CN101795299B - Internet hierarchy modeling method based on economic relation - Google Patents
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Abstract
本发明公开了一种互联网技术领域的基于经济关系的互联网层次化建模方法,包括以下步骤:基于连边所包含的经济关系,将整个互联网划分为五个层次;按照层次选择方法将网络中新加入的节点归为五个层次中的其中一层;按照属性选择方法确定新加入的节点的属性是网络供应商还是普通用户;按照连边方法,根据新加入节点的层次和属性,在互联网中建立新的连接关系。本发明不仅在网络信息上加入了节点和连边属性的划分,而且通过层次划分使模型网络在各层次内部尽量保持真实网络的拓扑特性,充分改进了以往模型中的不足之处。
The invention discloses an Internet hierarchical modeling method based on economic relations in the field of Internet technology, which includes the following steps: dividing the entire Internet into five levels based on the economic relations contained in the connecting edges; Newly added nodes are classified as one of the five levels; according to the attribute selection method, determine whether the attribute of the newly added node is a network provider or an ordinary user; according to the edge connection method, according to the level and attribute of the newly added node, Create a new connection relationship. The invention not only adds the division of node and edge attributes to the network information, but also makes the model network maintain the topological characteristics of the real network in each level through the hierarchical division, and fully improves the shortcomings of the previous models.
Description
技术领域 technical field
本发明涉及的是一种互联网技术领域的方法,具体是一种基于经济关系的互联网层次化建模方法。The invention relates to a method in the technical field of the Internet, in particular to an Internet hierarchical modeling method based on economic relations.
背景技术 Background technique
互联网拓扑建模作为互联网研究的重要组成部分,受到越来越广泛的关注。其中AS(自治系统)是处于一个管理机构控制之下的路由器和网络群组,相比路由器级互联网建模,AS(自治系统)级互联网拓扑建模的研究更加深入也更受人关注。目前研究人员普遍对基于互联网真实信息的拓扑研究达成共识,近年来很多模型的提出都致力于网络精确建模的发展。Internet topology modeling, as an important part of Internet research, has received more and more attention. Among them, AS (Autonomous System) is a group of routers and networks under the control of a management organization. Compared with router-level Internet modeling, research on AS (Autonomous System)-level Internet topology modeling is more in-depth and attracts more attention. At present, researchers have generally reached a consensus on the topology research based on the real information of the Internet. In recent years, many models have been proposed for the development of accurate network modeling.
经对现有文献检索发现,S.Shakkottai等人于2006年在arxiv网站上发表了题为“Economic evolution of the Internet AS-level ecosystem(自治系统级互联网生态系统的经济演化)”的文章,该文提出了MA模型(多级引力模型),通过将网络节点区分为ISP(网络供应商)和non-ISP(非网络供应商),较为准确地再现了真实网络中度分布的幂律特性,并得到极为近似的斜率。然而该模型尽管从整体角度而言有较高的保真度,但是不能保证在局部范围内仍然具备如此良好的特性。After searching the existing literature, it was found that S. Shakkottai et al published an article entitled "Economic evolution of the Internet AS-level ecosystem (Economic evolution of the autonomous system-level Internet ecosystem)" on the arxiv website in 2006. This paper proposes the MA model (multi-level gravity model), which accurately reproduces the power-law characteristics of the moderate distribution of the real network by dividing the network nodes into ISP (Internet Provider) and non-ISP (non-Internet Provider). And get a very similar slope. However, despite the high fidelity of the model from an overall point of view, there is no guarantee that the model still has such good properties on a local scale.
