CN101795299B - Internet hierarchy modeling method based on economic relation - Google Patents
Internet hierarchy modeling method based on economic relation Download PDFInfo
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Abstract
The invention relates to an internet hierarchy modeling method based on the economic relation, belonging to the technical field of the internet. The method comprises the following steps of: dividing the whole internet into five hierarchies based on the economic relation included by a connecting edge; classifying nodes newly added in a network into one of the five hierarchies according to a layering selection method; determining whether the attribute of the newly-added node is a supplier or a common user according to an attribute selection method; and establishing a new connection relation in the internet according to the hierarchy and the attribute of the newly-added nodes according to the method of the connecting edge. In the invention, the nodes and the attribute division of the connecting edge are added in the network information, and the model network maintains topology property of the real network in the interior of each hierarchy through layering division as much as possible, thereby the shortcoming of the conventional model is fully improved.
Description
Technical field
What the present invention relates to is a kind of method of Internet technical field, specifically is a kind of the Internet level modeling method based on economic relation.
Background technology
The Internet topology model construction receives concern more and more widely as the important component part of study Internet.Wherein AS (autonomous system) is in a router and a network group under management organization's control, compares the modeling of router level the Internet, and the research of AS (autonomous system) level the Internet topology model construction more deeply also more is concerned by people.The researcher generally reaches common understanding to the topology research based on the Internet real information at present, and the development of the accurate modeling of network all is devoted in the proposition of a lot of models in recent years.
Through existing literature search is found; People such as S.Shakkottai have delivered the article that is entitled as " Economic evolution of the Internet AS-level ecosystem (economy of the autonomic system the Internet ecosystem develops) " on the arxiv website in 2006; This article has proposed MA model (multistage gravity model); Through network node being divided into ISP (Network Provider) and non-ISP (non-Network Provider); Reproduce the Power Law that the live network moderate distributes comparatively exactly, and obtained very approximate slope.Although yet this model has higher fidelity from whole angle, can not guarantee in subrange, still to possess so good characteristic.
Find through retrieval again; Published the article that is entitled as " Accurately modeling theInternet topology (the accurate topology model construction in the Internet) " in 2004 on the Physical Review E; This article has proposed PFP model (positive feedback preference pattern); This model has kept the rich-club in the live network (Richman's Club) characteristic preferably; But this model is node and Lian Bian abstract on the graph theory meaning, does not consider the true markup information of network, never considers also whether the subrange characteristic of model is still good.
Summary of the invention
The objective of the invention is to overcome the above-mentioned deficiency that prior art exists, a kind of the Internet level modeling method based on economic relation is provided.The present invention is based on the economic relation that Lian Biansuo comprises; Whole the Internet is divided into five layer networks; The attribute that has taken into full account node and Lian Bian divides and regional level is divided, so all comparatively similar with live network on overall topological property and local topological property.
The present invention realizes through following technical scheme, may further comprise the steps:
The first step, the economic relation based on Lian Biansuo comprises is divided into five levels with whole the Internet, and model is carried out initialization.
Described five levels are respectively: will only have P2C (supplier-user) Lian Bian and P2P (equity-equity) and connect the limit, but the network top suppliers node that does not exist C2P (user-supplier) to connect the limit is classified as ground floor; To be classified as the second layer with the node that the ground floor node exists C2P to connect the limit; The node that will exist C2P to connect the limit with second layer node and not be included in the second layer is classified as the 3rd layer; To exist C2P to connect the limit with the 3rd node layer and be not included in the second layer or the 3rd layer in node be classified as the 4th layer; To exist C2P to connect the limit with the 4th node layer and be not included in the second layer or the 3rd layer or the 4th layer in node be classified as layer 5.
Describedly model carried out initialization be: confirm the ground floor network the node number, connect limit number, maximal degree and minimum degree information, and keep the ground floor network constant in the process of modeling in the back.
Second step obtained the network layer collection T that newly added node allows adding according to the level system of selection, and from network layer collection T, selected the concrete level that adds of newly added node by the level random number generator according to the speed of each network.
