CN101645104B - Complex network modeling method - Google Patents
Complex network modeling method Download PDFInfo
- Publication number
- CN101645104B CN101645104B CN2009101702180A CN200910170218A CN101645104B CN 101645104 B CN101645104 B CN 101645104B CN 2009101702180 A CN2009101702180 A CN 2009101702180A CN 200910170218 A CN200910170218 A CN 200910170218A CN 101645104 B CN101645104 B CN 101645104B
- Authority
- CN
- China
- Prior art keywords
- node
- network
- crystal lattice
- modeling method
- dimensional crystal
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Images
Abstract
The invention relates to a complex network modeling method, comprising the following steps: two-dimensional crystal lattice is built for being used as an evolution space of a complex network; a plurality of interconnected initial nodes are generated randomly, wherein each in initial node occupy one lattice of the two-dimensional crystal lattice; a new node is added randomly on the two-dimensional crystal lattice, and attractive forces between the new node and the existing nodes on the two-dimensional crystal lattice are respectively calculated; the connection of the new node and the existing nodes is built according to the size of the attractive force; the node adding and connecting steps are repeated to obtain an evolution network module of the complex network. The method can well reflect the attribute of a real network system.
Description
Technical field
The invention belongs to the system science field, relate in particular to a kind of complex network modeling method.
Background technology
In the last few years, become the research focus of being paid close attention to especially such as the Internet, WWW and all kinds of society and bio-networks.It is found that a large amount of real complex system can use network to describe, and can make us understand these complication systems more by studying these networks that take out.The doctor Watts of department of mathematics of Cornell Univ USA in 1998 and tutor Strogatz professor thereof publish an article on Nature, have proposed famous worldlet network model; The Barab á si professor and the doctor Albert thereof of U.S. Notre Dame College Physics system in 1999 have proposed famous no scale network model on Science.The work of these two laying a foundation property has caused every field researchist's extensive concern, and has caused a new field---the rise of complex network research.
Live network has mostly that power rate degree distributes, little mean distance and big convergence factor three big statistical natures.A most important direction is exactly how to make up the network model that more meets the live network statistical property in the complex network research, studies its microcosmic and forms mechanism and inherent mechanism.On the basis of worldlet network and no scale network, considered of the influence of factors such as aging effect, with dividend right mechanism, company's limit cost again to network modelling.
But the rule of " the preferential connection " in the no scale network model has only been considered in network modelling work in the past mostly, and promptly the node that degree is big more attracts the ability of new node also big more.But this rule has been ignored the influence of space and geographical distance: the attractive force of node is can be along with range attenuation.In fact, a lot of real networks have space constraint.Such as, the air net of a country can only be within its territorial limits; Electric power networks can not be layered in the exceedingly odious environment of natural conditions; The metabolism network of cell can not be broken through the restriction of cell membrane.
Therefore, there is certain one-sidedness in existing modeling method, and constructed model can not reflect the statistical property of live network well.
Summary of the invention
Purpose of the present invention is intended to one of solve the aforementioned problems in the prior at least.
For this reason, embodiments of the invention propose a kind of complex network modeling method, can better reflect the network model of live network system property with structure.
According to an aspect of the present invention, the embodiment of the invention has proposed a kind of complex network modeling method, and described modeling method may further comprise the steps: a) set up the evolution space of a two-dimensional crystal lattice as described complex network; B) generate the start node of a plurality of full-mesh at random, wherein each start node occupies a grid on the described two-dimensional crystal lattice; C) on described two-dimensional crystal lattice, add a new node at random, and calculate the attractive force between the existing node on described new node and the described two-dimensional crystal lattice respectively; D) set up being connected of described new node and existing node according to described attractive force size; E) repeating step c and steps d are to obtain the evolved network model of described complex network.
The further embodiment according to the present invention, described step c calculates described attractive force according to following formula:
K wherein
iAnd k
jThe degree of representing node i and j respectively, r
IjSpace length for i and j.
The further embodiment according to the present invention, described space length are Euclidean distance or geographic distance.
The further embodiment according to the present invention, described steps d comprises: the limit number according to described new node selects respective amount to have the node of big attractive force from existing node; And add company limit between described new node and the described selection node.
