CN110532697A - One kind dividing shape complex network global efficiency estimation method - Google Patents
One kind dividing shape complex network global efficiency estimation method Download PDFInfo
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Abstract
The method for quick estimating for the complex network global efficiency based on fractal theory that the invention discloses a kind of, this method comprises: the judgement of complex network fractal characteristic, complex network fractal dimension solve, the estimation of complex network global efficiency.The global efficiency estimating step of complex network is in the present invention, first determine whether network has fractal property i.e. self-similarity, the correlation dimension of the network can be estimated if the network is there are fractal property, finally since there are the characteristics of self similarity for the network, therefore the distance of all nodes pair is not needed to calculate when calculating the global efficiency of complex network, it only seeks part of nodes adjusting the distance, with part of nodes to estimating whole network efficiency.The present invention is estimated whole by dividing the self-similarity nature of shape complex network with part, and the global efficiency that the present invention can be estimated with lower time complexity is very close with true value, is the splendid complex network global efficiency estimation method of one kind.
Description
Technical field
The present invention relates to complex network technical fields, and in particular to one kind divides shape complex network global efficiency estimation method.
Background technique
Complex network is the network structure collectively formed by relationship complicated between node and node, complexity therein
Topological features can characterize in complication system interactive relation between element.Complex Networks Theory can fundamentally remold system
Complexity and solve various challenges, be a hot spot in scientific research now.The efficiency of network in Network Science
It is the standard of scaling information exchange efficiency and is applied to transportation network, bio-networks etc., in broad terms, the efficiency of network can be with
For quantifying the worldlet behavior in network.Efficiency can also be used to determine the cost-effectiveness structure in weighted sum unweighted network.
Two measurement indexs of network efficiency are compared with the random network of identical scale, with the economic construction feelings of awareness network
Condition.In addition, numerically path length more corresponding than its is easier to use global efficiency.The nerve connection effect of brain function network
Rate is found have close correlation with intelligence, but since brain network is often along with enormous amount node such as sum more than hundred
Ten thousand, lead to the time extremely length for calculating global network efficiency and consumption resource is huge, this also counteracts many progress of research.Net
The global efficiency of network is not only difficult to calculate in brain network, and high complexity is also owned by all large scale networks
Degree.Two big fundamental characteristics in complex network are that scaleless property and small world are accelerated to dynamic processes various in network
Research is influenced, these theory parts are by application extension to biology or physical network.And a point shape is also referred to as complex network
The third-largest fundamental characteristics is also and then applied to the sides such as the time series analysis under research fractal Brown motion, complex network visual angle
To.Self-similarity nature in complex network in fractal property reflection topological structure, many true complex networks are in all scales
On all there is self duplicate structures.Therefore do not need to calculate when calculating global network efficiency all nodes pair away from
From, it is only necessary to a portion further according to network self similarity rule from partially estimating whole, so that it may in the faster time
Inside obtain an accurate global network efficiency.
Although computing capability exponentially increases with the time, still complex network in large scale calculates power not at present
Foot estimates that the global efficiency of complex network has the advantage that one, to estimate quickly number of nodes huge using the present invention
Large scale network.Two, global network information is required no knowledge about, it is only necessary to know that the topological structure of partial region can also estimate this
The global network efficiency of network.Three, the global network efficiency accuracy estimated is high and accuracy and time complexity controllably adjust.
Summary of the invention
Problem to be solved by this invention is: one kind point shape complex network global efficiency estimation method is provided, resource by
It limits, lack in global network information, the huge situation of network node total quantity, how research analyzes the fractal property of complex network
And proposed by the characteristic based on the global network efficiency estimation method for dividing shape, to reduce redundant computation, reduction resource consumption, mention
Computationally efficient realizes the purpose that the global efficiency of network can be also estimated under loss of learning.
The present invention in order to solve the above problem provided by technical solution are as follows: one kind divides shape complex network global efficiency estimation side
Method the described method comprises the following steps,
(1), the fractal property of the network fractal characteristic judgement of complex network: is judged with part or all of node；
(2), the FRACTAL DIMENSION of the network solution of the fractal dimension of complex network: is calculated with all or part of node
Number；
(3), complex network global efficiency is estimated: by the fractal property of network, the structure feature of self similarity uses part
Node estimates that other scale lower nodes to quantity, then calculate global network efficiency to fractal dimension.
