CN105634905A - Global homogeneous dependent network coupling method - Google Patents

Abstract

The invention discloses a global homogeneous dependent network coupling method. The method is used for dynamically establishing dependency links between two sub-networks according to a uniform total degree distribution principle. The dependency links are established between the sub-networks with the total degree distribution uniformity of a single network A/B as the principle. The specific method comprises the following steps: firstly, figuring out the average degree <kA> of the original networks AB, and then the average degree of the coupled network A ' is <kA '> = <kA> +1; and then, establishing the dependency links in two networks marked with sequence numbers Ai and Bi according to a certain step. A simulation result indicates that the proposed global homogeneous dependent mode can improve the robust performance of dependent networks regardless of random attacks or deliberate attacks.

Description

A kind of overall situation interdependent network coupling process of homogeneity

Technical field

The present invention relates to interdependent networking technology area, in particular a kind of overall situation interdependent network coupling process of homogeneity.

Background technology

Most of infrastructure networks have uncalibrated visual servo characteristic (scale-free), as: electric power networks, communication network, internet net, air line network etc., and mutual dependence for existence between these networks, constitute interdependent network. The interdependent pattern (CGCM) of interdependent network is one of key factor affecting its robustness.

The modernization of human society is increasingly dependent on infrastructure network, such as power network, internet net, the network of communication lines, energy net, communication network etc. Acting on each other and mutual dependence for existence between these infrastructure networks, such as the relation of interdependence between power system and communication system, power system needs communication system to communicate and dispatches, and communication system needs power system to provide electric power support. Its robust performance is had large effect by this dependence relation between network, one nodes lost efficacy, it is possible to cause additionally and it has the nodes of dependence relation to lose efficacy, thus causing a series of reaction of losing efficacy, or even the inefficacy of whole network, i.e. cascading failure reaction. One the most typical example is exactly that the power breakdown accident in Italy occurs in JIUYUE, 2003, dependence relation due to supply network and communication network, when breaking down in a power station, directly results in its SCADA communication network to lose efficacy, communication network lost efficacy and had in turn resulted in the further inefficacy of electrical network power station, thus causing large area power breakdown accident. Within the more than ten years in past, people are for dynamic cascading inefficacy modeling in single network (real network and various analog network), and effectively protection has made substantial amounts of research work with control cascading failure communication strategy, the different attack strategies of contrast. But numerous similar 2003 Italian power station accidents excite people to having two and having the network of dependence relation above and study in the face of the survivability of cascading failure, it it is one of study hotspot about network security in current complex network.

2010, Buldyrew et al. proposes mutual dependence for existence network first in the face of the robustness theoretical analysis model [BuldyrevSV of cascading failure on " Nature " magazine, ParshaniR, PaulG, StanleyHE, HavlinS2010Nature4641025], open people's new page from complex network angle research mutual dependence for existence network. Buldyrew et al. analyzes cascading failure process, it has been found that interdependent network is more fragile than single layer network. Vespignani et al. obtains same conclusion at document [VespignaniA2010Nature464984], dependence relation between network, greatly reduce the robust performance of the infrastructure network with close coupled relation, so proposing to need to consider the cascading failure problem of interdependent network when the system of design. the each side research that thus interdependent cascade lost efficacy all constantly is carried out, the particularly research of relation between coupled relation and the network security performance between network, document [WangJW, ChenJ, QianJF2014PhysicaA393535] to BA/ER composition the interdependent network of difference at interdependent pattern (AssortativeLink (AL) three kinds different, DisassortativeLink (DL), RandomLink (RL)) under, after considering load capacity and loading failure, the reassignment situation of capacity has been studied, research finds that the robust performance of network is all had impact by network structure and internetwork CGCM, document [ChengZS, CaoJD2015PhysicaA430193] difference of robust performance of focusing on comparative analysis is identical and different sub-network network type is constituted under node Random Coupling pattern one to one interdependent network, research finds that the interdependent network that dissimilar sub-network is constituted is more fragile than the interdependent network that same type sub-network is constituted. the structure of interdependent network is all had certain directive significance by the studies above achievement, but the dependence relation of real interdependent network is flexible, not being fixed as in the situation that single-phase is complied with or multiplephase is complied with, the control such as power station may rely on one or more neighbouring communication website. therefore between two sub-networks, how to set up the interdependent limit between them so that it is there is stronger robustness dynamic flexible, be a problem being more worth research.

