Study on base-core Mode Coupling Networks

Transcription

1 Study on base-core Mode Couplng Networks XU-HUA YANG, JIU-QIANG ZHAO, GUANG CHEN College of Computer Scence and Technology Zheang Unversty of Technology Hangzhou, 30023, Chna P.R.Chna Abstract: - There exst a knd of networks composed of two coupled network whch are a base network and a core network respectvely. For nstance, an urban publc transport network conssts of a bus network (base network) and subway network (core network), the two networks are coupled together. We proposed a base-core couplng network model to study the performance of the knd of couplng network. In the model, the base network s generated frst, then the nodes of the core network are selected from the base network accordng to a preferental selecton scheme based on k α and b α, where k and b represent the node degree and betweenness respectvely, α represents the preferental selecton exponent. Under dfferent value of α, we nvestgate the performance of the couplng network n dfferent network structure and dfferent network sze collocatons. Smulaton result shows: the greater value of α, the hgher of the use rate of the core network and the smaller of the weghted average shortest path length of the couplng network. Namely, a hgher preferental selecton exponent corresponds to better couplng network performance. Key-Words: - base-core couplng network, preferental selecton exponent, the weghted average shortest path length, the use rate of the core network Introducton Recent years, researches n the feld of network scence, whch dedcates to study the features of complex systems by abstractng these systems nto networks, have attracted huge attenton from a varety of scence felds, such as predcton of proten functon [-4], detecton of communty structure n socal networks [5-8], control of wreless sensor networks [9-2], and so forth. At present, most of the researches about complex networks are lmted to sngle networks. But n fact a sngle network n many real crcumstances cannot suffcently represent a complex system composed of sub-systems wth dfferent structure and functon. For these systems, coupled, nterdependent or layered networks are better carrers to depct them [3-9]. The propertes of each network n a couplng network may be qute dfferent from each other, but they generally have some couplng on or mutual dependence wth others, such as the actvaton and nhbton relatonshp between proten and gene wth each other n a bologcal network [-2], the dependence of socal networks on the advanced Internet technology [20-2], the relance of the nternet on energy system [22-24], etc. The couplng relatonshp between coupled networks s mportant, therefore, scholars have done several researches on t. For example, Kurant et. al. proposed a logcal-physcal layer coupled network model to study the transport traffc features n real networks [25], Daren et. al. put forward a research on the robustness n coupled networks[26], Morrs et. al. researched the transport on coupled spatal networks[27], etc. Among many coupled networks, a common genre s the base-core mode coupled network whch conssts of two networks whle the man functons of the two networks are dfferently orented [28,29]. We call one of the network the base network and the other the core network; see Fg. for an llustraton. Usually, the man functon of the core network s to undertake some mportant tasks n a system whch has an mportant nfluence on the performance of the whole coupled network, such as the subway network n the publc transport system [30], but due to ts expensve constructonal or operatonal cost, E-ISSN: Volume 3, 204

2 ts cover range tend to be lmted n the real world [3, 32]. By contrast, the base network can be bult wth a relatvely lower cost such that t can be deployed n a wde range, such as the bus transport network n the publc transport system. However, the base network has a much weaker networkng functon. Couplng of the two knds of networks can offer us a satsfactory balance or tradeoff between network effcency and cost n real world stuatons. For example, n a publc transportaton network of a metropols, the subway network play the role of the core network to undertake the maorty passenger flow wthn the maor regons of the cty, on the other hand, the bus network severs as the base network assstng the subway system, responsble for local passenger transportaton and would be especally useful for people n the suburb [3,32]. The two networks complement each other have ensured a fast, convenent and cheap travelng for people n the cty. base network core network Fg. A smple