CN107391832A - The method for realizing network reconfiguration is accurately matched using a step phase iterative data - Google Patents

The method for realizing network reconfiguration is accurately matched using a step phase iterative data Download PDF

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CN107391832A
CN107391832A CN201710577599.9A CN201710577599A CN107391832A CN 107391832 A CN107391832 A CN 107391832A CN 201710577599 A CN201710577599 A CN 201710577599A CN 107391832 A CN107391832 A CN 107391832A
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network
phase
node
reconstructed
rebuild
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吴建设
党妮
焦李成
申星
李晓杰
王超民
焦杨
武晓敏
田小林
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Xidian University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The method for realizing network reconfiguration is accurately matched the invention discloses a step phase iterative data.Solves the technical problem for the supposition network topology structure that almost Perfect is only can be achieved with a step phase iterative data information.To a network to be reconstructed, some nodes that phase association reconstruction of relations network moderate is minimum are utilized；It will complete to rebuild node and even side remove from network to be reconstructed；Reduce network size to be reconstructed；New round reconstruction is carried out on new network to be reconstructed, removes work, is sky to network to be reconstructed so repeatedly.Because original phase association relation can be destroyed from removal operation, subsequent reconstruction is influenceed, invention defines a phase more new formula to update nodes phase to be reconstructed, phase association relation is still set up.The present invention only needs indivisible data message i.e. reconfigurable network.Present invention reconstruct validity is obtained for fine checking, and various artificial networks, especially BA scales-free networks and real network can be reconstructed by the present invention.

Description

The method for realizing network reconfiguration is accurately matched using a step phase iterative data
Technical field
The invention belongs to complex network technical field, is related to network dynamics behavior and complex network reconstructs, and specifically one Kind accurately matches the method for realizing network reconfiguration using a step phase iterative data.Reconstruct for real network.
Background technology
Network is ubiquitous in actual life, as interpersonal relationship, internet, power network, the network of communication lines, gene regulatory network, WWW etc., these networks are more and our life is closely bound up.Power network paralysis, traffic congestion, computer virus invasion etc. Either large or small network contingency also happens occasionally.Property and behavior of the mankind only to network have more deeper into understanding, It can more effectively prevent even to prevent the generation of disparate networks accident.The topological structure of network to the function of network and behavior often Conclusive effect is played, but directly can not measure or measure with the presence or absence of connection between each unit in network sometimes Get up to need to expend huge cost, at this moment just need to speculate the structure of network by measuring some signals of network indirectly.
Network reconfiguration is one branch of complex network research field, and reconstructing method speculates the topological structure of network, general feelings Under condition, the topological structure of network plays a decisive role to the function of network, thus the topological structure for obtaining network contribute to deeper into Research network function.Existing substantial amounts of researcher proposes to utilize response dynamics, energy spectrum analysis, pattra leaves in recent years The methods of this estimation, noise driving power, carries out network reconfiguration.
Generally, the dynamic information (e.g., phase information) of switching node can be observed in network, but network is opened up It is unknown to flutter structure.Many Network Reconfiguration Algorithms have been proposed in scientist at present, when network reconfiguration needs to measure substantial amounts of Between sequence data information, this demand is more very on large scale network.However, many times, the data volume that can be measured is that have Limit, existing Inner Constitution collimation technique can be using a small amount of time series data information come approximate reconstruction network, still The accuracy of reconstruct or not ideal enough.
The content of the invention
The purpose of the present invention is in view of the shortcomings of the prior art, to propose that one kind is accurately matched using a step phase iterative data The method for realizing network reconfiguration.According to the phase association relation of nodes, thus it is speculated that go out network topology structure.