Summary of the invention

The present invention is directed to the deficiencies in the prior art and propose a kind of overall situation interdependent network coupling process of homogeneity, the method dynamically sets up interdependent limit according to always spending the principle being evenly distributed between two sub-networks.

Compressing the degree distribution of interdependent network on the one hand, improving it in the face of the robust performance of random failure, the mutual dependence for existence of the another aspect big node of degree of avoiding again, thus being effectively improved it in the face of the robust performance of calculated attack. Owing to numerous infrastructure networks are respectively provided with uncalibrated visual servo characteristic, therefore the present invention builds two and has same node point number, the BA network composition interdependent network of BA-BA of different qualities, network robustness can be improved by the CGCM in order to carried interdependent network is better described, and three kinds of nodes coupled relation one to one (ALDLRL) and one-to-many random dependence pattern that employing literature research is conventional compare. Simulation result shows, no matter attacks or calculated attack in the face of random, is put forward the overall situation interdependent pattern of homogeneity and can both improve the robust performance of interdependent network.

Technical scheme is as follows:

A kind of overall situation interdependent network coupling process of homogeneity, is evenly distributed with total degree of single network A/B and turns to principle, set up interdependent limit between sub-network. First concrete grammar obtains the average degree < k of primitive network AB_A>, then coupling after network A ' average degree be < k_A'>=< k_A>+1; Sequence number A has been marked in accordance with the following steps at two_iAnd B_iNetwork in set up interdependent limit:

The first step: select the node A that A network moderate is minimum₁, successively with B network before m node B₁,B₂,��,B_mSet up interdependent limit, wherein $m=<k_{A^{\&prime;}}>-K_{A_1},k_{B_1}\&le;k_{B_2}\&le;,...,\&le;k_{B_{m-1}}\&le;k_{B_m}\&le;,...,\&le;k_{B_N}$ Make node A₁Total degree equal to average degree < k_A'>;

Second step: recalculate network A interior joint degree, is ranked up from small to large according to degree, and is labeled as A_i(i=1,2 ..., N), i.e. Representation node A_iDegree, if node has identical degree, prioritization not yet set up the node on interdependent limit;

3rd step: recalculate network B interior joint degree, sorts successively from small to large according to degree to the node in network B, and is labeled as B_iIf two nodes have identical degree, then prioritization not yet set up the node on interdependent limit;

Judge whether before setting up interdependent limit to have created the interdependent limit of N bar every time, otherwise repeat the first step to the 3rd step, set up interdependent limit successively, until completing the interdependent limit of N bar.

The present invention is directed to two sub-networks with uncalibrated visual servo characteristic and propose a kind of overall situation interdependent network CGCM of homogeneity. This pattern sets up the interdependent limit of interdependent network so that the degree of sub-network is evenly distributed for principle, the degree of compression dispersion of distribution on the one hand, improving its survivability to random failure, the big node of degree of avoiding (key node) is interdependent on the other hand, improves its survivability to calculated attack. The present invention by its with common node man-to-man with joining, different join and random dependence pattern and one-to-many random dependence pattern have done relative analysis, its robust performance under random failure and calculated attack of simulation study. Result of study shows, the interdependent network CGCM of the overall homogeneity that the present invention carries can be greatly improved the anti-cascading failure ability of interdependent network that uncalibrated visual servo sub-network is constituted. Achievement in research of the present invention can provide directive significance for the safe design of network etc.

Accompanying drawing explanation

Fig. 1 is interdependent cascade failure model schematic diagram, (a) network initial conditions (b) first step inefficacy (c) second step inefficacy (d) steady statue;

Fig. 2 is interdependent network CGCM schematic diagram, and (a) coupling (b) is different joins coupling (c) Random Coupling (d) overall situation homogeneity coupling (e) overall situation Random Coupling with joining;

Fig. 3 is BA-BA calculated attack schematic diagram; A () attacks ratio 0-40%, (b) attacks ratio 0-14%;

Fig. 4 is that BA-BA attacks schematic diagram at random; (a) random failure ratio 0-40%, (b) random failure ratio 0-55%;

Detailed description of the invention

Below in conjunction with specific embodiment, the present invention is described in detail.

1. cascading failure model and CGCM

1.1 interdependent cascade failure models

Present invention definition interdependent network model as shown in Fig. 1 (a) is the incomplete interdependent network with multiple corresponding relation, wherein not exclusively refer in network containing isolated node, it is man-to-man interdependent that multiple correspondence refers to that dependence relation had both included, and comprises again the interdependent of one-to-many. When isolated node number is zero and when being absent from one-to-many dependence relation, this model degenerates into complete single-phase according to model. Therefore this interdependent network model portrays basis of reality facility relation of interdependence is finer, has more Research Significance.