又经检索发现,2004年Physical Review E上刊登了题为“Accurately modeling theInternet topology(互联网精确拓扑建模)”的文章,该文提出了PFP模型(正反馈偏好模型),该模型较好的保持了真实网络中的rich-club(富人俱乐部)特性,但该模型是图论意义上抽象的节点和连边,没有考虑网络的真实标注信息,也不曾考虑模型的局部范围特性是否依然良好。After searching, it was found that an article entitled "Accurately modeling the Internet topology (Internet precise topology modeling)" was published on Physical Review E in 2004. This article proposed a PFP model (positive feedback preference model), which maintains The rich-club (rich club) characteristics in the real network are described, but the model is an abstract node and connection edge in the sense of graph theory, without considering the real label information of the network, and whether the local range characteristics of the model are still good.
发明内容 Contents of the invention
本发明的目的在于克服现有技术存在的上述不足,提供一种基于经济关系的互联网层次化建模方法。本发明基于连边所包含的经济关系,将整个互联网划分为五层网络,充分考虑了节点和连边的属性划分以及区域性层次划分,所以在全局拓扑特性和局部拓扑特性上都与真实网络较为相似。The purpose of the present invention is to overcome the above-mentioned deficiencies in the prior art, and provide a hierarchical modeling method of the Internet based on economic relations. The present invention divides the entire Internet into a five-layer network based on the economic relationship contained in the connection, and fully considers the attribute division and regional hierarchical division of nodes and connection edges, so it is consistent with the real network in terms of global topological characteristics and local topological characteristics. Relatively similar.
本发明是通过以下技术方案实现的,包括以下步骤:The present invention is achieved through the following technical solutions, comprising the following steps:
第一步,基于连边所包含的经济关系,将整个互联网划分为五个层次,并对模型进行初始化。In the first step, the entire Internet is divided into five levels based on the economic relations contained in the edges, and the model is initialized.
所述的五个层次分别为:将只具有P2C(供应商-用户)连边和P2P(对等-对等)连边,但不存在C2P(用户-供应商)连边的网络顶级供应商节点归为第一层;将与第一层节点存在C2P连边的节点归为第二层;将与第二层节点存在C2P连边且不包含在第二层中的节点归为第三层;将与第三层节点存在C2P连边且不包含在第二层或第三层中的节点归为第四层;将与第四层节点存在C2P连边且不包含在第二层或第三层或第四层中的节点归为第五层。The five levels mentioned are respectively: top-level network suppliers that will only have P2C (supplier-user) connections and P2P (peer-to-peer) connections, but no C2P (user-provider) connections Nodes are classified into the first layer; nodes that have C2P connections with nodes in the first layer are classified into the second layer; nodes that have C2P connections with nodes in the second layer and are not included in the second layer are classified into the third layer ; Classify the nodes that have C2P connections with the third layer nodes and are not included in the second layer or the third layer into the fourth layer; will have C2P connections with the fourth layer nodes and are not included in the second layer or the third layer Nodes in layers three or four are grouped in layer five.
所述的对模型进行初始化是:确定第一层网络的节点数、连边数、最大度和最小度信息,并在后面建模的过程中保持第一层网络不变。The initialization of the model is to determine the number of nodes, the number of edges, the maximum degree and the minimum degree information of the first-layer network, and keep the first-layer network unchanged in the subsequent modeling process.
第二步,按照层次选择方法得到新加入节点允许加入的网络层次集T,并由层次随机数生成器按照各网络的速率从网络层次集T中选择新加入节点具体加入的层次。In the second step, according to the layer selection method, the network layer set T that the new node is allowed to join is obtained, and the layer random number generator selects the specific layer that the new node joins from the network layer set T according to the speed of each network.