Described level system of selection is to obtain the layered subset T that newly added node allows adding, specifically:
1) judges whether AS is arranged in the second layer network, put into T with 2,, then carry out 2) if having; If no, then finish;
2) judge whether AS is arranged in the three-layer network, if having, then put into T, and carry out 3) 3; If no, judge further then whether the quantity of the Network Provider node in the second layer network surpasses second layer threshold value, if surpass, then put into T with 3, and carry out 3), if do not surpass, then finish;
3) judge whether AS is arranged in the four-layer network network, if having, then put into T, and carry out 4) 4; If no, judge further then whether the quantity of the Network Provider node in the three-layer network surpasses the 3rd layer of threshold value, if surpass, then put into T with 4, and carry out 4), if do not surpass, then finish;
4) judge whether AS is arranged in the layer 5 network,, then put into T, and finish 5 if having; If no, judge further then whether the quantity of the Network Provider node in the four-layer network network surpasses the 4th layer of threshold value, if surpass, then put into T, and finish 5, if do not surpass, then finish.
In the 3rd step, confirm that according to the attribute system of selection attribute of initiate node is ISP or NI (domestic consumer).
Described attribute system of selection is: the attribute that adds the new node of layer 5 network all is NI; The attribute that adds the new node of second layer network, three-layer network and four-layer network network is then confirmed by the attribute random number generator; Wherein: the new node that adds second layer network is that the probable range of ISP is 0.21-0.3; The new node that adds three-layer network is that the probable range of ISP is 0.2-0.25, and the new node that adds the four-layer network network is that the probable range of ISP is 0.1-0.13.
The 4th step according to the level and the attribute of newly added node, obtained allowing between node the new annexation set up according to connecting the limit method, and finally confirmed the new annexation set up in the Internet by the annexation random number generator according to connecting limit velocity vectors L.
The described limit method that connects is: when the attribute that adds n layer network and this new node when new node is NI, new node respectively with n-1 layer network, n layer network and n+1 layer network in original ISP node adopt linearity preferentially to carry out C2P according to the ordering of node degree to be connected; When the attribute that adds m layer network and this new node when new node is ISP; New node respectively with m-1 layer network, m layer network and m+1 layer network in original ISP node adopt linearity preferentially to carry out C2P according to the ordering of node degree to be connected; And the inner original ISP node of m layer network carries out P2P in proper order according to the product of node degree and connects, and the original ISP node between m layer and the m-1 layer network carries out P2P in proper order according to the product of node degree and is connected;
Wherein: n gets 2 or 3 or 3 or 5, but when n gets 5, new node only with the four-layer network network in original ISP node form the C2P annexation; M gets 2 or 3 or 4, but when m gets 4, new node only respectively with three-layer network and layer 5 network in original ISP node form C2P and be connected.
Described velocity vectors L is greater than 0 and less than 1 o'clock, will be with one of the L shaped one-tenth of probability even limit, or with probability (1-L) company of formation limit not; When velocity vectors L greater than 1 and less than 2 the time, will form two even limits with probability (L-1), perhaps form an even limit with probability (2-L).
Compared with prior art; The invention has the beneficial effects as follows: not only on the network information, added node and the division that connects side attribute; And divide through level and to make prototype network keep the topological property of live network in each level inside as far as possible, fully improved the weak point in the model in the past.
Description of drawings
Fig. 1 is that sketch map is compared in the emulation that the integral node degree of embodiment prototype network and live network distributes;
Fig. 2 is that sketch map is compared in the emulation that embodiment second layer interior nodes degree distributes;
Fig. 3 is that sketch map is compared in the emulation that the 3rd layer of interior nodes degree of embodiment distributes;
Fig. 4 is that sketch map is compared in the emulation that the 4th layer of interior nodes degree of embodiment distributes.
Embodiment
Below in conjunction with accompanying drawing method of the present invention is further described: present embodiment provided detailed execution mode and concrete operating process, but protection scope of the present invention is not limited to following embodiment being to implement under the prerequisite with technical scheme of the present invention.