The present invention is that a kind of one step phase iterative data of utilization accurately matches the method for realizing network reconfiguration, and its feature exists In comprising the following steps：
(1) phase information of original network to be reconstructed is inputted：Input and original treat reconstructed network arbitrary continuation iteration twice Phase information, the phase information of * iteration of kth is Θ0(k*)=(θ1(k*),θ2(k*),...,θN(k*))T, kth*+ 1 iteration Phase information be Θ0(k*+ 1)=(θ1(k*+1),θ2(k*+1),...,θN(k*+1))T, (*)TCalculated for transposition, N is original The nodes of network to be reconstructed；
(2) initializing variable：It is the degree of the node to be reconstructed assumed to make d=1, d, makes Θ (k*+ 1)=Θ0(k*+ 1), Θ (k*+ 1) it is phase vectors, it is complete zero square formation of N ranks to make T, and T is the adjacency matrix for having rebuild network；
(3) network reconnection is carried out using phase association relation：In the phase association reconstruction of relations net using nodes During node in network, often wheel, which is rebuild, all only rebuilds the minimum node (node degree is unknown) of network moderate to be reconstructed, after often wheel is rebuild The node for having completed to rebuild all is removed from network to be reconstructed, that is, network to be reconstructed is updated, so repeatedly, until network to be reconstructed For sky, now primitive network has been folly reconstructed；
(4) reconstructed results are exported：Network to be reconstructed is that space-time reconstruction terminates, the current adjacency matrix for having rebuild network of output T。
The present invention has the advantage that compared with prior art：
1. the present invention carries out network reconfiguration using single-step iteration data, there is this openness feature using real network, it is existing Some technologies can be using a small amount of time series data information come approximate reconstruction network, but utilizes single-step iteration time series number Do not have also according to information realization network reconfiguration, the method in the present invention is than the data volume much less needed for existing method.
2. the present invention realizes network reconfiguration with the method accurately matched, reconstruct accuracy rate height, small scale network substantially can be with Realize completely correct rebuild.
3. the present invention has obviously advantage when rebuilding scales-free network, the scales-free network of identical scale is reconstructed During with random network, scales-free network reconstructs time-consuming less.
4. the present invention carries out network reconfiguration merely with single-step iteration data, the nodal information in network is surveyed in reality Amount generally requires to expend huge manpower and materials cost, and the present invention carries out network reconfiguration merely with few data volume, saved significantly The manpower and materials cost needed for measurement data has been saved, has been easy to engineering and realizes and apply.
Brief description of the drawings
Fig. 1 is the process schematic that 5 meshed networks are rebuild with the present invention.
Fig. 2 is that present invention renewal rebuilds network and rebuild the schematic diagram of network, and Fig. 2 (a) represents original network to be reconstructed, Fig. 2 (b) represents the reconstruction network after renewal, and Fig. 2 (c) represents the network to be reconstructed after renewal.
Fig. 3 is the flow chart of the present invention.
Fig. 4 is the experimental result statistical conditions of the present invention four real networks of reconstruct, and wherein Fig. 4 (a) represents to rebuild correctly Rate, Fig. 4 (b) represent wrong side number.
Experimental result statistical conditions when Fig. 5 is the LFR Benchmark networks that the present invention reconstructs different node scales, its Middle Fig. 5 (a) represents to rebuild accuracy, the wrong side number of Fig. 5 (b) expressions.
Fig. 6 is the time-consuming statistical chart of present invention reconstruct ER random networks and BA scales-free networks.
Embodiment
Below in conjunction with the accompanying drawings to the detailed description of the invention：
Embodiment 1
Network is ubiquitous in actual life, as interpersonal relationship, internet, power network, the network of communication lines, gene regulatory network, WWW etc., these networks are more and the life of people is closely bound up.The topological structure of network to the function of network and behavior often Conclusive effect is played, but directly can not measure or measure with the presence or absence of connection between each unit in network sometimes Get up to need to expend huge cost, at this moment just need to speculate that the topology of network is tied by measuring some signals of network indirectly Structure.
Generally, the dynamic information (e.g., phase information) of switching node is priori in network, and the topology knot of network Structure is unknown message.Network reconfiguration needs to measure substantial amounts of time series data information, and this demand is more on large scale network Very.However, detectable data volume is typically limited, prior art can be using a small amount of time series data information come near Not yet occur come the method for reconstructed network like reconstructed network, but using single-step iteration time series data information.