Assume that interdependent network is made up of two sub-network A and B, node connection within each sub-network is defined as connection limit (connectivitylinks), and the intermediate node connection of network A and network B is defined as interdependent limit (dependencylinks). when in interdependent network, the node of A or B network is under attack or when random failure, network A or B can be broken into several fragment, this model assumption only belongs to the node of (Giantcomponet) in network A or the huge tuple of network B can keep function, and the node belonging to other fragment can lose function, assuming that part of nodes is subject to initial attack and lost efficacy in network A, network A can be broken for some fragments, the node being not belonging to the huge tuple of A network also can lose efficacy, failure node in A network also results in corresponding node failure in B network, thus causing the broken of network B, therefore the node being not belonging to the huge tuple of network B also lost efficacy, further the failure node in B network causes corresponding node failure in A network, thus causing that network A crushes again, so it is repeatedly performed down, after experiencing the inefficacy of certain step number, system is finally reached stable.

The process of whole cascading failure is as shown in Figure 1, system initial conditions such as Fig. 1 (a), assume that the node A1 that A network moderate is big is subject to calculated attack, first stage failure procedure: remove node A1 and connect limit and interdependent limit accordingly, owing to the node A6 in network A is not in huge tuple, so A6 loses function, removing A6 and Lian Bianhou, system is such as shown in Fig. 1 (b). Second stage failure procedure: the node B1B6 in network B, owing to losing the interdependent limit of network A, thus losing efficacy, is shown in Fig. 1 (c). Phase III failure procedure: the inefficacy of node B1B6 makes B4 node not at largest connected, causes further inefficacy reaction to make node A4 lose interdependent limit and lost efficacy. Cascading failure stops, and final network stabilization is such as shown in Fig. 1 (d).

The 1.2 anti-cascading failure robustness of interdependent network are estimated

When nodes is attacked, in network, part of nodes is removed, propagation due to cascading failure, cause that in network, the node of other parts also lost efficacy, when cascading failure terminates, there is isolated node or scattered connected subgraph in network, and people choose subgraph maximum in the middle of these subgraphs, huge tuple (Giantcomponet) is as network topology structure after networks encounter cascading failure. The network size of maximal connected subgraphs and huge tuple is set to N', and the present invention adopts the index being used for tolerance network robustness of largest connected scale and former network (not being subjected to network when attacking) scale N^[32], namelyG-value is more big, and the robust performance that network has is more good. Wherein, N'=N_A'+N_B', N=N_A+N_B, N_ARepresent the nodes of sub-network A, N_BRepresent the nodes of sub-network B, N_A' represent the surviving node number in sub-network A under fire rear huge tuple, N_B' represent the surviving node number in sub-network B under fire rear huge tuple.

1.3 CGCMs

The present invention seeks to verify that being put forward the overall situation interdependent pattern of homogeneity can improve interdependent network robustness energy, in order to without loss of generality, we select two network A with same node point N and network B, and assume have the interdependent limit of N bar to be present in AB network. Node in network A is ranked up from small to large according to degree, and is labeled as A_i(i=1,2 ..., N), i.e.Representation node A_iDegree, if two nodes have identical degree, then they are carried out randomly ordered; Same to being ranked up from small to large according to degree of the node in network B, and it is labeled as B_i(i=1,2 ..., N) namelyRepresentation node B_iIf degree two nodes there is identical degree, then they are carried out randomly ordered.

The interdependent network CGCM now comparative study of the present invention used is described below:

1) with joining pattern (AssortativeLink) i.e. relevant connection, the node of network A and B is set up interdependent connection according to degree dependency, namelyThe node spending little node little with degree is interdependent, and the node spending big node big with degree is interdependent, as shown in Fig. 2 (a).

2) different join the uncorrelated connection of pattern (DisassortativeLink) i.e., the degree minor node spending big node and network B in network A is set up interdependent, namelyAs shown in Fig. 2 (b).

3) random model (RondomLink) namely randomly chooses a pair node, sets up interdependent limit, as shown in Fig. 2 (c).