Embodiment
Present embodiment may further comprise the steps:
The first step, the economic relation based on Lian Biansuo comprises is divided into five levels with whole the Internet, and model is carried out initialization.
Described five levels are respectively: will only have that P2C connects the limit and P2P connects the limit, but the network top suppliers node that does not exist C2P to connect the limit is classified as ground floor; To be classified as the second layer with the node that the ground floor node exists C2P to connect the limit; The node that will exist C2P to connect the limit with second layer node and not be included in the second layer is classified as the 3rd layer; To exist C2P to connect the limit with the 3rd node layer and be not included in the second layer or the 3rd layer in node be classified as the 4th layer; To exist C2P to connect the limit with the 4th node layer and be not included in the second layer or the 3rd layer or the 4th layer in node be classified as layer 5.
Describedly model carried out initialization be: confirm the ground floor network the node number, connect limit number, maximal degree and minimum degree information, and keep the ground floor network constant in the process of modeling in the back.
The ground floor network of present embodiment comprises: 11 nodes and 41 company limits; Wherein: maximal degree is 10, and minimum degree is 4, and first node links to each other with Section Point-Di 11 nodes respectively; Section Point links to each other with the 3rd node-protelum point respectively; The 3rd node links to each other with the 4th node-protelum point respectively, and the 4th node links to each other with the 7th node-the 11 node respectively, and the 5th node links to each other with the 7th node-the 11 node respectively; The 6th node links to each other with the 7th node-the 11 node respectively, and the 7th node links to each other with the 8th node.
Second step obtained the network layer collection T that newly added node allows adding according to the level system of selection, and from network layer collection T, selected the concrete level that adds of newly added node by the level random number generator according to the speed of each network.
Described level system of selection is to obtain the layered subset T that newly added node allows adding, specifically:
1) judges whether AS is arranged in the second layer network, put into T with 2,, then carry out 2) if having; If no, then finish;
2) judge whether AS is arranged in the three-layer network, if having, then put into T, and carry out 3) 3; If no, judge further then whether the quantity of the Network Provider node in the second layer network surpasses second layer threshold value, if surpass, then put into T with 3, and carry out 3), if do not surpass, then finish;
3) judge whether AS is arranged in the four-layer network network, if having, then put into T, and carry out 4) 4; If no, judge further then whether the quantity of the Network Provider node in the three-layer network surpasses the 3rd layer of threshold value, if surpass, then put into T with 4, and carry out 4), if do not surpass, then finish;
4) judge whether AS is arranged in the layer 5 network,, then put into T, and finish 5 if having; If no, judge further then whether the quantity of the Network Provider node in the four-layer network network surpasses the 4th layer of threshold value, if surpass, then put into T, and finish 5, if do not surpass, then finish.
Through above-mentioned judgement; It is { 2,3,4 that the present embodiment newly added node allows the layered subset T that adds; 5}; The ratio of the speed V5 of the speed V4 of the speed V2 of second layer network, the speed V3 of three-layer network, four-layer network network and layer 5 time is V2: V3: V4: V5=242: 550: 193: 21, so newly added node adds second layer network with the probability of 242/ (242+550+193+21), perhaps the probability with 550/ (242+550+193+21) adds three-layer network; Perhaps the probability with 193/ (242+550+193+21) adds the four-layer network network, and perhaps the probability with 21/ (242+550+193+21) adds the layer 5 network.
The final three-layer network that adds of present embodiment newly added node.
In the 3rd step, confirm that according to the attribute system of selection attribute of initiate node is ISP or NI.
1) if newly added node is selected to join the second layer, then its probability that becomes ISP does
Wherein N is the node sum in the network before newly added node adds; The probability that newly added node becomes NI is 1-p2.
2) if newly added node is selected to join the 3rd layer, then its probability that becomes ISP is p3=0.22, and the probability that becomes NI is 1-p3.
3) if newly added node is selected to join the 4th layer, then its probability that becomes ISP is p4=0.11, and the probability that becomes NI is 1-p4.
4) if newly added node is selected to join layer 5, then its nodal community all is NI.
The final attribute of present embodiment newly added node is ISP.
