degree of a verex equal o 1. In he expermens, we changed he dense beween communes by adusng p n and p ou. When p ou ncreases, decreases, he nra-lnks decrease and ner-lnks pn ncrease. Ths makes communy dvson more dffcul. The proposed algorhm was used n he communy deecon of he above nework, and several oher classcal algorhms for comparson. Inal p s, whch means no connecon beween he communes. The expermenal resuls of FN algorhm, specral cluserng, DPSO algorhm and DBA are shown n Fg 1. In Fg 1, he horzonal axs represens ou p ou, he vercal axs represens FVIC. Orgnal DPSO algorhm s used for communy deecon of sgned nework, so we changed and appled o undreced nework. We ran each algorhm 1 mes for each p ou, akng he bes resul. We can see from Fg 1 ha FVIC obaned by DBA was 1 wh pou. Ths means ha f pou, communy dvson of DBA s compleely correc. pou of FN algorhm and DPSO algorhm n hs case are 5 and 5.5 respecvely, whch s sgnfcanly lower han DBA. Only for pou 7 does FVIC of DBA sar o fall off subsanally. In oher words, he algorhm performs very well almos o he pon a whch each communy has as many nra-lnks as ner-lnks. The curve of DBA s above DPSO and FN all he me, whch means accuracy of DBA s beer han he oher wo algorhms. For specral cluserng, when pou 1, FVIC s less han 1. The process of specral cluserng s he process o relax he FVIC... DBA DPSO FN Specral Pou Fg. 1. Expermen resuls of arfcal nework (Advance onlne publcaon: 9 February 1

5 IAENG Inernaonal Journal of Compuer Scence, 3:1, IJCS_3_1_5 accuracy of communy dvson, so he resuls wll always have a lle error. Bu when pou 7.5, FVIC obaned by TABLE II SPECIFICATIONS OF REAL-WORD NETWORKS Nework Fooball Karae Club Polcal Books Verces Edges specral cluserng s he hghes. The reason s ha he number of communes s gven n advance for specral cluserng, so he communes are dvded more evenly. Therefore, a hgher FVIC does no mean ha specral cluserng has advanages compared wh oher algorhms. In summary, for he arfcal nework communy deecon, DBA algorhm performed beer han he oher hree algorhms. Fg.. Communy deecon resul of Fooball Fg. 3. Communy deecon resul of Karae Club Fg.. Communy deecon resul of Polcal Books B. Real-world neworks In hs secon we appled our algorhm o hree real-word neworks. They are he Amercan fooball nework [5], Zachary karae club nework [] and he Amercan polcal books neworks [1]. Amercan fooball nework s a represenaon of he game schedule of Amercan college fooball n season. These eams are from 1 leagues. Verces represen eams and edges represen regular-season games beween he wo eams hey connec. Games are more frequen beween members of he same league han beween members of dfferen league. Zachary karae club nework represens he relaonshp of he members. Because of dspue whn he organzaon, he nework s dvded no wo dsnc communes. Verces of Amercan polcal books nework represen polcal books sold on Amazon. If wo books were bough by he same buyer, here s an edge beween he correspondng verces. Specfcaons are shown n Table II. We ran DBA, DPSO algorhm and specral cluserng 1 mes on each nework, recorded he number of communes obaned by he bes resuls, he correspondng Q max, and he average value Q avg. Communy deecon resuls are shown n Table III. We use a graphcal ool Cyoscape o show he bes resuls go by DBA. The communy deecon resuls of Fooball, Karae Club and Polcal Books are shown n Fg, Fg 3 and Fg respecvely. DBA and specral cluserng algorhms deeced all 1 communes n he fooball nework; DPSO and FN were 1 and 9 respecvely. The number of communes s se n advance for specral cluserng, bu DBA algorhm deeced auomacally. As can be seen from Table III, FN algorhm obaned he larges Qavg n he fooball nework. Bu all resuls obaned by FN algorhm are exacly he same, so Qavg Qmax. Qmax