4) the overall situation interdependent pattern of homogeneity (GlobalHomogenizingLink): be evenly distributed with total degree of single network A/B and turn to principle, set up interdependent limit between sub-network. First concrete grammar obtains the average degree < k of primitive network AB_A>, then coupling after network A ' average degree be < k_A'>=< k_A>+1. Sequence number A has been marked in accordance with the following steps at two_iAnd B_iNetwork in set up interdependent limit,

The first step: select the node A that A network moderate is minimum₁, successively with B network before m node B₁,B₂,��,B_mSet up interdependent limit, wherein $m=<k_{A^{\&prime;}}>-K_{A_1},k_{B_1}\&le;k_{B_2}\&le;,...,\&le;k_{B_{m-1}}\&le;k_{B_m}\&le;,...,\&le;k_{B_N}$ Make node A₁Total degree equal to average degree < k_A'����

Second step: recalculate network A interior joint degree, is ranked up from small to large according to degree, and is labeled as A_i(i=1,2 ..., N), i.e.Representation node A_iDegree, if node has identical degree, prioritization not yet set up the node on interdependent limit.

3rd step: recalculate network B interior joint degree, sorts successively from small to large according to degree to the node in network B, and is labeled as B_iIf two nodes have identical degree, then prioritization not yet set up the node on interdependent limit.

Judge whether before setting up interdependent limit to have created the interdependent limit of N bar every time, otherwise repeat the first step to the 3rd step, set up interdependent limit successively, until completing the interdependent limit of N bar.

As in figure 2 it is shown, Fig. 2 (d) neutron network A B is respectively arranged with 7 nodes, N=7. The degree that a column data is initial node under first in figure, it is seen that < k_A>=4, if producing 7 coupling edge, then average degree < the k of sub-network A after coupling_A'>=5, the node A that therefore first degree is minimum₁On can produce the interdependent limit of 5-2=3 bar. The first step sets up dependence relation with three the minimum nodes of spending in sub-network B, i.e. three solid black lines in Fig. 2 (d), the node degree recalculating sub-network B is a column data below step1. Node A₂On can produce the interdependent limit of 5-3=2 bar, set up dependence relation with spending minimum two node under step1 in network B, i.e. two red short dash lines in figure. The node degree recalculating sub-network B is a column data below step2. Node A₃On can produce the interdependent limit of 5-3=2 bar, and under step2 in network B, spend minimum node B₁And prioritizing selection B₄Set up dependence relation, i.e. two long dotted lines of blueness in figure. So far establishing 7 interdependent limits altogether, the degree that posterior nodal point has been set up total in interdependent limit distributes very evenly, and sees the data under final in Fig. 2 (d).

5) overall situation random dependence pattern (GlobalRandomLink), in order to better illustrate the advantage of GH pattern, special builds this overall situation random dependence pattern according to practical situation, and its rule is, limit interdependent limit that each node produces at most asWhen set up interdependent limit between the two networks at random, as shown in Fig. 2 (e).

2. simulation result and analysis

2.1 emulation are implemented

BA network model building mode is: given start node m₀, each time step increases a node and m bar limit, and is connected on existing node according to preferentially probability, generates parameter difference AB network. Network A has 500 nodes, and average degree is 4; Network B has 500 nodes, and average degree is 6. Build interdependent network A-B according to 5 kinds of CGCMs in Fig. 2, and A network is attacked.

Random failure strategy is the node failure (removal) randomly choosing certain proportion f, utilizes interdependent cascade failure model, calculates the huge tuple scale of five kinds of CGCM lower network survivals and the ratio G of former network size, and result is as shown in Figure 3. In figure, result is run the average result of 20 times. Calculated attack strategy is that network A interior joint degree carries out descending, the node that ratio is f that squencing attack is forward. Utilizing interdependent cascade failure model, calculate the huge tuple scale of five kinds of CGCM lower network survivals and the ratio G of former network size, result is as shown in Figure 4. In figure, result is run the average result of 20 times.

2.2 analysiss of simulation result

Observe Fig. 3 Fig. 4, plots changes corresponding to GH pattern is the slowest, data in table 1-table 4 it is also seen that, identical remove under ratio, the value of Network Survivability scale G corresponding under GH pattern is maximum, therefore no matter random failure or calculated attack, the survivability of the overall situation interdependent pattern of homogeneity is better than other pattern.