llustraton of the base-core mode couplng network. A system made of two coupled networks, where the nodes of the base network coupled wth the core network are selected accordng to a gven strategy. The nodes colored n red are consdered to be coupled. Edges of base network are shown n black, whle edges of core network are shown n blue. We note that, there are two common problems n the base-core mode couplng networks. The frst one s that how the core network couples wth the base network, namely whch type of nodes n the base network should be chosen to be coupled wth the nodes of the core network, to make the whole network acheve a relatvely good network performance. The second s how to decde the network sze for the core network and the base network. As we all know that, the constructon costs of core networks often tend to be hgher than base networks. So how to choose the couplng strategy and the sze of the two networks to nsure a balance between the network cost and network performances s worth explorng. It s known that, the mportance and features of nodes n a network can usually be characterzed by ndces lke node degree [33], betweenness, clusterng coeffcent [34,35] and so forth. So the nodes couplng strateges can have a varety of optons. For example, the nodes of the base network may be selected as arbtrary nodes to couple wth the core network, or be selected as the nodes that have partcular node propertes. As a result, t s mportant to assess the mpacts of dfferent couplng strateges on the whole network performances, because t can help us to understand what knd of couplng strategy s good or not good or even bad, and t can further help us n the network desgn and optmzaton. Based on these questons, n ths paper we desgned a base-core couplng network model to study the performance of the couplng network whch s composed of a base network and a core network. In the model, the base network s generated frst, then the nodes of the core network are selected from the base network accordng to a preferental selecton scheme based on node degree or betweenness. Under dfferent value of preferental selecton exponent α, we nvestgate the performance of the couplng network n dfferent network structure and dfferent network sze collocatons. As we wll show n the followng content that, these factors do nfluence the network performance. The result may provde some gudance n the desgn or optmzaton of real-world networks. The remander of ths paper s organzed as follows. In secton 2, the base-core mode couplng network model and the preferental selecton scheme strateges are ntroduced. In secton 3, we conduct a smulaton based on the model and the couplng scheme to nvestgate the network performance of the whole network under dfferent crcumstances. Then the concluson and some dscusson are lsted n Secton Base-core mode couplng network model and ts couplng strateges 2. Base-core mode couplng network model In ths secton, we frst present the base-core couplng network model. In ths model, each of the nodes n the core network s coupled wth one of the nodes n the base network. Besdes, the base network and the core network have dfferent edge E-ISSN: Volume 3, 204

3 cost. The cost assocated wth each edge s the length of that edge multpled by a factor λ. Worth notng that, n ths paper we defne all the edge length for unwegthed networks to be, such as ER networks and BA networks [33]. In graph theory, the Erdős Rény model s ether of two closely related models for generatng random graphs, ncludng one that sets an edge between each par of nodes wth equal probablty, ndependently of the other edges. They are named for Paul Erdős and Alfréd Rény, who frst ntroduced one of the two models n 959; the other model was ntroduced ndependently and contemporaneously by Edgar Glbert. These models can be used n the probablstc method to prove the exstence of graphs satsfyng varous propertes, or to provde a rgorous defnton of what t means for a property to hold for almost all graphs. A typcal drawng s dsplayed n Fg. 2(a). A BA scale-free network s a network whose degree dstrbuton follows a power law, at least asymptotcally. That s, the fracton pk ( ) of nodes n the network havng k connectons to other nodes goes for large values of k as pk ( )~ k γ where γ s a parameter whose value s typcally n the range 2< γ < 3, although occasonally t may le outsde these bounds. Many networks are conectured to be scale-free, ncludng World Wde Web lnks, bologcal networks, and socal networks, although the scentfc communty s stll dscussng these clams as more sophstcated data analyss technques become avalable. Preferental attachment and the ftness model have been proposed as mechansms to explan conectured power law degree dstrbutons n real networks[29]. A typcal drawng s dsplayed n Fg. 2(b). For the base and core networks, the factors mentoned above s denoted by λ b and λ c, respectvely. Wthout loss of generalty, we set λ = b and λc [0,] n ths paper. Note that, the smaller the factor s, n physcal meanngs the faster or wth fewer cost materal can be transferred. Specfcally, a base-core couplng network can be generated n the followng steps: ). Base network: an ER graph or a scale free network wth n nodes. 