In view of the above-mentioned problems, the present invention expands research and development, propose a kind of accurate using a step phase iterative data The method for realizing network reconfiguration is matched, referring to Fig. 3, is comprised the following steps：
(1) phase information of original network to be reconstructed is inputted：Input and original treat reconstructed network arbitrary continuation iteration twice Phase information, kth*The phase information of secondary iteration is Θ0(k*)=(θ1(k*),θ2(k*),...,θN(k*))T, kth*+ 1 iteration Phase information be Θ0(k*+ 1)=(θ1(k*+1),θ2(k*+1),...,θN(k*+1))T, (*) T is that transposition calculates, N is original The nodes of network to be reconstructed.
During the present invention inputs the phase information of original network to be reconstructed, input data only needs arbitrary continuation twice Iterative data.
(2) initializing variable：It is the degree of the node to be reconstructed assumed to make d=1, d, makes Θ (k*+ 1)=Θ0(k*+ 1), Θ (k*+ 1) it is phase vectors, it is complete zero square formation of N ranks to make T, and T is the adjacency matrix for having rebuild network.D, phase vectors in the present invention Θ(k*+ 1) and N rank square formations T is variable.
(3) network reconnection is carried out using phase association relation：In the phase association reconstruction of relations net using nodes During node in network, often wheel, which is rebuild, all only rebuilds the minimum node (node degree is unknown) of network moderate to be reconstructed, after often wheel is rebuild The node for having completed to rebuild all is removed from network to be reconstructed, that is, network to be reconstructed is updated, so repeatedly, until network to be reconstructed For sky, now primitive network has been folly reconstructed.Remove the node for having completed to rebuild and refer to theoretic, actually have no this behaviour Make.
(4) reconstructed results are exported：Network to be reconstructed is that space-time reconstruction terminates, the current adjacency matrix for having rebuild network of output T。
The present invention carries out network reconfiguration using single-step iteration data, has this openness feature using real network, existing Technology can be using a small amount of time series data information come approximate reconstruction network, but utilize single-step iteration time series data Information realization network reconfiguration does not have also, and the method in the present invention is than the data volume much less needed for existing method.
Embodiment 2
Using a step phase iterative data, accurately matching realizes the method for network reconfiguration with embodiment 1, the profit in step (3) The process that network reconnection is carried out with phase association relation has specifically included：
(3.1) judge whether process of reconstruction terminates：Acquiescence utilizes the phase association relation of nodes during first reconstruct Process of reconstruction has begun to, and judges whether network to be reconstructed is empty, if Θ (k*+ 1) ≠ 0, i.e., network to be reconstructed is not sky, net Network, which is rebuild, not to be completed, and is performed step (3.2), is continued to rebuild；Otherwise, step (4) is performed, network reconnection is completed.
(3.2) search degree is d node in network to be reconstructed；If searching for successfully, that is, degree of searching is d node, is held Row step (3.3), update network to be reconstructed and rebuild network；Otherwise, step (3.8), the bigger node of search degree are performed.
(3.3) update network to be reconstructed and rebuild network：In network to be reconstructed, the degree that is searched in step (3.2) Node and its all company sides for d are considered as the removal from network to be reconstructed, and (it is the reality to describe in theory conveniently to remove operation , it is necessary to which the information for the network to be reconstructed used is only the phase information when front-wheel network to be reconstructed in process of reconstruction), lower whorl is rebuild When network to be reconstructed scale down.To the neighbour for having rebuild the node searched in network in addition step (3.2), these nodes Occupy node (this operation is not needed then to the node for having been added to reconstruction portion molecular network) and these nodes save with its neighbour Company side between point.Referring to Fig. 2, Fig. 2 is represented during 5 meshed networks are reconstructed, right after reconstructing minimum degree node 1 Network to be reconstructed and the schematic diagram that network is updated is rebuild.Fig. 2 (a) represents original network to be reconstructed, and Fig. 2 (b) is represented more Reconstruction network after new, Fig. 2 (c) represent the network to be reconstructed after renewal.
(3.4) adjacency matrix of network has been rebuild in renewal：Determine the current adjacency matrix for having rebuild network in step (3.3) T；
(3.5) more new phase：Utilize phase more new formula renewal Θ (k*+1)。Θ(k*+ 1) it can be used as and judge network reconfiguration The criterion whether completed, as Θ (k*+ 1) when=0, corresponding network to be reconstructed is sky, it is believed that network reconfiguration has been completed, otherwise, Reconstruction is not yet completed, and carries out next round reconstruction.