of DBA algorhm s no only far greaer han FN algorhm, bu also hgher han DPSO algorhms and specral cluserng. Resuls of he Karae Club nework and he Polcal Books nework are smlar o he resuls of he fooball nework. FN algorhm can ge he max Q avg. Because of he oneness of resul, Qmax of FN algorhm s much smaller han ha of DBA and DPSO. Wha s more, DPSO algorhm s ends o fall no local opmum, Qmax and Q avg are smaller han hose of DBA. Thus, we can see he advanages of DBA. I can no only auomacally deec he number of communes, bu also oban more accurae resuls han he radonal algorhms. (Advance onlne publcaon: 9 February 1

6 IAENG Inernaonal Journal of Compuer Scence, 3:1, IJCS_3_1_5 TABLE III EPERIMENT RESULTS OF REAL-WORD NETWORKS Nework Algorhm Number of communes DBA DPSO Fooball FN Specral DBA.3.39 DPSO Karae Club FN Specral DBA DPSO.5.7 Polcal Books FN.7.7 Specral Q avg Q max number of he communes Elecrcy sze of he communes Transporaon number of he communes Consrucon sze of he communes Waer Conservancy number of he communes 1 1 number of he communes sze of he communes sze of he communes Fg. 5. Communy deecon resuls of bddng neworks C. Bddng neworks Expermen resuls of he above wo secons show ha DBA algorhm has advanages n deecng he small scale neworks compared wh he radonal algorhms. In hs secon we appled DBA o deec communes n a large complex neworks. Expermenal daa s he 1-1 bddng daa of a Chnese provnce, provded by he publc resources radng cener of he provnce. There wll be group phenomenon when companes bd, whch means some companes always appear n he same proec. These companes have suspcon of surround-bddng accordng o some expers. We can fnd ou hese companes by communy deecon. Frs we classfed he daa accordng o ype of proec. Then for each class, we consruced neworks of he companes parcpaed n he bddng. Verces represen companes. If wo companes bd n he same proec, here s an edge beween hem. If hey bd n mes ogeher, wegh of he beween edge s n. We chose bddng neworks of four caegores for communy deecon, elecrcy (1 verces, consrucon (39 verces, ransporaon (3 verces and waer conservancy (39 verces. The resuls were shown n Fg 5. The horzonal axs represens he sze of he communes and he vercal axs represens he number of he communes. Bddng expers poned ou ha because of some reasons, he scale of a group s generally beween 3 and 15. As can be seen from Fg 5, he sze of communes concenraed n he range of 3 and 15. The percenage of communes wh sze beween 3 and 15 s above 7%. Tha s, 7% of he communes deeced by DBA are n lne wh he acual suaon, whch s of grea praccal value. We can (Advance onlne publcaon: 9 February 1

7 IAENG Inernaonal Journal of Compuer Scence, 3:1, IJCS_3_1_5 regard as a udgmen of surround-bddng. We summarze he above four caegores (elecrcy, consrucon, ransporaon and waer conservancy. These communes have a broad dsrbuon of szes from 1 o nearly 15. The dsrbuon s shown n cumulave form n Fg. We observe ha he dsrbuon of he communy sze s approxmaely power law n form. communes wh s ndvduals or more sze of commnuny s Fg.. Cumulave dsrbuon of he summary resul of four caegores: elecrcy (5 communes, consrucon ( communes, ransporaon ( communes and waer conservancy (7 communes. A oal of 35 communes were found. In Fg, he black lne represens he slope he plo would have f he dsrbuon followed a power law wh exponen roughly equalng o -1. The same knd of expermen was done by Newman n paper [], usng a nework of collaboraons beween physcss. Newman go he resul ha he dsrbuon s approxmaely power law wh exponen 1.. Compared wh Newman s expermen, our expermen resul s more close o a perfec power law [], whch means our resul s even beer. V. CONCLUSIONS In hs paper we proposed a new communy deecon algorhm DBA based on swarm nellgence. DBA