Preferably, in the fractal characteristic judgement of the complex network, expanded using some or all of network node i
It dissipates, the node in dilation angle r is less than r at a distance from i, according in dilation angle in part or all of node and dilation angle
Number of nodes judges whether complex network possesses fractal characteristic.
Preferably, the solution of the fractal dimension of the complex network measures the fractal dimension of its self-similarity from the expansion
Radius r and dilation angle number of nodes are dissipated in log-log coordinate dimensionless interzone fitting a straight line, and fitting a straight line slope is as the network
Fractal dimension.
Preferably, the complex network global efficiency estimation will pass through fractal characteristic, that is, self-similarity of complex network to lack
Number estimation is most, and then the global network efficiency for estimating the network is not exclusively calculated with part of nodes.
Compared with prior art, the invention has the advantages that one, the huge extensive net of number of nodes can be estimated quickly
Network；Two, global network information is required no knowledge about, it is only necessary to know that the topological structure of partial region can also estimate the overall situation of the network
Network efficiency；Three, the global network efficiency accuracy estimated is high and accuracy and time complexity controllably adjust.
Detailed description of the invention
The drawings described herein are used to provide a further understanding of the present invention, constitutes a part of the invention, this hair
Bright illustrative embodiments and their description are used to explain the present invention, and are not constituted improper limitations of the present invention.
Fig. 1 is that the node chosen is diffused figure.
Fig. 2 is association and function and dilation angle relational graph, rMFor the radius for stopping diffusion.
Specific embodiment
Carry out the embodiment that the present invention will be described in detail below in conjunction with accompanying drawings and embodiments, how the present invention is applied whereby
Technological means solves technical problem and reaches the realization process of technical effect to fully understand and implement.
One kind dividing shape complex network global efficiency estimation method, the described method comprises the following steps,
(1), the fractal property of the network fractal characteristic judgement of complex network: is judged with part or all of node；
(2), the FRACTAL DIMENSION of the network solution of the fractal dimension of complex network: is calculated with all or part of node
Number；
(3), complex network global efficiency is estimated: by the fractal property of network, the structure feature of self similarity uses part
Node estimates that other scale lower nodes to quantity, then calculate global network efficiency to fractal dimension.
It in the fractal characteristic judgement of the complex network, is spread using some or all of network node i, diffusion half
Node in diameter r is less than r at a distance from i, according to the number of nodes in dilation angle in part or all of node and dilation angle come
Judge whether complex network possesses fractal characteristic.
The solution of the fractal dimension of the complex network measures the fractal dimension of its self-similarity from the dilation angle r
With dilation angle number of nodes in log-log coordinate dimensionless interzone fitting a straight line, FRACTAL DIMENSION of the fitting a straight line slope as the network
Number.
The complex network global efficiency estimation will be estimated by fractal characteristic, that is, self-similarity of complex network with minority
Majority, and then the global network efficiency for estimating the network is not exclusively calculated with part of nodes.
Fractal characteristics are different from conventional method in the complex network, randomly select a node i first, take diffusion
Radius r is 1 i.e. to neighbor node diffusion, as shown in attached drawing 1.The node then spread is equally spread to neighbours, repeats to expand
It is scattered will be not counted in including, at this time dilation angle be 2.The number of nodes N that single node is spread when spreadingrTo increase with dilation angle and
Increase, in log-log coordinate axis plot r and NrRelational graph, it is heavy-tailed when occurring, situations such as long-tail, i.e. NrIt is significantly not linear with r
Terminate to spread when growth, the radius for terminating diffusion at this time is denoted as rM.The node other than i is chosen again to be diffused and average,
The the node of selection the more, divide the judgement of shape more accurate.There is fitting a straight line in the accompanying drawings, then the network possesses fractal property.