(3.6) d=1 is made；Find the node that network moderate to be reconstructed is 1；
(3.7) step (3.1) is performed, judges whether to need next round to rebuild；
(3.8) d=d+1, the bigger node of network moderate to be reconstructed is searched for；
(3.9) step (3.1) is performed, judges whether to need next round to rebuild.
Referring to Fig. 1.To have rebuild network, lower section is network to be reconstructed for top in Fig. 1, when rebuilding beginning, has rebuild network For sky, network to be reconstructed is original network to be reconstructed.By taking Fig. 1 as an example, Fig. 1 is the restructuring procedure of simple 5 meshed network Schematic diagram, share three-wheel and rebuild.When 1st wheel carries out network reconnection, the minimum node 1 of network moderate is reconstructed, then node 1, section The neighbor node 4 and node 1 of point 1 are added with the company side of node 4 and have rebuild network, and node 1 and node 1 are removed in network to be reconstructed Company side.Similarly, network moderate to be reconstructed minimum node 4 is reconstructed when the 2nd wheel is rebuild, and to having rebuild network and to be reconstructed Network is updated；Third round reconstructs network moderate minimum node 2, node 3 and node 5 when rebuilding, and updates to be reconstructed Network and network is rebuild, so far network to be reconstructed is sky, and it is the original network to be reconstructed to be reconstructed to have rebuild network.
The present invention realizes network reconfiguration with the method accurately matched, and reconstruct accuracy rate is high, and small scale network substantially can be real It is now completely correct to rebuild.
Embodiment 3
Using a step phase iterative data, accurately matching realizes the method for network reconfiguration with embodiment 1-2, step (3.5) institute The utilization phase more new formula renewal Θ (k stated*+ 1), specifically included：
More new phase Θ (k*+ 1) formula used in is Θ (k*+ 1)=Θ0(k*+1)-T*Θ0(k*), vector theta0(k*) and Θ0(k*+ 1) phase of the node all in original network to be reconstructed in kth * times and kth+1 iteration of * is represented respectively；Vector Θ(k*+ 1) current phase of the network to be reconstructed in kth+1 iteration of * is represented；
The purpose of more new phase is to ensure the phase between the nodes to be reconstructed during network reconnection after often wheel renewal Position incidence relation is still set up, because often taking turns the node during removal node, not being folly reconstructed from network to be reconstructed Be also removed with the side that Perfect Reconstruction node is connected, then the non-Perfect Reconstruction on even side with the node of Perfect Reconstruction be present Company's side situation of node is changed, then the phase association relation of last round of network to be reconstructed is broken, if do not recovered again Phase association relation, the reconstruction of next round will be unable to carry out；
Phase association relation isθi(k) phase of the node i in kth time iteration is represented； aijNode i and j annexation are represented, if even side, a between node i and j be presentij=1, otherwise, aij=0；N represents network Nodes；kmIt is the factor for reaching stable state for adjusting phase, whether phase reaches stable state without influence, here for simplicity, Make kmFor 1.The matrix form of phase association relation is Θ (k+1)=A Θ (k), and vector theta (k) represents all sections in network here Phase of the point in kth time iteration, A represent the adjacency matrix of network.