The present invention is based on the network evolution rule of attractive force between node, by taking all factors into consideration the attractive force of nodal community and distance calculation of the two and existing node, thereby select node to set up the evolved network model that complex network is set up in new connection.Complex network modeling of the present invention has simultaneously that power rate degree distributes, three big statistical natures of little mean distance and big convergence factor, can reflect the attribute of real system preferably, meets the statistical property of live network more.
Aspect that the present invention adds and advantage part in the following description provide, and part will become obviously from the following description, or recognize by practice of the present invention.
Description of drawings
Above-mentioned and/or additional aspect of the present invention and advantage are from obviously and easily understanding becoming the description of embodiment below in conjunction with accompanying drawing, wherein:
Fig. 1 is the flow chart of steps of the complex network modeling method of the embodiment of the invention;
Fig. 2 is the degree distribution schematic diagram of the evolved network model of the embodiment of the invention;
Fig. 3 is the mean distance synoptic diagram of the evolved network model of the embodiment of the invention;
Fig. 4 is the convergence factor synoptic diagram of the evolved network model of the embodiment of the invention.
Embodiment
Describe embodiments of the invention below in detail, the example of described embodiment is shown in the drawings, and wherein identical from start to finish or similar label is represented identical or similar elements or the element with identical or similar functions.Below by the embodiment that is described with reference to the drawings is exemplary, only is used to explain the present invention, and can not be interpreted as limitation of the present invention.
With reference to figure 1, this figure is the flow chart of steps of the complex network modeling method of the embodiment of the invention.
As shown in the figure, initialization two-dimensional crystal lattice (step 202) at first.For example set up the evolution space of the two-dimensional crystal lattice of a Q * Q as complex network, network just develops within the scope of this lattice.Each node all has a two-dimensional coordinate on this space.Then, on this two-dimensional crystal lattice, carry out initialization (step 204): produce m0 start node combination at random, and with full-mesh or at random ways of connecting connect, each node all occupy a grid (x, y), and 0≤x, y＜Q.
Carry out evolutionary process on above-mentioned two-dimensional crystal lattice: add a new node i (step 206) on two-dimensional crystal lattice at random, wherein i has m bar limit, and m≤m0.Then, calculate the attractive force (step 208) between the existing node on new node i and the two-dimensional crystal lattice respectively.The calculating of attractive force can obtain according to following formula:
K wherein
iAnd k
jThe degree (neighbours' number) of representing node i and j respectively, r
IjSpace length for i and j.This distance can be Euclidean space, is defined as
Be geographic distance perhaps, be defined as r
Ij=| x
i-x
j|+| y
i-y
j|, (x wherein
i, y
i) and (x
j, y
j) be respectively the volume coordinate of node i and j.It can certainly be the space length of other expression modes.
As can be seen, above-mentioned attractive force formula is extremely similar to Newton's law of gravitation:
Wherein G is a universal gravitational constant, M
iAnd M
jBe respectively the quality of object i and j, r is the distance of object i and j.Because gravitational constant does not have practical significance in network modelling, the present invention has done suitable simplification, makes it equal 1.And, proving that according to theoretical research in the past and positive research the weight of node is often closely related with the degree of node, the degree with node is proportional under many circumstances, so has adopted the degree of node to be used as the quality of node among the present invention.
According to each the internodal attractive force that calculates, in existing node, select m node of attractive force maximum to connect the limit with new node i, require nothing to weigh limit (step 210).Then, judge whether the finish condition that develops satisfies (step 212), and promptly the new node of Tian Jiaing satisfies predetermined quantitative requirement, and perhaps the two-dimensional crystal lattice of Q * Q is filled.If satisfy, end loop and obtain the evolved network model (step 214) of complex network then.Otherwise, return step 206, and repeating step 206 to 210.
The present invention proposes a kind of network evolution rule based on attractive force between node, has taken all factors into consideration the influence of nodal community and space length factor.Newly add node by taking all factors into consideration nodal community and the distance of the two, the attractive force of calculating and existing node selects node to set up new connection.
Fig. 2, Fig. 3 and Fig. 4 have provided the synoptic diagram that degree distributes, mean distance distributes and convergence factor distributes of the evolved network model of the embodiment of the invention respectively.Network characteristic by complex network model that modeling of the present invention is obtained is carried out statistical study, can obtain about the characteristics of network node degree, mean distance and convergence factor as follows.
