CN108462610A - A kind of information radiation model building method having across neighbours' transmission capacity - Google Patents
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- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract
A kind of information radiation model building method having across neighbours' transmission capacity, using Complex Networks Theory, mean field theory and theory of radiation, by network structure of physical layer basis, using radiating layer as information communication environments, the layer three information radial network model counted by radiation regimes of state layer.The transformation rule and network of relation statistic between complex network node state are defined first, are then introduced radiation scope and radiation decrement, then by radiation mechanism and derived radiation threshold value expression formula, are established layer three information radial network model；Finally by between this model analysis node state transition probability and radiation decrement to the affecting laws of information radiation.
Description
Technical field
The invention belongs to complex network technical fields, are related to node state and divide and convert, three layers of radial network model structure
It builds and radiation mechanism is theoretical, more particularly to a kind of information radiation model building method having across neighbours' transmission capacity.
Background technology
In complex network, information is propagated, the research of information radiation is a critical issue, currently, most of information pass
The research broadcast only considers the problems of neighbours, but across the information radiation of neighbours' transmission capacity transportation network and disease immune etc. no
With in network each node influence each other and effect seems extremely important.Analyze the state transition probability between complex network node
It is great to the research significance of the affecting laws of information radiation with radiation decrement.
Information propagation refers to the process of that information is diffused into other groups from initial disseminator.For example：Disease, public opinion, meter
The propagation of calculation machine virus etc..Research to information communication process is it can be found that rule are propagated in individual interaction and information under varying environment
Rule finds the key node in network, information propagates trend prediction, accident early warning and internet security assessment offer are theoretical
Basis.
Propagated using complex network research information and have become research hotspot in recent years, wherein based on mean field theory come
The document that research information is propagated is most, and in mean field theory, Information Propagation Model defines the propagation rule of information, between individual
Usually interacted in the form of probability, the macroscopic propagation range and transmission threshold of last observed information.Therefore, mean field
Theory remains the main information and essential attribute of system by simplifying system, it is notable that almost all of text
It offers the information that all only considered between node and neighbor node to propagate, the information for having ignored node and the exterior node except its neighbour passes
Broadcast situation.
In conclusion the information radiation model across neighbours' transmission capacity is solved and is only only accounted for saving based on mean field theory
Information between point and neighbor node is propagated, and has ignored the information propagation problem of node and the exterior node of its neighbour.And this mould
Type can more preferably, comprehensively reflect the problem of each nodal information radiation in complex network.
Invention content
In order to overcome the above-mentioned deficiencies of the prior art, have across neighbours' transmission capacity the object of the present invention is to provide a kind of
Information radiation model building method, mutual transition probability and attenuation between the model analysis Node Contraction in Complex Networks state
The influence to information radiation is measured, passes through model hypothesis, node state division and conversion and modelling so that the exterior node of neighbours
Informational influence and propagation problem know about method certainly.Using Complex Networks Theory, mean field theory and theory of radiation, with object
Reason layer is network structure basis, using radiating layer as information communication environments, the layer three information spoke counted by radiation regimes of state layer
Penetrate network model.The transformation rule and network of relation statistic between complex network node state are defined first, then introduce spoke
Range and radiation decrement are penetrated, then by radiation mechanism and has derived radiation threshold value expression formula, establishes layer three information radial network
Model；Influence rule finally by the state transition probability and radiation decrement between this model analysis node to information radiation
Rule.