2). Core network: an ER graph or a scale free network wth n 2 nodes whch are selected from the base network accordng to specfc couplng strateges n secton 2.2. The base network and the core network couple wth each other due to sharng the same nodes selected from ths step. After the above steps, a base-core mode couplng network has been establshed. An llustraton of a generated couplng network s dsplayed n Fg.. Fg. 2 A smple llustraton of ER random network and scale-free network. 2.2 The preferental selecton scheme based on k α and b α The mportance and features of nodes n a network can usually be characterzed by node degree or node betweenness, clusterng coeffcent and so forth. The degree feature of complex network s usually frst studed. In network theory, the degree of a node s defned as the number of ts neghbor nodes. The degree reflects the mportance of a node as a hub. In drected networks, a degree can be dvded nto two categores: out-degree and ndegree. The out-degree of a node s defned as the number of nodes that a node can reach through an edge, whereas the n-degree s defned as the number of nodes reachng the node through an edge. Specfcally, we have k out n = a ; k = a () out n where k and k denote the out-degree and the ndegree of node, respectvely; a denotes the exstence of the edge ( a = when edge exsts; otherwse, a = 0 ). But for undrected network, We manly focus on the total node degree of a node n the network, n ths paper, the total node degree of a node n the network s studed. Betweenness s usually dvded nto two knds of types, whch are edge betweenness and node betweenness. Betweenness s a measure of how often a node or vertex s located on the shortest path or geodesc between other nodes n the network. It thus measures the degree to whch the node under study can functon as a pont of control n the communcaton. If a node wth a hgh level of betweenness were to be deleted from a network, the network would fall apart nto otherwse coherent clusters. Unlke degree, whch s a count, E-ISSN: Volume 3, 204

4 betweenness s normalzed by defnton as the proporton of all geodescs that nclude the vertex under study. Betweenness s a relatonal measure. One can expect that a ournal whch s between wll load on dfferent factors because t does not belong to one of the dense groups, but relates them. The factor loadngs of such ournals may depend heavly on the factor-analytc model (e.g., the number of factors to be extracted by the analyst). For example, one mght expect nter-factoral complexty among the factor loadngs n the case of nter- or multdscplnary ournals (Van den Besselaar & Hemerks, 200; Leydesdorff, 2004). Closeness s less dependent on relatons between ndvdual vertces because a vertex can be close to two (or more) densly connected clusters. Closeness can thus be expected to provde us wth a measure of multdscplnarty wthn a set whle betweenness may provde us wth a measure of specfc nterdscplnarty at nterfaces. In network theory, the clusterng coeffcent of a node measures the tghtness of the connectons among nodes and ther neghbors. The clusterng coeffcent s defned as the number of drected lnk trangles that exst among nodes and ther neghbors aganst the total number of trangles that can exst among nodes (Fagolo, 2007). The defnton for the clusterng coeffcent s wrtten as ( a + a )( ak + ak )( ak + ak ) k c = (2) tot tot 2[ d ( d ) 2 d ] where c denotes the clusterng coeffcent of tot out n node ; and d = ( a + a ) = k + k and d = aa are the total degree and the number of b-drected edges of node, respectvely. In ths paper, we manly study two parameters whch are degree and betweenness. So we defne preferental selecton schemes accordng to node degree and node betweenness for the model. They are detaled as below. ). Preferental selecton accordng to node degree: the probablty Pk () of node n the base network that s selected to be the coupled node s proportonal to k α, namely α k Pk () = (3) α k where k s the node degree of node. Accordng to the defnton, α s the preferental selecton exponent. If α > 0, the selecton scheme wll be prorty to select the nodes wth hgher degree. Specally, f α +, the selecton scheme wll select all the nodes wth the hghest degree. On the contrary, f α < 0, the result s opposte, t wll be prorty to select the nodes wth lower degree. Specally, f α, the selecton scheme wll select all the nodes wth the lowest degree. Besdes, f α = 0, the selecton scheme wll randomly select the nodes wth unform probablty. 