(1) degree distributes.Positive research finds that the approximate power rate of node degree obedience of a large amount of live networks distributes, and the degree of some nodes is meant the number of the neighbor node that this node has here.Node degree is obeyed power-law distribution in other words, and having the interstitial content of certain specific degree and the relation between this degree can represent with a power function.Power function curve is a decline curve relatively slowly, that is to say that the degree of most nodes is all smaller in the network, but also has the very big node of degree of only a few.Among Fig. 2 (a), horizontal ordinate k is the degree of node, and ordinate P (k) is the ratio of the degree of node more than or equal to k; From Fig. 2 (a) as can be seen, the degree of the network that obtains by modeling method of the present invention is distributed as very that the power rate of standard distributes.And the size of network size no matter, for example network node shown in Fig. 2 (b) is 1000,2000 still to be 10000, the degree of network distributes and all satisfies the power rate and distribute, and power rate index be consistent (see Fig. 2 (b), wherein n (k) is the interstitial content of network degree more than or equal to k).This illustrates that it is very sane that the power rate degree of this network distributes.
(2) mean distance.In network, the distance of point-to-point transmission is defined as connecting the number on 2 the limit that shortest path comprised, and the right distance of all nodes is asked on average, has just obtained the mean distance of network.The robustness and the stability of mean distance and system have vital role.Maximally related with it phenomenon is exactly famous " six degree separate " law.As can be seen from Figure 3, the mean distance of modeling network of the present invention increases and increases along with network size.For size is the network of 10000 nodes, and its mean distance is about 4.5, and this illustrates that this network is the worldlet network of a standard.
(3) convergence factor.For certain node, the number that its convergence factor is defined as connecting between its all adjacent node the limit accounts for the ratio of possible limit, Dalian number, and the convergence factor of network then is the mean value of all node convergence factors, and it has reflected the dense degree that network connects.Studies show that in a large number live network has bigger convergence factor.As can be seen from Figure 4, the convergence factor of modeling network of the present invention increases and reduces along with network size.For size is the network of 10000 nodes, and its mean distance is about 0.60, very approaching with live network, is higher than the convergence factor (about 0.005) of no scale network far away.
From the description of above-mentioned example as can be known, complex network modeling of the present invention has simultaneously that power rate degree distributes, three big statistical natures of little mean distance and big convergence factor, can reflect the attribute of real system preferably, meets the statistical property of live network more.
Although illustrated and described embodiments of the invention, for the ordinary skill in the art, be appreciated that without departing from the principles and spirit of the present invention and can carry out multiple variation, modification, replacement and modification that scope of the present invention is by claims and be equal to and limit to these embodiment.
Claims (5)
1. a complex network modeling method is characterized in that, described modeling method may further comprise the steps:
A) set up the evolution space of a two-dimensional crystal lattice as described complex network;
B) generate the start node of a plurality of full-mesh at random, wherein each start node occupies a grid on the described two-dimensional crystal lattice;
C) on described two-dimensional crystal lattice, add a new node at random, and calculate the attractive force between the existing node on described new node and the described two-dimensional crystal lattice respectively according to following formula:
K wherein
iAnd k
jThe degree of representing node i and j respectively, r
IjBe the space length of i and j, the degree of some nodes is meant the number of the neighbor node that this node has;
D) from existing node, select respective amount to have the node of big attractive force according to the limit number of described new node; And
Add the company limit between described new node and the described selection node;
E) judge whether the finish condition that develops satisfies, if do not satisfy, then repeating step c and steps d if satisfy, stop repetition to obtain the evolved network model of described complex network.
2. modeling method as claimed in claim 1 is characterized in that, described space length is an Euclidean distance.
3. modeling method as claimed in claim 1 is characterized in that, described space length is a geographic distance.
4. modeling method as claimed in claim 1 is characterized in that, the finish condition of described step e is that the new node that adds satisfies predetermined quantitative requirement.