所述的层次选择方法是得到新加入节点允许加入的层次集T,具体是:The layer selection method is to obtain the layer set T that the newly added node is allowed to join, specifically:
1)判断第二层网络中是否有AS,将2放入T中,如果有,则执行2);如果没有,则结束;1) Determine whether there is an AS in the second layer network, put 2 into T, if yes, execute 2); if not, end;
2)判断第三层网络中是否有AS,如果有,则将3放入T中,并执行3);如果没有,则进一步判断第二层网络中的网络供应商节点的数量是否超过第二层阈值,如果超过,则将3放入T,并执行3),如果没有超过,则结束;2) Judging whether there is an AS in the third layer network, if so, put 3 into T, and execute 3); if not, then further judge whether the number of network provider nodes in the second layer network exceeds the second Layer threshold, if exceeded, put 3 into T, and execute 3), if not exceeded, end;
3)判断第四层网络中是否有AS,如果有,则将4放入T中,并执行4);如果没有,则进一步判断第三层网络中的网络供应商节点的数量是否超过第三层阈值,如果超过,则将4放入T,并执行4),如果没有超过,则结束;3) Judging whether there is an AS in the fourth layer network, if so, put 4 into T, and execute 4); if not, then further judge whether the number of network provider nodes in the third layer network exceeds the third Layer threshold, if exceeded, put 4 into T, and execute 4), if not exceeded, end;
4)判断第五层网络中是否有AS,如果有,则将5放入T中,并结束;如果没有,则进一步判断第四层网络中的网络供应商节点的数量是否超过第四层阈值,如果超过,则将5放入T,并结束,如果没有超过,则结束。4) Determine whether there is an AS in the fifth-layer network, and if so, put 5 into T and end; if not, then further judge whether the number of network provider nodes in the fourth-layer network exceeds the fourth-layer threshold , if it exceeds, put 5 into T, and end, if not, end.
第三步,按照属性选择方法确定新加入的节点的属性是ISP还是NI(普通用户)。The third step is to determine whether the attribute of the newly added node is ISP or NI (ordinary user) according to the attribute selection method.
所述的属性选择方法是:加入第五层网络的新节点的属性都是NI,加入第二层网络、第三层网络和第四层网络的新节点的属性则由属性随机数生成器确定,其中:加入第二层网络的新节点是ISP的概率范围是0.21-0.3,加入第三层网络的新节点是ISP的概率范围是0.2-0.25,加入第四层网络的新节点是ISP的概率范围是0.1-0.13。The attribute selection method is: the attributes of the new nodes joining the fifth layer network are all NI, and the attributes of the new nodes joining the second layer network, the third layer network and the fourth layer network are determined by the attribute random number generator , where the probability range of a new node joining the second layer network being an ISP is 0.21-0.3, the probability range of a new node joining the third layer network being an ISP is 0.2-0.25, and the new node joining the fourth layer network being an ISP The probability range is 0.1-0.13.
第四步,根据新加入节点的层次和属性,按照连边方法得到节点间允许建立的新连接关系,并由连接关系随机数生成器根据连边速率向量L最终确定互联网中建立的新连接关系。In the fourth step, according to the level and attributes of the newly added nodes, the new connection relationship allowed to be established between nodes is obtained according to the edge connection method, and the new connection relationship established in the Internet is finally determined by the connection relationship random number generator according to the connection rate vector L .
所述的连边方法是:当新节点加入第n层网络且该新节点的属性是NI时,新节点分别与第n-1层网络、第n层网络和第n+1层网络中的原有ISP节点按照节点度的排序采用线性优先进行C2P连接;当新节点加入第m层网络且该新节点的属性是ISP时,新节点分别与第m-1层网络、第m层网络和第m+1层网络中的原有ISP节点按照节点度的排序采用线性优先进行C2P连接,且第m层网络内部原有ISP节点按照节点度的乘积顺序进行P2P连接,第m层与第m-1层网络之间的原有ISP节点按照节点度的乘积顺序进行P2P连接;The method of connecting edges is: when a new node joins the nth layer network and the attribute of the new node is NI, the new node is connected with the n-1th layer network, the nth layer network and the n+1th layer network respectively. The original ISP nodes use linear priority to connect C2P according to the order of node degree; when a new node joins the m-th layer network and the attribute of the new node is ISP, the new node is respectively connected to the m-1 layer network, the m-th layer network and The original ISP nodes in the m+1 layer network use linear priority to perform C2P connections according to the order of node degrees, and the original ISP nodes in the m layer network perform P2P connections according to the product order of node degrees. - The original ISP nodes between layer 1 networks perform P2P connections according to the order of the product of node degrees;
其中:n取2或者3或者3或者5,但当n取5时,新节点仅与第四层网络中原有的ISP节点形成C2P连接关系;m取2或者3或者4,但当m取4时,新节点仅分别与第三层网络和第五层网络中原有的ISP节点形成C2P连接。Among them: n is 2 or 3 or 3 or 5, but when n is 5, the new node only forms a C2P connection relationship with the original ISP node in the fourth layer network; m is 2 or 3 or 4, but when m is 4 When , the new node only forms a C2P connection with the original ISP node in the third layer network and the fifth layer network respectively.