2). Preferental selecton accordng to node betweenness: the probablty Pb () of node n the base network that s selected to be the coupled node s proportonal to k α b, namely α () b Pb = (4) α b where b s the node betweenness of node. Accordng to the defnton, α also s the preferental selecton exponent. If α > 0, the selecton scheme wll be prorty to select the nodes wth hgher betweenness. Specally, f α +, the selecton scheme wll select all the nodes wth the hghest betweenness. On the contrary, f α < 0, the result s opposte, t wll be prorty to select the nodes wth lower betweenness. Specally, f α, the selecton scheme wll select all the nodes wth the lowest betweenness. Besdes, f α = 0, the selecton scheme wll randomly select the nodes wth unform probablty. 2.3 The performance ndcators of the couplng network In the study, we determne two ndcators, the weghted average shortest path length and the use rate of the core network respectvely, as the measurements of the network performance. The weghted average shortest path length s defned as d d = (5) NN ( ) where d s the shortest path length between nodes and, N s the total number of nodes n the network. For a well-desgned real-world network, d s usually found to be small, such as the water supply networks, the Internet or transportaton networks, etc, whch we call the small-world phenomenon[35]. Another ndcator s the use rate of the core network η whch ranges n[ 0, ]. The use rate of the core network was used to characterze the proporton of flows on the core network, We defne the use rate of the core subnet η as E-ISSN: Volume 3, 204

5 δ η = 00% ζ (6) where δ s the number of the shortest paths whch pass through the core subnet n the couplng network, whle δ s the total number of the shortest paths n the couplng network. In the next secton, we wll explore the mpacts of dfferent couplng strateges wth dfferent preferental selecton exponent α on the network performances of dfferent structured base-core mode couplng networks based on our model. core network nodes. Namely, the greater n 2 / n s, the smaller < d > s. 3. Numercal smulaton To nvestgate the problems mentoned above, we conduct a numercal smulaton. In utlzaton, the ER random network model and the BA scale-free network model[33-35] are used for the generaton processes (step and step 2) of the base network and core network. It results n 4 dfferent assembles of the fnal couplng networks, whch are ER base network wth ER core network (ER-ER), ER base network wth BA core network (ER-BA), BA base network wth ER core network (BA-ER), and BA base network wth BA core network (BA-BA), respectvely. Of all these networks, specfcally we set up the number n of nodes n the base network to 000, the number n 2 of nodes n the core network to 00, 200 and 300 respectvely, the average node degree k for both the base network and the core network to 6, and the edge cost factor λ c for the core networks to 0.. We smulated under dfferent szes of the core networks and dfferent settngs of preferental selecton exponent α. The weghted average shortest path length of the base networks and the whole couplng network for each smulaton are recorded, for whch we denote as d 0 and d, respectvely. Fg. 3 shows the weghted average shortest path length rato < d > ( d = d d0, < d > represents an ensemble average.) decreases when the node degree or betweenness preferental selecton exponent α ncreases n ER-ER couplng networks. Namely, a hgher value of preferental selecton exponent α corresponds to a smaller weghted average shortest path length of the couplng network. In addton, the weghted average shortest path length decreases wth the ncreasng of the proporton of Fg. 3 Smulaton results for the weghted average shortest path length rato < d > n ER-ER couplng networks. The number n of nodes n the base network s set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental selecton scheme. Fg. 4 shows the weghted average shortest path length rato < d > ( d = d d0, < d > represents an ensemble average.) decreases when the node degree or betweenness preferental selecton exponent α ncreases n ER-BA couplng networks