5. modeling method as claimed in claim 1 is characterized in that, the finish condition of described step e is the evolution space that node fills up described two-dimensional crystal lattice.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2009101702180A CN101645104B (en) | 2009-09-04 | 2009-09-04 | Complex network modeling method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2009101702180A CN101645104B (en) | 2009-09-04 | 2009-09-04 | Complex network modeling method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN101645104A CN101645104A (en) | 2010-02-10 |
| CN101645104B true CN101645104B (en) | 2011-05-25 |
Family
ID=41656990
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN2009101702180A Expired - Fee Related CN101645104B (en) | 2009-09-04 | 2009-09-04 | Complex network modeling method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN101645104B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104883224B (en) * | 2014-02-27 | 2017-05-10 | 北京邮电大学 | Method of constructing data center switching network and node apparatus |
| CN104836711B (en) * | 2015-03-29 | 2018-07-27 | 朱江 | A kind of command and control network generates the construction method of model |
| CN105629728B (en) * | 2015-12-23 | 2018-07-17 | 辽宁石油化工大学 | The modeling method of complex dynamic network and the design method of model controller |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7069180B1 (en) * | 2004-05-11 | 2006-06-27 | Cisco Technology, Inc. | Method and apparatus for availability measurement of complex networks |
| CN101114968A (en) * | 2007-08-31 | 2008-01-30 | 安徽大学 | Complex network quotient space model based path search method |
| CN101477490A (en) * | 2009-01-23 | 2009-07-08 | 上海第二工业大学 | Complex network-based object-oriented integration testing method |
-
2009
- 2009-09-04 CN CN2009101702180A patent/CN101645104B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7069180B1 (en) * | 2004-05-11 | 2006-06-27 | Cisco Technology, Inc. | Method and apparatus for availability measurement of complex networks |
| CN101114968A (en) * | 2007-08-31 | 2008-01-30 | 安徽大学 | Complex network quotient space model based path search method |
| CN101477490A (en) * | 2009-01-23 | 2009-07-08 | 上海第二工业大学 | Complex network-based object-oriented integration testing method |
Non-Patent Citations (1)
| Title |
|---|
| JP特开2001-251301A 2001.09.14 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN101645104A (en) | 2010-02-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Aland et al. | Exact price of anarchy for polynomial congestion games | |
| Gairing et al. | Routing (un-) splittable flow in games with player-specific linear latency functions | |
| CN101645104B (en) | Complex network modeling method | |
| CN103678669A (en) | Evaluating system and method for community influence in social network | |
| CN110826164B (en) | Complex network node importance evaluation method based on local and global connectivity | |
| CN106845712B (en) | The extracting method of scheduling rule is decomposed in polymerization towards big system multi-reservoir | |
| CN106227599A (en) | The method and system of scheduling of resource in a kind of cloud computing system | |
| Hua et al. | Voltage/frequency deviations control via distributed battery energy storage system considering state of charge | |
| Han et al. | Determining the minimal power capacity of energy storage to accommodate renewable generation | |
| CN104618134A (en) | Method for optimizing multi-grade light-splitting passive optical network of distribution communication network | |
| Tang et al. | A hardware-in-the-loop based co-simulation platform of cyber-physical power systems for wide area protection applications | |
| Menesy et al. | Optimal configuration of a hybrid photovoltaic/wind turbine/biomass/hydro-pumped storage-based energy system using a heap-based optimization algorithm | |
| Amoussou et al. | Optimal modeling and feasibility analysis of grid-interfaced solar PV/Wind/Pumped hydro energy storage based hybrid system | |
| Mondragón et al. | Random networks with given rich-club coefficient | |
| Yang et al. | An improved solving approach for interval-parameter programming and application to an optimal allocation of irrigation water problem | |
| Khezri et al. | Optimal planning of remote area electricity supply systems: Comprehensive review, recent developments and future scopes | |
| CN102457425A (en) | Large-scale virtual network topology generation method | |
| CN101872445A (en) | Space partition zone optimizing method for considering balanced allocation of resources | |
| Nsaif et al. | An adaptive routing framework for efficient power consumption in software-defined datacenter networks | |
| CN105989154A (en) | Similarity measurement method and equipment | |
| Enshaee et al. | Transmission loss allocation based on power adjacency matrix in pool electricity markets | |
| CN104133944A (en) | Supernetwork building method | |
| CN106533651A (en) | Cost-based complex network side attack method under weight changing | |
| Enshaee et al. | Approach to evaluate active loss contributions for transmission systems | |
| Sun et al. | Multi-attribute group decision making method of ecological water compensation program based on preference of decision makers |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20110525 Termination date: 20150904 |
|
| EXPY | Termination of patent right or utility model |