Observe Fig. 3 Fig. 4, plots changes corresponding to GH/GRL pattern relatively other Three models (AL/DL/RL) is slow, data in table 1-table 4 it is also seen that, identical remove under ratio, the value of Network Survivability scale G corresponding under GH/GRL pattern is all higher than other Three models, therefore no matter random failure or calculated attack, when setting up identical interdependent limit, the incomplete interdependent pattern (GH/GRL) of one-to-many is better than man-to-man complete interdependent pattern (AL/DL/RL). And in the incomplete interdependent pattern of one-to-many, the overall situation interdependent pattern of homogeneity (GH) is better than one-to-many random dependence (GRL), particularly in calculated attack situation, its effect becomes apparent from. Under calculated attack same attack 14% node, the survival scale of GH pattern lower network is 35.2%, and the survival scale of GRL pattern lower network is 26.7%, quite a lot of saved about 9% node. The node of random failure 65%, the survival scale of GH pattern lower network is 36.44%, and the survival scale of GRL pattern lower network is 29.37%, quite a lot of saved about 7% node.

The change curve of relative analysis three kinds complete interdependent pattern (AL/DL/RL) one to one, it can be seen that for random failure, is better than random model with joining pattern, and random model is better than different joining pattern. But for calculated attack, the data from table 1, table 2 are it can be seen that the node of attack 6% equally, and the Network Survivability scale of AL pattern is only 37.9%, and the Network Survivability scale of RL pattern is 72.73%, and the Network Survivability scale of DL pattern is only 81%. Therefore under calculated attack, different pattern of joining is better than random model, and pattern is better than with joining pattern immediately. This is because with joining under pattern, the node spending big node big with degree is interdependent, the node that calculated attack degree is big, the breaking-up caused is maximum, therefore join pattern seems more fragile under calculated attack together, and different pattern of joining, interdependent owing to spending big node and the little node of degree, so having certain survivability for calculated attack.

It can be seen that the important node of about attack 15% in comparison diagram 3 and Fig. 4, A network is just on the verge of paralysis, and the ratio of random failure is about 75%, and A network is just on the verge of paralysis, it is seen that calculated attack is powerful to the destruction of network. Therefore in network security research, identification and the protection to key node, there is important Research Significance.

Conclusions is obtained by numerical simulation, next explains these conclusions more intuitively from Fig. 2. Assume the number of degrees of AB digitized representation node below in figure, for instance in figure, A2 represents the number of degrees of this node is 2. Comparison diagram 2 (a) and Fig. 2 (b), it has been found that the node that calculated attack degree is big, in Fig. 2 (a), A7 and B7 is interdependent, once attacks, and removes 14 limits, so network cannot withstand a single blow; And Fig. 2 (b), if attacking A7, then destroy 8 limits altogether, therefore network is good relative to survivability. For random attack, Fig. 2 (b) attacks every time and all destroys 8 even limits, therefore more fragile, has then disperseed risk with joining pattern, and therefore robust performance is better than different joining pattern. Randomness due to Random Coupling pattern so that its for the robust performance of random failure and calculated attack all between AL and DL.

Analysis chart 2 (d) and Fig. 2 (e), it can be seen that the interdependent pattern of one-to-many can improve the robust performance of interdependent network. In Fig. 2 (d), it is assumed that A2 node failure, due to the existence of the multiple dependence relation in network, the interdependent node failure in B network can't be caused. And for interdependent network one to one, the inefficacy of A network node necessarily causes the interdependent node failure in B network, therefore GH and GRL pattern robust performance is better than AL, DL and RL.

The degree distribution of interdependent network is more wide, and network is more fragile in the face of the robustness of random failure, and GH pattern makes the degree distribution uniformity of network, and namely the width of degree of have compressed distribution, therefore improves survivability during interdependent network random failure. And GH pattern turn avoid spending the interdependent of big node, survivability when thus also improving interdependent network to calculated attack.

Table 1 calculated attack emulation data

	0.0200	0.0400	0.0600	0.0800	0.1000	0.1200	0.1400	0.1600	0.1800	0.2000
											GH	0.9740	0.9160	0.8780	0.8030	0.7180	0.6190	0.3520	0.2720	0.2420	0.2030
GRL	0.9724	0.9123	0.8666	0.7777	0.7150	0.5626	0.2670	0.2210	0.1933	0.1714
											AL	0.9500	0.8540	0.3790	0.3190	0.2540	0.1550	0	0	0	0
RL	0.9600	0.8543	0.7273	0.4056	0.3041	0.2252	0.0192	0	0	0
											DL	0.9600	0.8740	0.8100	0.7120	0.3060	0.2330	0.3166	0	0	0