Embodiment 4
Using a step phase iterative data, accurately matching realizes the method for network reconfiguration with embodiment 1-3, in step (3.2) The search degree in network to be reconstructed be d node, including have the following steps：Assuming that it is intended to rebuild the network that a nodes are N Moderate is d node, and all nodes are arbitrarily iteration (being designated as k* and k*+1) phase vectors are respectively Θ twice in succession in network (k*) and Θ (k*+1)。
(3.2.1) enumerates combination of nodes Matrix C omnode：Enumerate the node of optional d in N number of nodeKind combination Situation, hereThe scale of obtaining isNode group and Matrix C omnode, ComnodeIn often row storage A kind of combined situation, its element are nodal scheme；
(3.2.2) obtains phase combination Matrix C omphase：By ComnodeEach nodal scheme changes it into * iteration of kth Phase, the scale of obtaining arePhase combination Matrix C omphase；
(3.2.3) obtains phase and vectorial Sumphase：To ComphaseObtained accordingly by row summation, modulusDimension Phase and vectorial Sumphase；
(3.2.4) searches vectorial SumphaseWith phase vectors Θ (k*+ 1) the equal element of value in：Compare vector theta (k* + 1) and vectorial Sumphase, observe with the presence or absence of equal element is worth in two vectors, if in the presence of presence is d in the network Node, e.g., if vectorial SumphaseIn k-th element and vector theta (k*+ 1) (i.e. node i is for i-th of element value in Phase during k*+1 iteration) equal, then vectorial ComnodeAll d nodes of row k be all d of node i adjacent Occupy node；Otherwise degree of not having is d node in the network.
Apply the thought that phase accurately matches in the present invention to carry out finding the node that network moderate is d, and if only if goes out The phase of certain existing two node is almost equal, or several node phase sums of several node phase sums and other are equal During situation, erroneous matching just occurs.And when network size is smaller, both of these case occur probability be it is very small, i.e., The probability of appearance erroneous matching is minimum, and when node scale is very big in a network, the probability for both of these case occur also can be Increase, but now its erroneous matching rate is micro- atomic compared with network size.
The present invention realizes network reconfiguration with the method accurately matched, and reconstruct accuracy rate is high, and small scale network substantially can be real It is now completely correct to rebuild.
Present invention advantage when rebuilding scales-free network is particularly evident, reconstructs the scales-free network and Stochastic Networks of identical scale During network, scales-free network reconstructs time-consuming less.
A more detailed example is given below, the present invention is further described
Embodiment 5
Using the step phase iterative data method that accurately network reconfiguration is realized in matching with embodiment 1-4, specific degree is rebuild Node be the present invention a key content, the present invention utilize phase association reconstruction of relations network in specific degree node side Method is as follows：
Assuming that the nodes of network to be reconstructed are N, network moderate to be rebuild is d node：
All nodes are arbitrarily iteration (being designated as k* and k*+1) phase vectors are respectively Θ (k twice in succession in network*) and Θ(k*+1).Enumerate the node of optional d in N number of nodeKind combined situation, the scale of obtaining areNode group With Matrix C omnode, ComnodeIn often row deposit a kind of combined situation；By ComnodeEach nodal scheme changes it into * iteration of kth Phase, the scale of obtaining isPhase combination Matrix C omphase；To ComphaseCarry out obtaining phase by row summation, modulus AnswerTie up phase and vectorial Sumphase；Compare vector theta (k*+ 1) and vectorial Sumphase, observe and whether there is in two vectors It is worth equal element, if in the presence of presence is d node in the network, e.g., if vectorial SumphaseIn k-th element with Vector theta (k*+ 1) i-th of element value (i.e. phase of the node i in kth+1 iteration of *) in is equal, then vectorial Comnode's All d nodes of row k are all d neighbor nodes of node i；Otherwise degree of not having is d node in the network.
Step phase iterative data of the present invention accurately matches the method for realizing network reconfiguration, comprises the following steps：
(1) phase information of original network to be reconstructed is inputted：Input and original treat reconstructed network arbitrary continuation iteration twice Phase information, kth*The phase information of secondary iteration is Θ0(k*)=(θ1(k*),θ2(k*),...,θN(k*))T, kth*+ 1 iteration Phase information be Θ0(k*+ 1)=(θ1(k*+1),θ2(k*+1),...,θN(k*+1))T, (*)TCalculated for transposition, N is original The nodes of network to be reconstructed；
(2) initializing variable：It is the degree of the node to be reconstructed assumed to make d=1, d, makes Θ (k*+ 1)=Θ0(k*+ 1), Θ (k*+ 1) it is phase vectors, it is complete zero square formation of N ranks to make T, and T is the adjacency matrix for having rebuild network；
(3) the network reconnection process of phase association relation is utilized：
(3.1) if Θ (k*+ 1) (3.2) ≠ 0, are performed；Otherwise, (4) are performed；
(3.2) search degree is d node in network to be reconstructed；If searching for successfully, perform (3.3)；Otherwise；Perform (3.8)；
(3.3) added into reconstruction portion molecular network in (3.1) and search node, the neighbor node of node is (to Adding the node of reconstruction portion molecular network then need not this operation), the also company side between node and its neighbor node；
(3.4) the adjacency matrix T of reconstruction portion molecular network is rewritten；
(3.5) more new phase Θ (k*+1)：Θ(k*+ 1)=Θ0(k*+1)-T*Θ0(k*)；
(3.6) d=1；
(3.7) (3.1) are performed；
(3.8) d=d+1；
(3.9) (3.1) are performed；
(4) rebuild and terminate.