所述的速率向量L大于0且小于1时,将以概率L形成一条连边,或以概率(1-L)不形成连边;当速率向量L大于1且小于2时,将以概率(L-1)形成两条连边,或者以概率(2-L)形成一条连边。When the speed vector L is greater than 0 and less than 1, a connection edge will be formed with probability L, or no connection edge will be formed with probability (1-L); when the speed vector L is greater than 1 and less than 2, a connection edge will be formed with probability ( L-1) form two connected edges, or form a connected edge with probability (2-L).
与现有技术相比,本发明的有益效果是:不仅在网络信息上加入了节点和连边属性的划分,而且通过层次划分使模型网络在各层次内部尽量保持真实网络的拓扑特性,充分改进了以往模型中的不足之处。Compared with the prior art, the beneficial effect of the present invention is: not only the division of node and edge attributes is added to the network information, but also the model network keeps the topological characteristics of the real network in each level as far as possible through the hierarchical division, fully improving shortcomings in previous models.
附图说明 Description of drawings
图1是实施例模型网络与真实网络的整体节点度分布的仿真比较示意图;Fig. 1 is the simulation comparison schematic diagram of the overall node degree distribution of embodiment model network and real network;
图2是实施例第二层内节点度分布的仿真比较示意图;Fig. 2 is a schematic diagram of the simulation comparison of node degree distribution in the second layer of the embodiment;
图3是实施例第三层内节点度分布的仿真比较示意图;Fig. 3 is a schematic diagram of the simulation comparison of node degree distribution in the third layer of the embodiment;
图4是实施例第四层内节点度分布的仿真比较示意图。Fig. 4 is a schematic diagram of a simulation comparison of node degree distribution in the fourth layer of the embodiment.
具体实施方式 Detailed ways
以下结合附图对本发明的方法进一步描述:本实施例在以本发明技术方案为前提下进行实施,给出了详细的实施方式和具体的操作过程,但本发明的保护范围不限于下述的实施例。Below in conjunction with accompanying drawing, the method of the present invention is further described: present embodiment is carried out under the premise of technical solution of the present invention, has provided detailed implementation and specific operation process, but protection scope of the present invention is not limited to following Example.
实施例Example
本实施例包括以下步骤:This embodiment includes the following steps:
第一步,基于连边所包含的经济关系,将整个互联网划分为五个层次,并对模型进行初始化。In the first step, the entire Internet is divided into five levels based on the economic relations contained in the edges, and the model is initialized.
所述的五个层次分别为:将只具有P2C连边和P2P连边,但不存在C2P连边的网络顶级供应商节点归为第一层;将与第一层节点存在C2P连边的节点归为第二层;将与第二层节点存在C2P连边且不包含在第二层中的节点归为第三层;将与第三层节点存在C2P连边且不包含在第二层或第三层中的节点归为第四层;将与第四层节点存在C2P连边且不包含在第二层或第三层或第四层中的节点归为第五层。The five levels mentioned are: the top network supplier nodes that only have P2C and P2P connections but no C2P connections are classified as the first layer; the nodes that have C2P connections with the first layer nodes Classify into the second layer; classify the nodes that have C2P connections with the second layer nodes and are not included in the second layer into the third layer; have C2P connections with the third layer nodes and are not included in the second layer or The nodes in the third layer are classified as the fourth layer; the nodes that have C2P connection with the fourth layer nodes and are not included in the second layer or the third layer or the fourth layer are classified as the fifth layer.