To achieve the goals above, the technical solution adopted by the present invention is：
A kind of information radiation model building method having across neighbours' transmission capacity, includes the following steps：
Step 1：Model hypothesis
Three kinds of hypothesis below：
Assuming that 1：Network is connection, and interaction and information radiation is presented between group member, isolated constituent element is not present, because
This, this model will not consider situation existing for isolated constituent element；
Assuming that 2：Connection relation between nodes is two-way, and the network involved by this model is indirected net
Network；
Assuming that 3：Only radiant state constituent element can carry out security information radiation, and radiant state constituent element is only to known state and unknown state
Constituent element radiated；
Step 2：Node state divides and conversion
In information radiation network model, one network individual of each node on behalf, and connect and then indicate between them
In correspondence with, wherein each node is likely to be at one kind in following three kinds of states；
1) radiant state:Information content be higher than radiant state threshold value, and in a network radiation information when state, be denoted as R, original net
Information radiation source is in radiant state in network, and during information radiation, the node in radiant state has an opportunity by releasing energy
Be converted to known state；
2) state known to：Information content is higher than minimum information amount, i.e., known state threshold value, and is less than radiant state threshold value, can't spoke
State when information is penetrated, K. is denoted as, during information radiation, the node in known state has an opportunity by receiving energy conversion
For radiant state；
3) unknown state:Information content is less than state when known state threshold value, is denoted as U, and most of node is in initial network
Unknown state, during information radiation, the node in unknown state has an opportunity to be converted to known state or radiation by receiving energy
State；
It was found from node state transformational relation, during information radiation, radiant state can be converted to known state or continuation
Keep radiant state, it is known that state can be converted to radiant state or continue and keep known state, and unknown state can be converted to radiant state or
Know state or continues to keep unknown state；
Step 3：Three layers of radial network model foundation
1) first according to step 2 come judge actual node connection build complex network foundation structure mould
Type, the i.e. physical layer of network；
2) according to the capability of influence of node, i.e. radianting capacity, the radiation scope of different nodes is determined in network, i.e. network
Radiating layer；
The radiation scope of different nodes is such as set as m distance length, wherein m=1；2；···；N-1；
3) state of node is determined according to the acquisition situation of nodal information amount, carries out statistic, the i.e. state layer of network；
4) physical layer of the network described in, radiating layer, state layer constitute three layers of radial network model.
If information content increases continuously in the step two, when being converted to radiant state by unknown state, due to unknown
The information content of state is less than the information content of known state, so known state will necessarily be undergone when being converted to radiant state, in order to realize node
Known state is skipped by unknown state and is converted to radiant state, the state conversion time of defining node is more than information content transformation period here,
The information content variation of node carries out node state conversion again after being finally completed, and waits for carrying out network again after the state conversion of node
After information radiation, wherein unknown state node are by information radiation, there is probability α to be converted to known state, there is probability γ to be converted to radiation
State；After known state node is by information radiation, there is probability β to be converted to radiant state；Radiant state node has after once radiate
It is Net long wave radiation rate that probability δ, which is converted to known state and defines λ=β/δ,.
The change of the step two interior joint information content can influence the change of node state, and the change of node state can also
Radiant state number of nodes is influenced, and then influences radiating layer in turn and changes radial network.Therefore, deposited between radiating layer and state layer
In action and reaction.
Three layers of radial network model described in the step three are right it is found that information radiation is mainly carried out in radiating layer
Some concepts in radial network are defined；
Described in following formula:
The number for the node that the n gradients of node are defined as with this nodal distance is n, is indicated with kn；Average n gradient networks
In the average value of n gradients of all nodes be known as the average n gradients of network or node, indicated with kn；The n ranks of nodes
What the distribution situation of degree can describe .Pn (kn) expressions with distribution function Pn (kn) is the n gradients of a node selected at random
Exactly the probability of kn R (t) (t) (t) indicate R in network respectively, K, U states node t moment density, with Rk (t) k (t)
K (t) indicate respectively network moderate be k R, K, U states node t moment density, then：
+ Uk (t)=1 Rk (t)+Kk (t): (2)
Assuming that the radiation scope of node is m, according to mean field theory, information radiation model is irradiated in complex network
Journey can be indicated with following differential equation group:
DRk (t)/1 (t)+τ β k2Kk (t) θ 2 (t) of dt=β k1Kk (t) θ+
+τm-1βkmKk(t)θm(t)+γk1Uk(t)θ1(t)+τγk2Uk(t)θ2(t)+···+τm-1γkmUk
(t)θm(t)-δRk(t)；
DKk (t)/1 (t)+τ α k2Uk (t) θ 2 (t) of dt=α k1Uk (t) θ+
τm-1αkmUk(t)θm(t)-(βk1Kk(t)θ1(t)+τβk2Kk(t)θ2(t)+···+τm-1βkmKk(t)θm
(t))+δRk(t)；
DUk (t)/dt=- (1 (t)+τ α k2Uk (t) θ 2 (t) of α k1Uk (t) θ+
+τm-1αkmUk(t)θm(t))-(γk1Uk(t)θ1(t)+τγk2Uk(t)θ2(t)+···+τm-1γkmUk
(t)θm(t)) (3)
Wherein：
θi(t)=∑ kiPi(ki)Rk(t)/<ki＞ (i=1；2；···；m) (4)
Formula (4) is to indicate that the node that t moment is arbitrarily chosen in the range of i gradients is the general of radiant state node
Rate.It enables：
θ (t)=1 (t)+τ k2 θ 2 (t) of k1 θ+rm-1kmθm(t) (5)
Simplified style (3)：
dRk(t)/dt=β kk(t)θ(t)+γUk(t)θ(t)-δRk(t)
dRk(t)/dt=α Uk(t)θ(t)+βKk(t)θ(t)+δRk(t)
dUk(t)/dt=- α Uk(t)θ(t)-γUk(t)θ(t) (6)
By state transition rules it is found that can be obtained by (6) under limit：
(7) are substituted into (2) to obtain：
The beneficial effects of the invention are as follows：
Mutual transition probability and radiation decrement between the model analysis Node Contraction in Complex Networks state is to information radiation
Influence, pass through model hypothesis, node state divide and conversion and modelling so that the informational influence of the exterior node of neighbours and
Propagation problem knows about method certainly.