The 4th step according to the level and the attribute of newly added node, obtained allowing between node the new annexation set up according to connecting the limit method, and finally confirmed the new annexation set up in the Internet by the annexation random number generator according to connecting limit velocity vectors L.
The present embodiment newly added node adds three-layer network; And the attribute of this newly added node is ISP; Then in the three-layer network newly added node and original node to form the velocity vectors L33_C2P that C2P connects the limit be 0.53; Forming the velocity vectors L33_P2P that P2P connects the limit in the three-layer network between original node is 0.02; It is 1.88 that the original node of three-layer network newly added node and second layer network forms the velocity vectors L32_C2P that C2P connects the limit, forms velocity vectors L32_P2P that P2P connects the limit in the second layer network between original node and be that to form the velocity vectors L34_C2P that C2P connects the limit between 0.13, the three-layer network newly added node and the original node of four-layer network network be 0.05.
Present embodiment obtains according to connecting the limit method: newly added node and original node form a C2P with 0.53 probability and connect the limit in the three-layer network, perhaps do not form C2P with 0.47 probability and connect the limit; Form a P2P with 0.02 probability between original ISP node in the three-layer network and connect the limit, perhaps do not form P2P and connect the limit with 0.98 probability; Three-layer network newly added node and the original node of second layer network form two C2P with 0.88 probability and connect the limit, perhaps form a C2P with 0.12 probability and connect the limit; Form a P2P with 0.13 probability between original ISP node in second layer network and the three-layer network and connect the limit, perhaps do not form P2P and connect the limit with 0.87 probability; Form a C2P with 0.05 probability between three-layer network newly added node and the original node of four-layer network network and connect the limit, perhaps do not form C2P and connect the limit with 0.95 probability.
The final annexation of setting up of this newly added node of present embodiment is: newly added node is as the 3rd layer of ISP attribute node; Form two C2P respectively with original two ISP nodes in the second layer and connect the limit; And and C2P of original ISP node formation connects the limit in the 3rd layer; Newly added node not with the 4th layer in the ISP node form C2P and connect the limit; An ISP node in ISP node in the second layer network and the three-layer network forms P2P and connects the limit, does not form P2P between the ISP node in the three-layer network and connects the limit.
The 5th step repeated for second step, the 3rd step and the 4th step successively, constantly increased the node and the Lian Bian quantity of prototype network.
Relatively sketch map is as shown in Figure 1 in the emulation that the integral node degree of present embodiment prototype network and live network distributes; Wherein: relatively sketch map is as shown in Figure 2 in the emulation that second layer interior nodes degree distributes; Relatively sketch map is as shown in Figure 3 in the emulation of the 3rd layer of interior nodes degree distribution; Relatively sketch map is as shown in Figure 4 in the emulation of the 4th layer of interior nodes degree distribution, can find out that through above-mentioned four kinds of simulation results the present embodiment prototype network is not only closely similar with live network on global property; And very good fidelity also arranged on local characteristics, to be the present embodiment method compare most important advantage with the Internet topological modelling approach in the past for this.
Claims (6)
1. the Internet level modeling method based on economic relation is characterized in that, may further comprise the steps:
The first step, the economic relation based on Lian Biansuo comprises is divided into five levels with whole the Internet, and model is carried out initialization;
Described five levels are respectively: will have that P2C connects the limit and P2P connects the limit, but the network top suppliers node that does not exist C2P to connect the limit is classified as the ground floor network; To be classified as second layer network with the node that the ground floor node exists C2P to connect the limit; The node that will exist C2P to connect the limit with second layer node and not be included in the second layer is classified as three-layer network; To exist C2P to connect the limit with the 3rd node layer and be not included in the second layer or the 3rd layer in node be classified as the four-layer network network; To exist C2P to connect the limit with the 4th node layer and be not included in the second layer or the 3rd layer or the 4th layer in node be classified as the layer 5 network;
Second step obtained the network layer collection T that newly added node allows adding according to the level system of selection, and from network layer collection T, selected the concrete level that adds of newly added node by the level random number generator according to the speed of each network;
In the 3rd step, confirm that according to the attribute system of selection attribute of initiate node is ISP or NI;
The 4th step according to the level and the attribute of newly added node, obtained allowing between node the new annexation set up according to connecting the limit method, and finally confirmed the new annexation set up in the Internet by the annexation random number generator according to connecting limit velocity vectors L.