Rebuild using the incidence relation between node phase during network topology and used the accurate matching of phasetophase, when going out The phase of certain existing two node is almost equal, or several node phase sums of several node phase sums and other are equal During situation, it may appear that erroneous matching, and nodes number is bigger, the probability for such case occur is bigger.With nodes Increase, rebuild in network development process and the company side of mistake occurs, rebuilding accuracy rate can decline, but wrong side number is advised with network Mould is compared, and error rate is fairly small.
The effect of the present invention can be verified by following experiment：
Embodiment 6
Using a step phase iterative data, accurately matching realizes the method for network reconfiguration with embodiment 1-5,
Experiment condition is：Make on the computer that parameter is (Intel (R) Core (TM) i5-3230M CPU 2.60GHz) Emulated with software MATLAB r2015b.
Emulation content：
1) tested using the present invention on four real network Karate, Dolphins, Lesmis and Adjnoun, Company's side situation of the accuracy rate rebuild and reconstruction errors is counted, demonstrates the validity of algorithm；
2) tested using the present invention on LFR Benchmark networks, count increasing with nodes, network Rebuild accuracy rate and mistake even side situation；
3) tested respectively on ER random networks and BA scales-free networks using the present invention, count time-consuming situation.
Experimental result：
1) aforementioned four network is rebuild using the present invention, experimental result is that four networks can be folly reconstructed out Come, referring to Fig. 4, rebuild accuracy absolutely, illustrate the profit of the present invention without there is mistake even side in four network reconnections With a step phase iterative data, accurately matching realizes that the method for network reconfiguration is effective.
Referring to Fig. 4.Fig. 4 is four real network Karate, Dolphins, Lesmis and Adjnoun of present invention reconstruct Experimental result statistical conditions, wherein Fig. 4 (a) represent reconstruction accuracy, and the reconstruction accuracy of four networks is 1, Fig. 4 (b) tables Show mistake side number, the reconstruction errors side number of four networks is 0.
Using a step phase iterative data, accurately matching realizes that the method for network reconfiguration reconstructs real network although simply sharp It with a step phase iterative data, but can correctly reconstruct completely, illustrate the accuracy of the reconstruct of the invention.
Embodiment 7
Using a step phase iterative data, accurately matching realizes the method for network reconfiguration with embodiment 1-5, experiment condition and Experiment content is the same as example 6.
With the increase of network node scale, occur that mistake connects side when rebuilding LFR Benchmark networks.
Referring to Fig. 5.Experimental result system when Fig. 5 is the LFR Benchmark networks that the present invention reconstructs different node scales Meter situation, wherein Fig. 5 (b) represent wrong side number, and with the increase of network node scale, the present invention can also go out in process of reconstruction The side number of existing mistake, but wrong side number is very small compared with network node scale, with the increase of network node scale, Referring to Fig. 5 (b), there is wrong side number when nodes are 1000, mistake side number is only 5, even in nodes be 18000 When, mistake side number is also only 19, and referring to Fig. 5 (a), these wrong side numbers are when network size is very big to the correct of network reconfiguration The influence of rate is very small, and accuracy is still close to 1 in the corresponding points in Fig. 5 (a).Fig. 5 (a) represents reconstruction accuracy, With the increase of network node scale, although occurring wrong side number when nodes are more than 1000, whole network is rebuild just True rate is still all close to 1.