所述的对模型进行初始化是:确定第一层网络的节点数、连边数、最大度和最小度信息,并在后面建模的过程中保持第一层网络不变。The initialization of the model is to determine the number of nodes, the number of edges, the maximum degree and the minimum degree information of the first-layer network, and keep the first-layer network unchanged in the subsequent modeling process.
本实施例的第一层网络包括:11个节点和41条连边,其中:最大度为10,最小度为4,第一节点分别和第二节点-第十一节点相连,第二节点分别和第三节点-第十节点相连,第三节点分别和第四节点-第十节点相连,第四节点分别和第七节点-第十一节点相连,第五节点分别和第七节点-第十一节点相连,第六节点分别和第七节点-第十一节点相连,第七节点和第八节点相连。The first-layer network of this embodiment includes: 11 nodes and 41 connecting edges, wherein: the maximum degree is 10, the minimum degree is 4, the first node is connected to the second node-the eleventh node respectively, and the second node is respectively It is connected with the third node-the tenth node, the third node is respectively connected with the fourth node-the tenth node, the fourth node is connected with the seventh node-the eleventh node respectively, and the fifth node is respectively connected with the seventh node-the tenth node One node is connected, the sixth node is respectively connected with the seventh node-the eleventh node, and the seventh node is connected with the eighth node.
第二步,按照层次选择方法得到新加入节点允许加入的网络层次集T,并由层次随机数生成器按照各网络的速率从网络层次集T中选择新加入节点具体加入的层次。In the second step, according to the layer selection method, the network layer set T that the new node is allowed to join is obtained, and the layer random number generator selects the specific layer that the new node joins from the network layer set T according to the speed of each network.
所述的层次选择方法是得到新加入节点允许加入的层次集T,具体是:The layer selection method is to obtain the layer set T that the newly added node is allowed to join, specifically:
1)判断第二层网络中是否有AS,将2放入T中,如果有,则执行2);如果没有,则结束;1) Determine whether there is an AS in the second layer network, put 2 into T, if yes, execute 2); if not, end;
2)判断第三层网络中是否有AS,如果有,则将3放入T中,并执行3);如果没有,则进一步判断第二层网络中的网络供应商节点的数量是否超过第二层阈值,如果超过,则将3放入T,并执行3),如果没有超过,则结束;2) Judging whether there is an AS in the third layer network, if so, put 3 into T, and execute 3); if not, then further judge whether the number of network provider nodes in the second layer network exceeds the second Layer threshold, if exceeded, put 3 into T, and execute 3), if not exceeded, end;
3)判断第四层网络中是否有AS,如果有,则将4放入T中,并执行4);如果没有,则进一步判断第三层网络中的网络供应商节点的数量是否超过第三层阈值,如果超过,则将4放入T,并执行4),如果没有超过,则结束;3) Judging whether there is an AS in the fourth layer network, if so, put 4 into T, and execute 4); if not, then further judge whether the number of network provider nodes in the third layer network exceeds the third Layer threshold, if exceeded, put 4 into T, and execute 4), if not exceeded, end;
4)判断第五层网络中是否有AS,如果有,则将5放入T中,并结束;如果没有,则进一步判断第四层网络中的网络供应商节点的数量是否超过第四层阈值,如果超过,则将5放入T,并结束,如果没有超过,则结束。4) Determine whether there is an AS in the fifth-layer network, and if so, put 5 into T and end; if not, then further judge whether the number of network provider nodes in the fourth-layer network exceeds the fourth-layer threshold , if it exceeds, put 5 into T, and end, if not, end.