2. the Internet level modeling method based on economic relation according to claim 1; It is characterized in that; Model carried out initialization be described in the first step: confirm the ground floor network the node number, connect limit number, maximal degree and minimum degree information, and keep the ground floor network constant in the process of modeling in the back.
3. the Internet level modeling method based on economic relation according to claim 1 is characterized in that, the level system of selection described in second step is to obtain the layered subset T that newly added node allows adding, comprising:
1) judges whether AS is arranged in the second layer network, put into T with 2,, then carry out 2) if having; If no, then finish;
2) judge whether AS is arranged in the three-layer network, if having, then put into T, and carry out 3) 3; If no, judge further then whether the quantity of the Network Provider node in the second layer network surpasses second layer threshold value, if surpass, then put into T with 3, and carry out 3), if do not surpass, then finish;
3) judge whether AS is arranged in the four-layer network network, if having, then put into T, and carry out 4) 4; If no, judge further then whether the quantity of the Network Provider node in the three-layer network surpasses the 3rd layer of threshold value, if surpass, then put into T with 4, and carry out 4), if do not surpass, then finish;
4) judge whether AS is arranged in the layer 5 network,, then put into T, and finish 5 if having; If no, judge further then whether the quantity of the Network Provider node in the four-layer network network surpasses the 4th layer of threshold value, if surpass, then put into T, and finish 5, if do not surpass, then finish.
4. the Internet level modeling method based on economic relation according to claim 1; It is characterized in that; Attribute system of selection described in the 3rd step is: the attribute that adds the new node of layer 5 network all is NI; The attribute that adds the new node of second layer network, three-layer network and four-layer network network is then confirmed by the attribute random number generator; Wherein: the new node that adds second layer network is that the probable range of ISP is 0.21-0.3, and the new node that adds three-layer network is that the probable range of ISP is 0.2-0.25, and the new node that adds the four-layer network network is that the probable range of ISP is 0.1-0.13.
5. the Internet level modeling method based on economic relation according to claim 1; It is characterized in that; Company's limit method described in the 4th step is: when the attribute that adds n layer network and this new node when new node is NI, new node respectively with n-1 layer network, n layer network and n+1 layer network in original ISP node adopt linearity preferentially to carry out C2P according to the ordering of node degree to be connected; When the attribute that adds m layer network and this new node when new node is ISP; New node respectively with m-1 layer network, m layer network and m+1 layer network in original ISP node adopt linearity preferentially to carry out C2P according to the ordering of node degree to be connected; And the inner original ISP node of m layer network carries out P2P in proper order according to the product of node degree and connects, and the original ISP node between m layer and the m-1 layer network carries out P2P in proper order according to the product of node degree and is connected; Wherein: n gets 2 or 3 or 4 or 5, but when n gets 5, new node only with the four-layer network network in original ISP node form the C2P annexation; M gets 2 or 3 or 4, but when m gets 4, new node only with three-layer network and layer 5 network in original ISP node form C2P and be connected.
6. the Internet level modeling method based on economic relation according to claim 1 is characterized in that, the velocity vectors L described in the 4th step is greater than 0 and less than 1 o'clock, will be with one of the L shaped one-tenth of probability even limit, or with probability (1-L) company of formation limit not; When velocity vectors L greater than 1 and less than 2 the time, will form two even limits with probability (L-1), perhaps form an even limit with probability (2-L).
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Non-Patent Citations (2)
| Title |
|---|
| Shi Zhou et.al.Accurately modeling the internet topology.《PHYSICAL REVIEW E 70, 066108 (2004)》.2004, * |
| Srinivas Shakkottai.economic evolution of the internet AS-level ecosystem.《arXiv:cs.NI/0608058 v2 18 Aug 2006》.2006, * |
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