CN101795299B - Internet hierarchy modeling method based on economic relation - Google Patents

Abstract

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

Internet Hierarchical Modeling Method Based on Economic Relations

technical field

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.

Background technique

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.

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.

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.

Contents of the invention

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.

The present invention is achieved through the following technical solutions, comprising the following steps:

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.

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.

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.

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.

The layer selection method is to obtain the layer set T that the newly added node is allowed to join, specifically:

1) Determine whether there is an AS in the second layer network, put 2 into T, if yes, execute 2); if not, end;

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) 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) 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.

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.

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.

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 .

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;

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.

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).

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.

Description of drawings

Fig. 1 is the simulation comparison schematic diagram of the overall node degree distribution of embodiment model network and real network;

Fig. 2 is a schematic diagram of the simulation comparison of node degree distribution in the second layer of the embodiment;

Fig. 3 is a schematic diagram of the simulation comparison of node degree distribution in the third layer of the embodiment;

Fig. 4 is a schematic diagram of a simulation comparison of node degree distribution in the fourth layer of the embodiment.

Detailed ways

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.

Example

This embodiment includes the following steps:

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.

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.

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.

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.

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.

The layer selection method is to obtain the layer set T that the newly added node is allowed to join, specifically:

1) Determine whether there is an AS in the second layer network, put 2 into T, if yes, execute 2); if not, end;

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) 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) 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.

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.

In this embodiment, the newly added node finally joins the third-layer network.

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) If a new node chooses to join the second layer, its probability of becoming an ISP is

$\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="H201010300130920100108E000022.png"\; state="\{\{state\}\}">p</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 5.27</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.21</span>}& \mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 17077</span>}\\ \mathrm{<span\; class="notranslate">\; 0.3</span>}& \mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 17077</span>}\end{array}\right.<span\; class="notranslate">\; ,</span>$

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) 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) 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) If the newly added node chooses to join the fifth layer, its node attributes are all NI.

The final attribute of the newly added node in this embodiment is ISP.

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 .

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.

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.

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.

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.

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.

Claims (6)

1. A method for hierarchical modeling of the Internet based on economic relations, characterized in that, comprising the following steps: The first step is to divide the entire Internet into five levels based on the economic relationship contained in the edge, and initialize the model; The five levels mentioned are: the network top supplier nodes with P2C connection and P2P connection but no C2P connection are classified as the first layer network; the nodes with C2P connection with the first layer nodes are classified as It is classified as the second layer network; the nodes that have C2P connections with the second layer nodes and are not included in the second layer are classified as the third layer network; there will be C2P connections with the third layer nodes and are not included in the second layer The nodes in the layer or the third layer are classified as the fourth layer network; the nodes that have C2P connections 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 network; In the second step, according to the layer selection method, the network layer set T that the newly added node is allowed to join is obtained, and the layer random number generator selects the layer that the newly added node specifically joins from the network layer set T according to the speed of each network; The third step is to determine whether the attribute of the newly added node is ISP or NI according to the attribute selection method; 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 . 2. the Internet hierarchical modeling method based on economic relations according to claim 1, is characterized in that, the initialization of model described in the first step is: determine the number of nodes of the first layer network, the number of edges, The maximum and minimum degree information, and keep the first layer of the network unchanged during the subsequent modeling process. 3. The Internet hierarchical modeling method based on economic relations according to claim 1, characterized in that, the hierarchical selection method described in the second step is to obtain the hierarchical set T that a new joining node is allowed to join, comprising: 1) Determine whether there is an AS in the second layer network, put 2 into T, if yes, execute 2); if not, end; 2) Determine whether there is an AS in the third-tier network, if so, put 3 into T, and execute 3); if not, further determine whether the number of network provider nodes in the second-tier network exceeds the second Layer threshold, if exceeded, put 3 into T, and execute 3), if not exceeded, end; 3) Determine whether there is an AS in the fourth-layer network, if so, put 4 into T, and execute 4); if not, further determine 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) Determine whether there is an AS in the fifth-layer network, and if so, put 5 into T and end; if not, further determine 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. 4. the Internet hierarchical modeling method based on economic relationship according to claim 1, is characterized in that, the attribute selection method described in the 3rd step is: the attribute of the new node that joins the fifth layer network is all NI, 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, among which: the probability range of the new node joining the second layer network being an ISP is 0.21-0.3, adding The probability range of a new node in the third layer network being an ISP is 0.2-0.25, and the probability range of a new node joining the fourth layer network being an ISP is 0.1-0.13. 5. The Internet hierarchical modeling method based on economic relations according to claim 1, wherein the method for connecting edges described in the fourth step is: when a new node joins the n-th layer network and the attribute of the new node When it is NI, the new node is connected with the original ISP nodes in the n-1th layer network, the nth layer network and the n+1th layer network respectively according to the order of the node degree, using linear priority to perform C2P connection; when the new node joins the mth layer network and the attribute of the new node is an ISP, the new node and the original ISP nodes in the m-1th layer network, m-th layer network, and m+1-th layer network respectively use linear priority to perform C2P according to the order of node degrees. connection, and the original ISP nodes in the m-th layer network perform P2P connections according to the order of the product of node degrees, and the original ISP nodes between the m-th layer and the m-1th layer network perform P2P connections according to the order of the product of node degrees; : n is 2 or 3 or 4 or 5, but when n is 5, the new node only forms a C2P connection with the original ISP node in the fourth layer network; m is 2 or 3 or 4, but when m is 4 , the new node only forms a C2P connection with the original ISP node in the third layer network and the fifth layer network. 6. The Internet hierarchical modeling method based on economic relations according to claim 1, characterized in that, when the speed vector L described in the fourth step is greater than 0 and less than 1, a connecting edge will be formed with probability L, Or no edge is formed with probability (1-L); when the rate vector L is greater than 1 and less than 2, two edges will be formed with probability (L-1), or one edge will be formed with probability (2-L) .

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