经过上述判断,本实施例新加入节点允许加入的层次集T为{2,3,4,5},第二层网络的速率V2、第三层网络的速率V3、第四层网络的速率V4和第五层次的速率V5之比是V2∶V3∶V4∶V5=242∶550∶193∶21,因此新加入节点以242/(242+550+193+21)的概率加入第二层网络,或者以550/(242+550+193+21)的概率加入第三层网络,或者以193/(242+550+193+21)的概率加入第四层网络,或者以21/(242+550+193+21)的概率加入第五层网络。After the above judgments, the layer set T that the newly added node is allowed to join in this embodiment is {2, 3, 4, 5}, the rate of the second layer network is V2, the rate of the third layer network is V3, and the rate of the fourth layer network is V4 The ratio to the rate V5 of the fifth level is V2:V3:V4:V5=242:550:193:21, so the newly added node joins the second layer network with the probability of 242/(242+550+193+21), Either join the third-tier network with a probability of 550/(242+550+193+21), or join the fourth-tier network with a probability of 193/(242+550+193+21), or join the fourth-tier network with a probability of 21/(242+550 +193+21) probability to join the fifth layer network.
本实施例新加入节点最终加入第三层网络。In this embodiment, the newly added node finally joins the third-layer network.
第三步,按照属性选择方法确定新加入的节点的属性是ISP还是NI。The third step is to determine whether the attribute of the newly added node is ISP or NI according to the attribute selection method.
1)若新加入节点选择加入到第二层,则其成为ISP的概率为1) If a new node chooses to join the second layer, its probability of becoming an ISP is
其中N为新加入节点加入之前网络中的节点总数;新加入节点成为NI的概率为1-p2。Among them, N is the total number of nodes in the network before the new node joins; the probability of the new node becoming NI is 1-p2.
2)若新加入节点选择加入到第三层,则其成为ISP的概率为p3=0.22,成为NI的概率为1-p3。2) If a new node chooses to join the third layer, the probability of becoming an ISP is p3=0.22, and the probability of becoming an NI is 1-p3.
3)若新加入节点选择加入到第四层,则其成为ISP的概率为p4=0.11,成为NI的概率为1-p4。3) If the newly joined node chooses to join the fourth layer, the probability of becoming an ISP is p4=0.11, and the probability of becoming an NI is 1-p4.
4)若新加入节点选择加入到第五层,则其节点属性都为NI。4) If the newly added node chooses to join the fifth layer, its node attributes are all NI.
本实施例新加入节点的最终属性是ISP。The final attribute of the newly added node in this embodiment is ISP.
第四步,根据新加入节点的层次和属性,按照连边方法得到节点间允许建立的新连接关系,并由连接关系随机数生成器根据连边速率向量L最终确定互联网中建立的新连接关系。In the fourth step, according to the level and attributes of the newly added nodes, the new connection relationship allowed to be established between nodes is obtained according to the edge connection method, and the new connection relationship established in the Internet is finally determined by the connection relationship random number generator according to the connection rate vector L .
本实施例新加入节点加入第三层网络,且该新加入节点的属性是ISP,则第三层网络中新加入节点和原有节点形成C2P连边的速率向量L33_C2P是0.53,第三层网络中原有节点间形成P2P连边的速率向量L33_P2P是0.02,第三层网络新加入节点和第二层网络原有节点形成C2P连边的速率向量L32_C2P是1.88,第二层网络中原有节点间形成P2P连边的速率向量L32_P2P是0.13,第三层网络新加入节点和第四层网络原有节点间形成C2P连边的速率向量L34_C2P是0.05。In this embodiment, a newly added node joins the third layer network, and the attribute of the newly added node is ISP, then the rate vector L33_C2P of the C2P connection edge formed by the newly added node and the original node in the third layer network is 0.53, and the third layer network The rate vector L33_P2P of the P2P connection between the original nodes is 0.02, the rate vector L32_C2P of the C2P connection between the newly added node of the third layer network and the original node of the second layer network is 1.88, and the formation of the original node in the second layer network The rate vector L32_P2P of the P2P edge is 0.13, and the rate vector L34_C2P of the C2P edge formed between the newly added node of the third layer network and the original node of the fourth layer network is 0.05.