Description of the drawings
Fig. 1 is the node state transformational relation of the present invention.
Fig. 2 is that three layers of radial network model of the present invention constitute figure.
Specific implementation mode
The present invention is further discussed below below in conjunction with attached drawing.
A kind of information radiation model building method having across neighbours' transmission capacity, includes the following steps：
Step 1：Model hypothesis
Three kinds of hypothesis below：
Assuming that 1：Network is connection, and interaction and information radiation is presented between group member, isolated constituent element is not present, because
This, this model will not consider situation existing for isolated constituent element；
Assuming that 2：Connection relation between nodes is two-way, and the network involved by this model is indirected net
Network；
Assuming that 3：Only radiant state constituent element can carry out security information radiation, and radiant state constituent element is only to known state and unknown state
Constituent element radiated；
Step 2：Node state divides and conversion
In information radiation network model, one network individual of each node on behalf, and connect and then indicate between them
In correspondence with, wherein each node is likely to be at one kind in following three kinds of states；
1) radiant state:Information content be higher than radiant state threshold value, and in a network radiation information when state, be denoted as R, original net
Information radiation source is in radiant state in network, and during information radiation, the node in radiant state has an opportunity by releasing energy
Be converted to known state；
2) state known to：Information content is higher than minimum information amount, i.e., known state threshold value, and is less than radiant state threshold value, can't spoke
State when information is penetrated, K. is denoted as, during information radiation, the node in known state has an opportunity by receiving energy conversion
For radiant state；
3) unknown state:Information content is less than state when known state threshold value, is denoted as U, and most of node is in initial network
Unknown state, during information radiation, the node in unknown state has an opportunity to be converted to known state or radiation by receiving energy
State；If information content normalized, the information content of three kinds of states is as shown in Figure 1.
It was found from node state transformational relation, during information radiation, radiant state can be converted to known state or continuation
Keep radiant state, it is known that state can be converted to radiant state or continue and keep known state, and unknown state can be converted to radiant state or
Know state or continues to keep unknown state；
Step 3：Three layers of radial network model foundation
1) first according to step 2 come judge actual node connection build complex network foundation structure mould
Type, the i.e. physical layer of network；
2) according to the capability of influence of node, i.e. radianting capacity, the radiation scope of different nodes is determined in network, i.e. network
Radiating layer；
The radiation scope of different nodes is such as set as m distance length, wherein m=1；2；···；N-1；
3) state of node is determined according to the acquisition situation of nodal information amount, carries out statistic, the i.e. state layer of network；
4) physical layer of the network described in, radiating layer, state layer constitute three layers of radial network model.
If information content increases continuously in the step two, when being converted to radiant state by unknown state, due to unknown
The information content of state is less than the information content of known state, so known state will necessarily be undergone when being converted to radiant state, in order to realize node
Known state is skipped by unknown state and is converted to radiant state, the state conversion time of defining node is more than information content transformation period here,
The information content variation of node carries out node state conversion again after being finally completed, and waits for carrying out network again after the state conversion of node
After information radiation, wherein unknown state node are by information radiation, there is probability α to be converted to known state, there is probability γ to be converted to radiation
State；After known state node is by information radiation, there is probability β to be converted to radiant state；Radiant state node has after once radiate
It is Net long wave radiation rate that probability δ, which is converted to known state and defines λ=β/δ,.
The change of the step two interior joint information content can influence the change of node state, and the change of node state can also
Radiant state number of nodes is influenced, and then influences radiating layer in turn and changes radial network therefore, is deposited between radiating layer and state layer
It is in summary analyzed in action and reaction, three layers of radial network model constitute as shown in Figure 2.