Table 2 calculated attack emulation data (continued 1)

	0.2200	0.2400	0.2600	0.2800	0.3000	0.3200	0.3400	0.3600	0.3800	0.4000
											GH	0.2030	0.2030	0.1970	0.1970	0.1940	0.1940	0.1940	0.1940	0.1940	0.1940
GRL	0.1553	0.1553	0.1528	0.1506	0.1505	0.1505	0.1505	0.1505	0.1489	0.1489
											AL	0	0	0	0	0	0	0	0	0	0
RL	0	0	0	0	0	0	0	0	0	0
											DL	0	0	0	0	0	0	0	0	0	0

Table 3 random failure emulation data

Table 4 random failure emulation data (continued 3)

	0.55	0.6	0.65	0.7	0.75	0.8	0.85	0.9	0.95	1
											GH	0.4797	0.4159	0.3644	0.2970	0.2532	0.2240	0.2072	0.1987	0.1954	0.1940
GRL	0.4387	0.3608	0.2937	0.2297	0.2011	0.1792	0.1629	0.1520	0.1475	0.1447
											AL	0.1457	0.1021	0.0571	0.0244	0.0099	0.0064	0	0	0	0
RL	0.1096	0.0680	0.0310	0.0098	0.0035	0	0	0	0	0
											DL	0.1044	0.0543	0.0237	0.0054	0	0	0	0	0	0

The present invention is directed to two BA networks with same node point N, assume that it needs the foundation on the interdependent limit of N bar, the dependence relation establishment model of overall situation homogeneity is proposed, and by its with common node man-to-man with joining, different join and the overall random dependence pattern of random dependence pattern and one-to-many has made simulation analysis, its robust performance under random failure and calculated attack of comparative study, research conclusion is as follows:

1), no matter random failure or calculated attack, the survivability of the overall situation interdependent pattern of homogeneity is better than other pattern;

2), no matter random failure or calculated attack, when setting up identical interdependent limit, the incomplete interdependent pattern (GH/GRL) of one-to-many is better than man-to-man complete interdependent pattern (AL/DL/RL). And in the incomplete interdependent pattern of one-to-many, the overall situation interdependent pattern of homogeneity (GH) is better than one-to-many random dependence (GRL) pattern.

3), three kinds one to one in complete interdependent pattern (AL/DL/RL), for random failure, be better than random model with joining pattern, and random model is better than different pattern of joining, but for calculated attack, different pattern of joining is better than random model, and pattern is better than with joining pattern immediately.

4), calculated attack is powerful to the destruction of network. Therefore in network security research, identification and the protection to key node, there is important Research Significance.

To sum up, the dependence relation establishment model of the overall homogeneity that the present invention carries can improve the survivability faced under random failure and calculated attack of interdependent network, it is possible to the safe design for network provides directive significance.

It should be appreciated that for those of ordinary skills, it is possible to improved according to the above description or converted, and all these are improved and convert the protection domain that all should belong to claims of the present invention.

Claims (1)

1. the interdependent network coupling process of overall homogeneity, it is characterised in that be evenly distributed with total degree of single network A/B and turn to principle, set up interdependent limit between sub-network; First concrete grammar obtains the average degree < k of primitive network AB_A>, then coupling after network A ' average degree be < k_A'>=< k_A>+1; Sequence number A has been marked in accordance with the following steps at two_iAnd B_iNetwork in set up interdependent limit:

The first step: select the node A that A network moderate is minimum₁, successively with B network before m node B₁,B₂,��,B_mSet up interdependent limit, wherein $m=<k_{A\&prime;}>-{K_A}_1,$ ${k_B}_1\&le;{k_B}_2\&le;,...,\&le;{k_B}_{m-1}\&le;{k_B}_m,...,\&le;{k_B}_N$ Make node A₁Total degree equal to average degree < k_A'>;

Second step: recalculate network A interior joint degree, is ranked up from small to large according to degree, and is labeled as A_i(i=1,2 ..., N), i.e. Representation node A_iDegree, if node has identical degree, prioritization not yet set up the node on interdependent limit;

3rd step: recalculate network B interior joint degree, sorts successively from small to large according to degree to the node in network B, and is labeled as B_iIf two nodes have identical degree, then prioritization not yet set up the node on interdependent limit;

Judge whether before setting up interdependent limit to have created the interdependent limit of N bar every time, otherwise repeat the first step to the 3rd step, set up interdependent limit successively, until completing the interdependent limit of N bar.