respectvely. Namely, a hgher preferental selecton exponent corresponds to a smaller weghted average shortest path length of the couplng network. In addton, the weghted average shortest path length decreases wth the ncreasng of the proporton of core network nodes. Namely, the greater n 2 / n s, the smaller < d > s. Fg. 5 shows the weghted average shortest path length rato < d > ( d = d d0, < d > represents an ensemble average.) decreases when the node degree or betweenness preferental selecton exponent α ncreases n BA-ER couplng networks respectvely. Namely, a hgher value of preferental selecton exponent α corresponds to a smaller weghted average shortest path length of the couplng network. In addton, the weghted average shortest path length decreases wth the ncreasng of the proporton of core network nodes. Namely, the greater n2 / n s, the smaller < d > s. E-ISSN: Volume 3, 204

6 selecton scheme. Fg. 6 shows the weghted average shortest path length rato < d > ( d = d d0, < d > represents an ensemble average.) decreases when the node degree or betweenness preferental selecton exponent α ncreases n BA-BA couplng networks. Namely, preferental selecton exponent corresponds to a smaller weghted average shortest path length of the couplng network. In addton, the weghted average shortest path length decreases wth the ncreasng of the proporton of core network nodes. Namely, the greater n2 / n s, the smaller < d > s. Fg. 4 Smulaton results for the weghted average shortest path length rato < d >n ER-BA couplng networks. The number n of nodes n the base network s set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental selecton scheme. Fg. 5 Smulaton results for the weghted average shortest path length rato < d >n BA-ER couplng networks. The number n of nodes n the base network s set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental Fg. 6 Smulaton results for the weghted average shortest path length rato < d >n BA-BA couplng networks. The number n of nodes n the base network s set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental selecton scheme. The curve of the two strateges for < d > s roughly the same. The reason s that researches have ndcated that for networks lke ER and BA networks there exsts a lnear correlaton of the node degree wth the node betweenness [36]. Besdes, the use rate of the core network s also recorded, for whch we denote as η. We detal the result as Fg. 7~ Fg. 0. Fgure 7 shows that the use rate of the core network η decreases when the node degree or betweenness preferental selecton exponent α ncreases n ER-ER couplng networks. Namely, a hgher preferental selecton exponent corresponds to a hgher use rate of the core network. In addton, the use rate of the core network E-ISSN: Volume 3, 204

7 ncreases wth the ncreasng of the proporton of core network nodes. Namely, the greater n 2 / n s, the bgger η s. to a hgher use rate of the core network. In addton, the use rate of the core network ncreases wth the ncreasng of the proporton of core network nodes. Namely, the greater n2 / n s, the bgger η s. Fg. 7 Smulaton results for the use rate η of the core network n ER-ER couplng networks. The number n of nodes n the base network s also set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental selecton scheme. Fgure 8 shows that the use rate of the core network η decreases when the node degree or betweenness preferental selecton exponent α ncreases n ER-BA couplng networks. Namely, a hgher preferental selecton exponent corresponds to a hgher use rate of the core network. In addton, the use rate of the core network ncreases wth the ncreasng of the proporton of core network nodes. Namely, the greater n2 / n s, the bgger η s. Fgure 9 shows that the use rate of the core network η decreases when the node degree or betweenness preferental selecton exponent α ncreases n BA-ER couplng networks. Namely, a hgher preferental selecton exponent corresponds to a hgher use rate of the core network. In addton, the use rate of the core network ncreases wth the ncreasng of the proporton of core network nodes. Namely, the greater n2 / n s, the bgger η s. Fgure 0 shows that the use rate of the core network η decreases when the node degree or betweenness preferental selecton exponent α ncreases n BA-BA couplng networks. Namely, a hgher preferental selecton exponent corresponds Fg. 8 Smulaton results for the use rate η of the core network n ER-BA couplng networks. The number n of nodes n the base network s also set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental selecton scheme. Fg. 9 Smulaton results for the use rate η of the core network n BA-ER couplng networks. The number n of nodes n the base network s also set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected E-ISSN: Volume 3, 204