Three layers of radial network model described in the step three are right it is found that information radiation is mainly carried out in radiating layer
Some concepts in radial network are defined；
Described in following formula:
The number for the node that the n gradients of node are defined as with this nodal distance is n, is indicated with kn；Average n gradient networks
In the average value of n gradients of all nodes be known as the average n gradients of network or node, indicated with kn；The n ranks of nodes
What the distribution situation of degree can describe .Pn (kn) expressions with distribution function Pn (kn) is the n gradients of a node selected at random
Exactly the probability of kn R (t) (t) (t) indicate R in network respectively, K, U states node t moment density, with Rk (t) k (t)
K (t) indicate respectively network moderate be k R, K, U states node t moment density, then：
+ Uk (t)=1 Rk (t)+Kk (t):(2)
Assuming that the radiation scope of node is m, according to mean field theory, information radiation model is irradiated in complex network
Journey can be indicated with following differential equation group:
DRk (t)/1 (t)+τ β k2Kk (t) θ 2 (t) of dt=β k1Kk (t) θ+
+τm-1βkmKk(t)θm(t)+γk1Uk(t)θ1(t)+τγk2Uk(t)θ2(t)+···+τm-1γkmUk
(t)θm(t)-δRk(t)；
DKk (t)/1 (t)+τ α k2Uk (t) θ 2 (t) of dt=α k1Uk (t) θ+
τm-1αkmUk(t)θm(t)-(βk1Kk(t)θ1(t)+τβk2Kk(t)θ2(t)+···+τm-1βkmKk(t)θm
(t))+δRk(t)；
DUk (t)/dt=- (1 (t)+τ α k2Uk (t) θ 2 (t) of α k1Uk (t) θ+
+τm-1αkmUk(t)θm(t))-(γk1Uk(t)θ1(t)+τγk2Uk(t)θ2(t)+···+τm-1γkmUk
(t)θm(t)) (3)
Wherein：
θi(t)=∑ kiPi(ki)Rk(t)/<ki>(i=1；2；···；m) (4)
Formula (4) is to indicate that the node that t moment is arbitrarily chosen in the range of i gradients is the general of radiant state node
Rate.It enables：
θ (t)=1 (t)+τ k2 θ 2 (t) of k1 θ+rm-1kmθm(t) (5)
Simplified style (3)：
dRk(t)/dt=β kk(t)θ(t)+γUk(t)θ(t)-δRk(t)
dRk(t)/dt=α Uk(t)θ(t)+βKk(t)θ(t)+δRk(t)
dUk(t)/dt=- α Uk(t)θ(t)-γUk(t)θ(t) (6)
By state transition rules it is found that can be obtained by (6) under limit：
(7) are substituted into (2) to obtain：
Claims (4)
1. a kind of information radiation model building method having across neighbours' transmission capacity, which is characterized in that include the following steps：
Step 1：Model hypothesis
Three kinds of hypothesis below：
Assuming that 1：Network is connection, and interaction and information radiation is presented between group member, and there is no isolated constituent elements, therefore, this
Model will not consider situation existing for isolated constituent element；
Assuming that 2：Connection relation between nodes is two-way, and the network involved by this model is Undirected networks；
Assuming that 3：Only radiant state constituent element can carry out security information radiation, and group of the radiant state constituent element only to known state and unknown state
Member is radiated；
Step 2：Node state divides and conversion
In information radiation network model, one network individual of each node on behalf, and connect then indicate to have between them it is logical
Letter contact, wherein each node is likely to be at one kind in following three kinds of states.
1) radiant state (radiated):Information content be higher than radiant state threshold value, and in a network radiation information when state, be denoted as R,
Information radiation source is in radiant state in initial network, and during information radiation, the node in radiant state has an opportunity by releasing
Exoergic amount is converted to known state.
2) state known to (known):Information content is higher than minimum information amount (known state threshold value), and is less than radiant state threshold value, can't
State when radiation information, is denoted as K., and during information radiation, the node in known state has an opportunity to turn by receiving energy
It is changed to radiant state.