During reconstructed network of the present invention, with the increase of network size, there is wrong side number.There is the reason for wrong side number It is following two to be that the thought accurately matched using phase occur during finding the node that large scale network moderate is d The possibility of small probability event becomes big：The phase that certain two node occurs in situation 1 is almost equal, situation 2, several node phases Several node phase sums of sum and other are equal.When network size is smaller, the probability that both of these case occurs is very Small, that is, it is minimum the probability of erroneous matching occur, so basic without there is mistake even side in small scale network.Save in a network When point scale is very big, the probability for both of these case occur can also be increased, but now its erroneous matching rate is advised with network It is very little that mould, which is compared,.
Embodiment 8
Using a step phase iterative data, accurately matching realizes the method for network reconfiguration with embodiment 1-5, experiment condition and Experiment content has carried out reconstitution experiments, specific experiment result is referring to figure with the present invention with example 6 to two kinds of networks of different structure 6。
3) in the case of number of network node, average degree all identicals, using a step phase iterative data, accurately net is realized in matching The method reconstruction ER random network used times of network reconstruct are time-consuming more more than rebuilding BA scales-free networks, i.e., the present invention is more suitable for rebuilding BA scales-free networks.Blue diamonds curve represents ER random networks in Fig. 6, and red square curve represents BA scales-free networks.
Referring to Fig. 6.Fig. 6 is the time-consuming statistical chart of present invention reconstruct ER random networks and BA scales-free networks.
In summary, the specifically disclosed step phase iterative data of the present invention accurately matches the method for realizing network reconfiguration. Phase exact matching algorithm is proposed to speculate network topology：Solve and can be achieved with merely with a step phase iterative data information The technical problem of the supposition network topology structure of almost Perfect.To a network to be reconstructed, first, phase association relation weight is utilized The minimum some nodes of establishing network moderate；Then, by the node for having completed reconstruction and even, side removes from network to be reconstructed；So Afterwards, the scale of network to be reconstructed is reduced；Carry out the reconstruction of a new round on new network to be reconstructed again afterwards, remove work, such as This repeatedly, until network to be reconstructed for sky.It can be broken because removing node and Lian Bian from network to be reconstructed to update network to be reconstructed Bad original phase association relation, influences follow-up reconstruction, and a phase more new formula updates defined in the present invention The phase of nodes to be reconstructed, so that phase association relation is still set up.The present invention only need indivisible number of phases it is believed that Breath can carry out network reconfiguration.The present invention realizes Perfect Reconstruction on small-scale real network, and the validity of reconstruct all obtains Good checking is arrived, various artificial networks, especially BA scales-free networks and real network can be reconstructed by the present invention.

Claims (4)

1. a kind of accurately match the method for realizing network reconfiguration using a step phase iterative data, it is characterised in that including following Step：
(1) phase information of original network to be reconstructed is inputted：Input the original phase for treating reconstructed network arbitrary continuation iteration twice Information, kth*The phase information of secondary iteration is Θ0(k*)=(θ1(k*),θ2(k*),...,θN(k*))T, kth*The phase of+1 iteration Position information is Θ0(k*+ 1)=(θ1(k*+1),θ2(k*+1),...,θN(k*+1))T, (*)TCalculated for transposition, N treats weight to be original The nodes of establishing network；
(2) initializing variable：It is the degree of the node to be reconstructed assumed to make d=1, d, makes Θ (k*+ 1)=Θ0(k*+ 1), Θ (k*+1) For phase vectors, it is complete zero square formation of N ranks to make T, and T is the adjacency matrix for having rebuild network；
(3) network reconnection is carried out using phase association relation：In the phase association reconstruction of relations network using nodes Node when, often wheel, which is rebuild, all only rebuilds the minimum node of network moderate to be reconstructed, after often wheel is rebuild all from network to be reconstructed The node for having completed to rebuild is removed, that is, updates network to be reconstructed, so repeatedly, until network to be reconstructed is sky, now original net Network has been folly reconstructed；
(4) reconstructed results are exported：Network to be reconstructed is that space-time reconstruction terminates, the current adjacency matrix T for having rebuild network of output.