8 accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental selecton scheme. Fg. 0 Smulaton results for the use rate η of the core network n BA-BA couplng networks. The number n of nodes n the base network s also set to be 000 whle the number n 2 of nodes n the core network s set to be 00(blue color), 200(green color), 300(red color) respectvely. The crcular lne represents the nodes of the core network are selected accordng to degree preferental selecton scheme whle the cross mark lne represents the nodes of the core network are selected accordng to betweenness preferental selecton scheme. The curve of the two strateges for η s roughly the same. The reason s that researches have ndcated that for networks lke ER and BA networks there exsts a lnear correlaton of the node degree wth the node betweenness [36]. 4. Conclusons In ths paper, we proposed a base-core couplng network model composed by a base network and a core network n accordance wth many real-world networks. We conduct the nvestgaton wth four dfferent assembles of common structure couplng networks, whch are ER base network wth ER core network (ER-ER), ER base network wth BA core network (ER-BA), BA base network wth ER core network (BA-ER), BA base network wth BA core network (BA-BA) respectvely. In the model, the base network s generated frst, then the nodes of the core network are selected from the base network accordng to a preferental selecton scheme based on node degree or betweenness. Under dfferent preferental selecton exponent, we nvestgate the performance of the couplng network n dfferent network structure and dfferent network sze collocatons. Smulaton result shows that: the greater of the preferental selecton exponent s, the smaller of the weghted average shortest path length of the couplng network s and the hgher of the use rate of the core network s. Namely, a hgher preferental selecton exponent corresponds to better network performance. Our studes can provde some gudance n real world stuatons on how to choose the nodes of base networks as the couplng nodes wth the core network to acheve a good couplng network performance. For example, t can be appled to choose the locaton of subway statons n publc transport networks, makng the whole network to obtan a good network performance whle low down the constructon fee. More mportantly, we should take spatal factors nto account when desgn and optmze the real-world networks. And we should say that there are stll lots of problems left for us. For example, there should be some better selecton strateges f other factors are concerned. Besdes, the mult-layered complex networks, the couplng network traffc flow characterstcs consderng unevenly traffc demand and dfferent node capacty, and the dynamcal behavors on couplng networks are also worth studyng. As couplng and nterdependent networks have attracted more and more attentons, the research on ths feld should be more delghtng n the further. 5. Acknowledgements The work s supported by the Natonal Natural Scence Foundaton of Chna under Grant No References: [] Chua, Hon Nan; Sung, Wng-Kn; Wong, Lmsoon, Explotng ndrect neghbours and topologcal weght to predct proten functon from proten-proten nteractons, Bonformatcs, Vol. 22, No. 3, 2006, pp [2] Seo, Sangae; Jang, Yunho; Qan, Pengfe, Effcent predcton of proten conformatonal pathways based on the hybrd elastc network model, Journal of Molecular Graphcs & Modellng, Vol. 47, E-ISSN: Volume 3, 204

9 204, pp [3] Volos, C., Ner, F., An ntroducton to the specal ssue: Recent advances n defense systems: Applcatons, methodology, technology, WSEAS Transactons on Systems, Vol., No. 9, 202, pp [4] S. Stanes A., Ner F., A Matrx Transton Orented Net for Modelng Dstrbuted Complex Computer and Communcaton Systems, WSEAS Transactons on Systems, Vol. 3, 204, pp [5] Kothar, Anta; Hamel, Nada; MacDonald, Jo-Anne, Explorng Communty Collaboratons: Socal Network Analyss as a Reflectve Tool for Publc Health, Systemc Practce and Acton Research, Vol. 27, No. 2, 204, pp [6] Lu, Zhe-Mng; Wu, Zhen; Guo, Sh-Ze, A New Dynamc Communty Model for Socal Networks, Internatonal Journal of Modern Physcs C, Vol. 25, No. 2, 204, [7] Ner, F., An ntroducton to the specal ssue on computatonal technques for tradng systems, tme seres forecastng, stock market modelng, and fnancal assets modelng, WSEAS Transactons on Systems, Vol., No. 2, 202, pp [8] Camller M., Ner F., Papoutsdaks