3) unknown state (unknown):Information content is less than state when known state threshold value, is denoted as U, most of node in initial network
In unknown state, during information radiation, the node in unknown state have an opportunity by receive energy be converted to known state or
Radiant state；
Step 3：Three layers of radial network model foundation
1) first according to step 2 come judge actual node connection build complex network foundation structure model, i.e.,
The physical layer of network；
2) according to the capability of influence of node, i.e. radianting capacity, the radiation scope of different nodes in network, the i.e. radiation of network are determined
Layer；
The radiation scope of different nodes is such as set as m distance length, wherein m=1；2；…；N-1；
3) state of node is determined according to the acquisition situation of nodal information amount, carries out statistic, the i.e. state layer of network；
4) physical layer of the network described in, radiating layer, state layer constitute three layers of radial network model.
2. a kind of information radiation model building method having across neighbours' transmission capacity according to claim 1, feature
It is, if information content increases continuously in the step two, when being converted to radiant state by unknown state, due to unknown state
Information content is less than the information content of known state, so known state will necessarily be undergone when being converted to radiant state, in order to realize node by not
Know that state skips known state and is converted to radiant state, the state conversion time of defining node is more than information content transformation period, node here
Information content variation be finally completed after carry out node state conversion again, wait for carrying out the information of network again after the state conversion of node
After radiation, wherein unknown state node are by information radiation, there is probability α to be converted to known state, there is probability γ to be converted to radiant state；
After knowing state node by information radiation, there is probability β to be converted to radiant state；Radiant state node has probability δ after once radiate
It is Net long wave radiation rate to be converted to known state and define λ=β/δ.
3. a kind of information radiation model building method having across neighbours' transmission capacity according to claim 1, feature
It is, the change of the step two interior joint information content can influence the change of node state, and the change of node state can also shadow
Radiant state number of nodes is rung, and then influences radiating layer in turn and changes radial network.Therefore, exist between radiating layer and state layer
Action and reaction.
4. a kind of information radiation model building method having across neighbours' transmission capacity according to claim 1, feature
It is, three described in the step three layer radial network model is it is found that information radiation is mainly carried out in radiating layer, to radiation
Some concepts in network are defined；
Described in following formula:
The number for the node that the n gradients of node are defined as with this nodal distance is n, is indicated with kn；Institute in average n gradient networks
There is the average value of the n gradients of node to be known as the average n gradients of network or node, is indicated with kn；The n gradients of nodes
What distribution situation can describe .Pn (kn) expressions with distribution function Pn (kn) be a selected node at random n gradients it is lucky
Indicate R in network respectively with R (t) (t) (t) for the probability of kn, K, U states node t moment density, with Rk (t) k (t) k (t)
Respectively indicate network moderate be k R, K, U states node t moment density, then：
+ Uk (t)=1 Rk (t)+Kk (t): (2)
Assuming that the radiation scope of node is m, according to mean field theory, radiative process of the information radiation model in complex network can
To be indicated with following differential equation group:
DRk (t)/1 (t)+τ β k2Kk (t) θ 2 (t) of dt=β k1Kk (t) θ ++ τ m-1 β kmKk (t) θ m (t)+γ k1Uk (t) θ
1(t)+τγk2Uk(t)θ2(t)+…+τm-1γkmUk(t)θm(t)-δRk(t)；
DKk (t)/1 (t)+τ α k2Uk (t) θ of dt=α k1Uk (t) θ, 2 (t)+τ m-1 α kmUk (t) θ m (t)-(β k1Kk (t) θ 1
(t)+τβk2Kk(t)θ2(t)+…+τm-1βkmKk(t)θm(t))+δRk(t)；
DUk (t)/dt=- (1 (t)+τ α k2Uk (t) θ 2 (t) of α k1Uk (t) θ+...+τ m-1 α kmUk (t) θ m (t))-(γ k1Uk
(t)θ1(t)+τγk2Uk(t)θ2(t)+…+τm-1γkmUk(t)θm(t)) (3)
Wherein：
θi(t)=∑ kiPi(ki)Rk(t)/<ki>(i=1；2；…；m) (4)
Formula (4) is the probability for indicating the node that t moment is arbitrarily chosen in the range of i gradients as radiant state node.It enables：
θ (t)=1 (t)+τ k2 θ 2 (t) of k1 θ+rm-1kmθm(t) (5)
Simplified style (3)：
dRk(t)/dt=β kk(t)θ(t)+γUk(t)θ(t)-δRk(t)
dRk(t)/dt=α Uk(t)θ(t)+βKk(t)θ(t)+δRk(t)
dUk(t)/dt=- α Uk(t)θ(t)-γUk(t)θ(t) (6)
By state transition rules it is found that can be obtained by (6) under limit：
(7) are substituted into (2) to obtain：
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