本实施例根据连边方法得到:第三层网络中新加入节点和原有节点以0.53的概率形成一条C2P连边,或者以0.47的概率不形成C2P连边;第三层网络中原有ISP节点间以0.02的概率形成一条P2P连边,或者以0.98的概率不形成P2P连边;第三层网络新加入节点和第二层网络原有节点以0.88的概率形成两条C2P连边,或者以0.12的概率形成一条C2P连边;第二层网络与第三层网络中原有ISP节点间以0.13的概率形成一条P2P连边,或者以0.87的概率不形成P2P连边;第三层网络新加入节点和第四层网络原有节点间以0.05的概率形成一条C2P连边,或者以0.95的概率不形成C2P连边。This embodiment obtains according to the edge connection method: the newly added node and the original node in the third layer network form a C2P connection edge with a probability of 0.53, or do not form a C2P connection edge with a probability of 0.47; the original ISP node in the third layer network A P2P connection is formed with a probability of 0.02, or no P2P connection is formed with a probability of 0.98; two C2P connections are formed with a probability of 0.88 between a newly added node in the third layer network and an existing node in the second layer network, or with a probability of 0.98 A C2P connection is formed with a probability of 0.12; a P2P connection is formed between the second layer network and the original ISP node in the third layer network with a probability of 0.13, or no P2P connection is formed with a probability of 0.87; A C2P connection is formed between the node and the original node of the fourth layer network with a probability of 0.05, or no C2P connection is formed with a probability of 0.95.
本实施例该新加入节点最终建立的连接关系是:新加入节点作为第三层ISP属性节点,与第二层中原有的两个ISP节点分别形成两条C2P连边,并且和第三层中原有的一个ISP节点形成一条C2P连边,新加入节点未与第四层中的ISP节点形成C2P连边,第二层网络中的一个ISP节点与第三层网络中的一个ISP节点形成P2P连边,第三层网络中的ISP节点之间未形成P2P连边。In this embodiment, the connection relationship finally established by the newly added node is: the newly added node, as the third layer ISP attribute node, forms two C2P connection edges with the original two ISP nodes in the second layer, and connects with the original ISP node in the third layer Some ISP nodes form a C2P connection. The newly added node does not form a C2P connection with the ISP node in the fourth layer. An ISP node in the second layer network forms a P2P connection with an ISP node in the third layer network. There is no P2P connection between ISP nodes in the third layer network.
第五步,依次重复第二步、第三步和第四步,不断增加模型网络的节点和连边数量。In the fifth step, repeat the second, third and fourth steps in sequence to continuously increase the number of nodes and edges in the model network.
本实施例模型网络与真实网络的整体节点度分布的仿真比较示意图如图1所示,其中:第二层内节点度分布的仿真比较示意图如图2所示,第三层内节点度分布的仿真比较示意图如图3所示,第四层内节点度分布的仿真比较示意图如图4所示,通过上述四种仿真结果可以看出,本实施例模型网络不仅在全局特性上与真实网络非常相似,而且在局部特性上也有非常良好的保真度,这是本实施例方法与以往互联网拓扑建模方法相比最重要的优势。The simulation comparison schematic diagram of the overall node degree distribution of the model network and the real network in this embodiment is shown in Figure 1, wherein: the simulation comparison diagram of the node degree distribution in the second layer is shown in Figure 2, and the simulation comparison diagram of the node degree distribution in the third layer The simulation comparison diagram is shown in Figure 3, and the simulation comparison diagram of the node degree distribution in the fourth layer is shown in Figure 4. From the above four simulation results, it can be seen that the model network in this embodiment is not only very similar to the real network in terms of global characteristics. similarity, and also has very good fidelity in local characteristics, which is the most important advantage of the method in this embodiment compared with previous Internet topology modeling methods.
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