M., An Algorthmc Approach to Parameter Selecton n Machne Learnng usng Meta- Optmzaton Technques, WSEAS Transactons on Systems, Vol. 3, 204, pp [9] Guo, Wenng; Zhang, We, A survey on ntellgent routng protocols n wreless sensor networks, Journal of Network and Computer Applcatons, Vol. 38, specal ssue, 204, pp [0] Lee, Junghoon; Tepedelenloglu, Chan, Dstrbuted Detecton n Coexstng Large- Scale Sensor Networks, WSEAS Transactons on Systems, Vol. 4, No. 4, 204, pp [] Pandey, Manusha; Verma, Shekhar, Prvacy Provsonng n Wreless Sensor Networks, Wreless Personal Communcatons, Vol. 75, No. 2, 204, pp [2] M Papoutsdaks, D Promals, F Ner, M Camller, Intellgent Algorthms Based on Data Processng for Modular Robotc Vehcles Control, WSEAS Transactons on Systems, Vol. 3, 204, PP [3] Subashn, M. Monca; Sahoo, Sarat Kumar, Smulaton and evaluaton of urban bus-networks usng a multagent approach, Smulaton Modelng Practce and Theory, Vol. 5, No. 6, 2007, pp [4] Veremyev, Alexander; Sorokn, Alexey; Bognsk, Vladmr, Mnmum vertex cover problem for coupled nterdependent networks wth cascadng falures, European Journal of Operatonal Research, Vol. 232, No. 3, 204, pp [5] Hu, Yanqng; Zhou, Dong; Zhang, Ru, Percolaton of nterdependent networks wth ntersmlarty, Physcal Revew E, Vol. 88, No. 5, 203, [6] Schneder, Chrstan M.; Yazdan, Nur; Arauo, Nuno A. M., Towards desgnng robust coupled networks, Scentfc Reports, Vol. 3, 203, 969. [7] Xu-Hua Yang, Ju-Qang Zhao, Guang Chen, You-Yu Dong, Study on Propertes of Traffc Flow on Bus Transport Networks, WSEAS Transactons on Systems, Vol. 3, 204, pp [8] Zhou, D; Gao, Janx; Stanley, H. Eugene, Percolaton of partally nterdependent scale-free networks, Physcal Revew E, Vol. 87, No. 5, 203, [9] Xu-Hua Yang, Guang Chen, Bao Sun, Sheng-Yong Chen, Wan-Lang Wang, Bus transport network model wth deal n-depth clque network topology, Physca A: Statstcal Mechancs and ts Applcatons, Vol. 39, No. 3, 202, pp [20] Agosto, Dense E.; Abbas, June; Naughton, Robn, Relatonshps and socal rules: Teens' socal network and other ICT selecton practces, Journal of the Amercan Socety for Informaton Scence and Technology, Vol. 390, 20, pp [2] Rera-Fernandez, Pablo; Munteanu, Crstan R.; Pedrera-Souto, Neves, Defnton of Markov-Harary Invarants and Revew of Classc Topologcal Indces and Databases n Bology, Parastology, Technology, and Socal-Legal Networks, Current Bonformatcs, Vol. 6, No., 20, pp [22] Cuomo, Francesca; Canfran, Antono; Polvern, Marco, Network prunng for energy savng n the Internet, Computer Networks, Vol. 56, No. 0, specal ssue, 202, pp E-ISSN: Volume 3, 204

10 [23] Vespgnan, Alessandro, The fraglty of nterdependency Complex Networks, Nature, Vol. 464, No. 729, 200, pp [24] Panou, M., Ner, F., Open research ssues on Modelng, Smulaton and Optmzaton n Electrcal Systems, WSEAS Transactons on Systems, Vol. 3, n press. [25] Kurant, M; Thran, P, Layered complex networks, Physcal Revew Letters, Vol. 96, No. 3, 2006, [26] Zou, Sheng-Rong; Zhou, Ta; Lu, A-Fen, Topologcal relaton of layered complex networks, Physcs Letters A, Vol. 374, No. 43, 200, pp [27] Morrs, R. G.; Barthelemy, M., Transport on Coupled Spatal Networks, Physcal Revew Letters, Vol. 09, No.2, 202, [28] Parshan, Ron; Buldyrev, Sergey V.; Havln, Shlomo, Interdependent Networks: Reducng the Couplng Strength Leads to a Change from a Frst to Second Order Percolaton Transton, Physcal Revew Letters, Vol. 05, No.4, 200, [29] Parshan, R.; Rozenblat, C.; Ietr, D., Intersmlarty between coupled networks, EPL, Vol. 92, No. 6, 200, [30] Xu-Hua Yang; Bo Wang; Sheng-Yong Chen; Wan-Lang Wang, Epdemc Dynamcs Behavor n Some Bus Transport Networks, Physca A: Statstcal Mechancs and ts Applcatons, Vol. 39, No. 3, 202, pp [3] Ouyang, Mn; Duenas-Osoro, Leonardo, An approach to desgn nterface topologes across nterdependent urban nfrastructure systems, Relablty Engneerng & System Safety, Vol. 96, No., 20, pp [32] Tao, Xandng; Schonfeld, Paul, Selecton and schedulng of nterdependent transportaton proects wth sland models, Transportaton Research Record-Seres, Vol. 98, 2006, pp [33] Barabas, AL; Albert, R, Emergence of scalng n random networks, Relablty Scence, Vol. 286, No. 5439, 999, pp [34] Shang, Ylun, Dstnct Clusterngs and Characterstc Path Lengths n Dynamc Small-World Networks wth Identcal Lmt Degree Dstrbuton, Journal of Statstcal Physcs, Vol. 49, No. 3, 202, pp [35] Watts, DJ; Strogatz, SH, Collectve dynamcs of 'small-world' networks, Nature, Vol. 393, No. 6684, 998, pp [36] Cohen, R; Havln, S, Scale-free networks are ultrasmall, Physcal Revew Letters, Vol. 90, No. 5, 2003, pp E-ISSN: Volume 3, 204