auomacally deecs he number of communes and s able o ump ou of local opmum, whch overcomes he shorcomngs of radonal algorhms. Arfcal nework and real-word neworks expermens have proved DBA s superor o he radonal algorhms such as FN algorhm, DPSO algorhms and specral cluserng n all respecs. Furhermore, we appled DBA o he communy deecon of bddng neworks. The resuls are conssen wh he predcon of some expers, whch also valdaes he praccaly of DBA. We use only one obecve funcon, Q funcon, n hs paper and mul-obecve should be consdered n furher sudes. In addon, we wll focus on he parallelzaon of DBA o mee he challenges of larger neworks. [] FD Mallaros, M Vazrganns, Cluserng and Communy Deecon n Dreced Neworks: A Survey, Physcs Repors, vol. 533, no., pp Dec. 13. [3] Was DJ, Srogaz SH, Collecve dynamcs of Small-World neworks, Naure, vol. 393, no. 3, pp. -, Jun [] Barabás AL, Alber R, Emergence of scalng n random neworks, Scence, vol., no. 539, pp , Oc [5] Grvan M, Newman MEJ, Communy srucure n socal and bologcal neworks, Proceedngs of he Naonal Academy of Scences of he Uned Saes of Amerca, vol. 99, no. 1, pp. 71-7, Dec.. [] Yang Bo, Lu Dayou, Lu Jmng, Jn D, Complex Nework Cluserng Algorhms, Journal of Sofware, vol., no. 1, pp. 5-, Jan, 9. [7] Flake GW, Lawrence S, Gles CL, Coezee FM, Self-Organzaon and denfcaon of Web communes, IEEE Compuer, vol. 35, no. 3, pp. -71, Mar.. [] Newman MEJ, Fas algorhm for deecng communy srucure n neworks, Physcal Revew E, vol. 9, no., pp , Sep.. [9] Gumera R, Amaral LAN, Funconal carography of complex meabolc neworks, Naure, vol. 33, no. 7, pp. 95-9, Feb. 5. [1] Shga M, Takgawa I, Mamsuka H, A specral cluserng approach o opmally combnng numercal vecors wh a modular nework, Proceedngs of he 13h ACM SIGKDD nernaonal conference on Knowledge dscovery and daa mnng, New York, 7, pp [11] Ulrke von Luxburg, A uoral on specral cluserng, Sascs and Compung, vol. 17, no., pp , Dec. 7. [1] M. E. J. Newman, Communy deecon and graph paronng, Epl, vol. 13, no., pp , May. 13. [13] Ronghua Shang, Jng Ba, Lcheng Jao, Chao Jn, Communy deecon based on modulary and an mproved genec algorhm, Physca A Sascal Mechancs & Is Applcaons. Vol.39, no. 5, pp , Nov. 13. [1] H Chang, Z Feng, Z Ren, Communy deecon usng An Colony Opmzaon, IEEE Congress on Evoluonary Compuaon, Cancun, Jun. 13, pp [15] Q Ca, M Gong, B Shen, L Ma, L Jao, Dscree parcle swarm opmzaon for denfyng communy srucures n sgned socal neworks, Neural Neworks he Offcal Journal of he Inernaonal Neural Nework Socey, vol. 5, no. 1, pp. -13, May. 1. [1] n-she Yang, A New Meaheursc Ba-Inspred Algorhm, Naure Inspred Cooperave Sraeges for Opmzaon, pp. 5-7, Apr. 1. [17] Radcch F, Casellano C, Ceccon F, Loreo V, Pars D, Defnng and denfyng communes n neworks, Proceedngs of he Naonal Academy of Scences of he Uned Saes of Amerca, vol. 11, no. 9, pp. 5-3, Mar.. [1] Aaron Clause, M.E. J. Newman, Crsopher Moor, Fndng communy srucure n very large neworks, Physcal Revew, vol. 7, no., pp. -77, Dec.. [19] Newman MEJ, Grvan M, Fndng and evaluang communy srucure n neworks, Physcal Revew, vol. 9, no., Aug.. [] WW Zachary, An nformaon flow model for conflc and fsson n small groups, Journal of Anhropologcal Research, vol. 33, no., pp. 5-73, [1] V.Krebs, unpublshed, Avalable: hp://orgne.com. [] Gumerà R, Danon L, Díaz-Gulera A, Gral F and Arenas A, Self-smlar communy srucure n a nework of human neracons, Phys Rev E Sa Nonln Sof Maer Phys, vol., no., pp. 93-1, Dec. 3. [3] Jose Devezas, Alvaro Fguera, Fndng Language-Independen Conexual Supernodes on Coreference Neworks, IAENG Inernaonal Journal of Compuer Scence, vol. 39, no., pp. -7, 1. REFERENCES [1] Sau Elsa Schaeffer, Graph cluserng, Compuer Scence Revew, vol. 1, no. 1, pp. 7-, Aug 1. (Advance onlne publcaon: 9 February 1