2. accurately match the method for realizing network reconfiguration, its feature using a step phase iterative data as claimed in claim 1 It is, the process that network reconnection is carried out using phase association relation described in step (3) has been specifically included：
(3.1) judge whether process of reconstruction terminates：Judge whether network to be reconstructed is empty, if Θ (k*+ 1) ≠ 0 network reconnection is not Complete, perform step (3.2), continue to rebuild；Otherwise, step (4) is performed, network reconnection is completed；
(3.2) search degree is d node in network to be reconstructed；If searching for successfully, that is, degree of searching is d node, performs step Suddenly (3.3), update network to be reconstructed and rebuild network；Otherwise；Perform step (3.8), the bigger node of search degree；
(3.3) update network to be reconstructed and rebuild network：In network to be reconstructed, node and its institute spent for d that search Some company sides are considered as to be removed from network to be reconstructed, the scale down of network to be reconstructed when lower whorl is rebuild；To having rebuild in network The company added in step (3.2) between the neighbor node and these nodes and its neighbor node of the node searched, these nodes Side；
(3.4) adjacency matrix of network has been rebuild in renewal：It is determined that the current adjacency matrix T for having rebuild network；
(3.5) more new phase：Utilize phase more new formula renewal Θ (k*+1)；
(3.6) d=1 is made；Find the node that network moderate to be reconstructed is 1；
(3.7) step (3.1) is performed, judges whether to need next round to rebuild；
(3.8) d=d+1, the bigger node of network moderate to be reconstructed is searched for；
(3.9) step (3.1) is performed, judges whether to need next round to rebuild.
3. accurately match the method for realizing network reconfiguration, its feature using a step phase iterative data as claimed in claim 2 It is, the utilization phase more new formula renewal Θ (k described in step (3.5)*+1)；Specifically include：
More new phase Θ (k*+ 1) formula used in is Θ (k*+ 1)=Θ0(k*+1)-T*Θ0(k*), vector theta0(k*) and Θ0(k* + 1) phase of the node all in original network to be reconstructed in kth * times and kth+1 iteration of * is represented respectively；Vector theta (k* + 1) current phase of the network to be reconstructed in kth+1 iteration of * is represented；
Phase association relation isθi(k) phase of the node i in kth time iteration is represented；aijTable Show node i and j annexation, if even side, a between node i and j be presentij=1, otherwise, aij=0；N represents the section of network Points；kmIt is the factor for reaching stable state for adjusting phase, whether phase reaches stable state to dynamics as claimed in claim 1 Network Reconfiguration Algorithm, here for simplicity, makes k without influencemFor 1, the matrix form of phase association relation is Θ (k+1)=A Θ (k), vector theta (k) represents that phase of all nodes in kth time iteration, A represent the adjacency matrix of network in network here.
4. accurately match the method for realizing network reconfiguration, its feature using a step phase iterative data as claimed in claim 2 It is, the search degree in network to be reconstructed described in step (3.2) is d node, including has the following steps：
(3.2.1) enumerates combination of nodes Matrix C omnode：Enumerate the node of optional d in N number of nodeKind combined situation, HereThe scale of obtaining isNode group and Matrix C omnode, ComnodeIn often row storage a kind of group Conjunction situation, its element are nodal scheme；
(3.2.2) obtains phase combination Matrix C omphase：By ComnodeEach nodal scheme changes its phase in * iteration of kth into, The scale of obtaining isPhase combination Matrix C omphase；
(3.2.3) obtains phase and vectorial Sumphase：To ComphaseObtained accordingly by row summation, modulusTie up phase With vectorial Sumphase；
(3.2.4) searches vectorial SumphaseWith phase vectors Θ (k*+ 1) the equal element of value in：Compare vector theta (k*+ 1) and Vectorial Sumphase, observe with the presence or absence of equal element is worth in two vectors, if in the presence of presence is d section in the network Point, e.g., if vectorial SumphaseIn k-th element and vector theta (k*+ 1) i-th of element value in is equal, then vectorial Comnode Row k all d nodes be node i all d neighbor nodes；Otherwise degree of not having is d node in the network.
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