The fractal dimension is the correlation dimension (one kind that correlation dimension is FRACTAL DIMENSION) not exclusively calculated, if described
Fractal characteristics method has chosen all node diffusions, then the values of fractal dimension and correlation dimension numerical value are completely the same.Exist first
Correlation dimension described herein, correlation dimension are acquired by the linear relationship of association and function C (r) and r, and C (r) expression formula is as follows:
Wherein dijFor the Euclidean distance of node i and node j, θ (x) is jump function, and N is node total number.It is special in the presence of shape is divided
The network associate and function C (r) of property will be scaled in distance r, that is, C (r)~rβ, thenAs correlation dimension numerical value closes
Connection dimension solution procedure needs to calculate the distances of all nodes pair, but actually uses part of nodes to the correlation dimension of solution and true
It is worth also fairly close.As shown in Fig. 2, the relational graph of log-log coordinate axis r and C (r) is intended using least square fitting straight line
Closing straight slope is that shape is divided to be numerical value.
The global efficiency E (G) of network G in the complex network global efficiency estimation technique are as follows:
Wherein dijFor the Euclidean distance of node i and node j, N is node total number.By the derivation of equation can obtain efficiency E (G) with
It is associated with and has substantial connection as follows:
rMFor the stopping dilation angle of specific implementation.Finally association and C (r) can be solved by r and fractal dimension β to be obtained i.e.:
Thus it only needs two parameters that can estimate global efficiency, stops dilation angle rMIf being used with fractal dimension β
The average value of whole nodes is then that the more estimated values of node for being used to estimate will be more accurate for exact value.
The present invention will the fractal property technical application in complex network to global network efficiency estimation in, propose based on point
The complex network global efficiency estimation method of shape, can effective replacement time complexity larger complex network global efficiency calculating side
Method, so that large-scale complex network efficiency can also obtain an accurate estimated value in a relatively short period of time.
Only highly preferred embodiment of the present invention is described above, but is not to be construed as limiting the scope of the invention.This
Invention is not only limited to above embodiments, and specific structure is allowed to vary.All protection models in independent claims of the present invention
Interior made various change is enclosed to all fall in the scope of protection of the present invention.
Claims (4)
1. one kind divides shape complex network global efficiency estimation method, it is characterised in that: it the described method comprises the following steps,
(1), the fractal property of the network fractal characteristic judgement of complex network: is judged with part or all of node；
(2), the fractal dimension of the network solution of the fractal dimension of complex network: is calculated with all or part of node；
(3), complex network global efficiency is estimated: by the fractal property of network, the structure feature of self similarity uses part of nodes
Estimate that other scale lower nodes to quantity, then calculate global network efficiency to fractal dimension.
2. one kind according to claim 1 divides shape complex network global efficiency estimation method, it is characterised in that: the complexity
In the fractal characteristic judgement of network, spread using some or all of network node i, the node and i in dilation angle r
Distance is less than r, whether judges complex network according to the number of nodes in dilation angle in part or all of node and dilation angle
Possess fractal characteristic.
3. one kind according to claim 2 divides shape complex network global efficiency estimation method, it is characterised in that: the complexity
The solution of the fractal dimension of network measures the fractal dimension of its self-similarity from the dilation angle r and dilation angle number of nodes
In log-log coordinate dimensionless interzone fitting a straight line, fractal dimension of the fitting a straight line slope as the network.
4. one kind according to claim 3 divides shape complex network global efficiency estimation method, it is characterised in that: the complexity
The estimation of network global efficiency will be most with minority estimation by fractal characteristic, that is, self-similarity of complex network, and then partially to save
Point not exclusively calculates the global network efficiency for estimating the network.
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| CN112842261A (en) * | 2020-12-30 | 2021-05-28 | 西安交通大学 | Intelligent evaluation system for three-dimensional spontaneous movement of infant based on complex network |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112842261A (en) * | 2020-12-30 | 2021-05-28 | 西安交通大学 | Intelligent evaluation system for three-dimensional spontaneous movement of infant based on complex network |
| CN112842261B (en) * | 2020-12-30 | 2021-12-28 | 西安交通大学 | Intelligent evaluation system for three-dimensional spontaneous movement of infant based on complex network |
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