CN107592232A - A kind of low-cost is propagated or the method for the monitoring network information - Google Patents
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Abstract
The invention belongs to computer network communication technology field.More particularly to a kind of low-cost is propagated or the method for the monitoring network information, comprises the following steps：First, a node is randomly choosed in network topology structure data figure as disseminator, and adds activation node set Q；Then, side seepage flow processing is carried out to selected node so as to activate the adjacent node of the node according to preset probable value v, and the node of activation is added into activation node set Q.A node for never turning into disseminator is then randomly selected in node set Q is activated as new disseminator, next round propagation is carried out, until activation number of nodes reaches the quantitative value L pre-set.The invention provides a kind of node for only needing limited quantity, the method that just expeditiously can propagate or monitor the network information, step are simple, it is not necessary to the complete network information, and time complexity is calculated independent of network size.
Description
Technical field
The present invention relates to computer network communication technology field, and in particular to a kind of low-cost is propagated or the monitoring network information
Method.
Background technology
Human society is come into from Media Era, and everyone is publisher and the biography of information in social network-i i-platform
The person of broadcasting.Social network-i i-platform just progressively substitutes traditional media with its powerful propagation and communication function, and it is daily to turn into modern people
Important component in life.The information propagated recently in social network-i i-platform is monitored or collected low-cost, is contributed to
Focus social concern that solution ordinary populace is paid close attention to recently, the new trend of prediction etc..And information is efficiently propagated on social networks
Be advantageous to the popularization of new thought, new product again.It can be seen that the information monitoring and propagation on social networks have important theory significance
With application value.However, total number of users of online social networks is huge, such as Facebook, monthly any active ues already exceed
3000000000；QQ, Wechat any active ues are daily also above 200,000,000, and the network structure moment is all changing.Generally we can not possibly obtain
Obtain whole propagation information thereon.Therefore, how low-cost and to effectively monitor and promote in social networks information to propagate, one
It has been considered as one of major issue of Network Science circle since straight.
It is usually to utilize general indices and algorithm such as k-shell to the solution of two problems in currently available technology,
The Measure Indexes of overall importance such as closeness, networking character value, CI, propagation (monitoring) capabilities to single summit, and then
Using typical heuritic approach, such as belief propagation, degree discount, greedy scheduling algorithms are sought
Look for optimal disseminator (supervisor).But these methods are all to need to know just be able under conditions of network global structure
Carry out, and often assuming that the Initial travel or the summit quantity of monitoring elected are directly proportional to network size (such as
5% summit) etc. under the conditions of carry out.It will be appreciated that for huge network, such as Facebook or QQ, Wechat, transference
The suitable people of network size turns into Initial travel person, or round-the-clock these users of monitoring, and cost is all very high.
The content of the invention
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing one kind only needs
The node of limited quantity, it just can expeditiously monitor and promote the method that information is propagated in social networks.The letter of its method and step
It is single, it is not necessary to network global information, and algorithm complex is unrelated with network size.
The present invention adopts the following technical scheme that：
A kind of low-cost is propagated or the method for the monitoring network information, including：The topology data of network is expressed as figure；
The figure includes N number of node, and each node corresponds uniquely to a user in the network；The figure also includes institute
Stating any two in network has the company side being connected between two nodes corresponding to the user of incidence relation；Wherein N is
The natural number of non-zero.Incidence relation described in " any two has the user of incidence relation " can be described two
The friends (relation between the similar social network user of such as Tencent QQ, wechat, Facebook) of user, or close
Relation (such as microblogging, knowing relation between user) between note person and the person of being concerned.
The present invention comprises the following steps that：
S.1, set and initialized activation node set Q as empty set；
S.2 a node, is randomly choosed from above-mentioned figure as disseminator, and the node is added and has activated set of node
Close Q；
S.3, according to preset probable value v (βc≤ v≤1) to step, S.2 selected node carries out the processing of side seepage flow so as to swash
The adjacent node of the node living, and the adjacent node is added and has activated node set Q；The βcTo be opened up according to
Rush the net the predetermined percolation threshold of structured data of network.
Seepage flow processing in side includes in the present invention：The every company side possessed the node is deleted with 1-v probability, with
V probability retains, and the adjacent node that the side of reservation is connected is designated as having activated node.
S.4 one, is randomly selected in node set Q has been activated never as disseminator node as new disseminator,
S.3 preset probable value v and side seepage flow processing S.3 is carried out to the node as new disseminator according to step according to step
So as to activate the adjacent node of the node as new disseminator, and using having swashed as the node of new disseminator
The adjacent node living adds and has activated node set Q；
If process when number of nodes reaches the quantitative value L pre-set that activated S.5, activated in node set Q is stopped
Only, wherein L is the non-zero natural number less than N；Otherwise, step is returned to S.4.
After carrying out above-mentioned processing to the figure, L obtained user can be expeditiously low as need to obtain one
Cost is propagated or monitoring network information user set.
In order to be better understood from the present invention, the flow of method provided by the invention is now illustrated using accompanying drawing 1：In Fig. 1, by society
The topology data of network is handed over to be expressed as connecting the company side of two nodes between figure, including N number of node and the node, its
Middle N is the natural number of non-zero.Each node corresponds uniquely to a user in the social networks, and every company side is only
The incidence relation of corresponding two users in one ground.When presetting L=10, comprise the following steps that：
S.1 set initialization and activate node set Q as empty set；
S.2 a node 1 is randomly choosed from figure and is used as disseminator, and adds and has activated node set Q；
S.3 according to preset probable value v (βc≤ v≤1) to step, S.2 selected node 1 carries out the processing of side seepage flow so as to swash
The adjacent node 2,3 of the node living, and the node 2,3 of activation is added and has activated node set Q；The βcFor according to institute
State the predetermined percolation threshold of structured data of topological network.Seepage flow processing in side includes in the present invention：To the every of the node
Bar is connected side and deleted with 1-v probability, is retained with v probability, the adjacent node that the company side of reservation is connected is designated as having swashed
Movable joint point.
S.4 one is randomly selected in node set Q has been activated and is never used as new disseminator as the node 3 of disseminator,
The adjacent node 4,5 of new disseminator according to the rale activation of step S.3, and the node 4,5 of activation is added and has activated section
Point set Q；
S.5 the number of nodes of activation for having activated node set Q is 5, the quantitative value L=10 not up to pre-set, because
S.4 this continues back at step.Until the number of nodes that activated for having activated node set Q reaches the quantitative value L=pre-set
Process stops when 10.Now, activated and figure interior joint 1,2,3,4,5,6,7,8,9,10 is included in node set Q.To described
After figure carries out above-mentioned processing, 10 obtained users expeditiously low-cost can propagate or supervise as need to obtain one
Control network information user set.
Method of the present invention, it is in setting probability of spreading β (βc<β) and propagate enter under conditions of monitoring threshold value P
Capable.It is described propagate monitoring threshold value P in selected gather, at least one node falls into the huge group of UNICOM of given information
Probability；The selected collection is combined into the propagation being made up of L user obtained using method provided by the invention or monitoring network
Information user gathers.Probability of spreading β is desirable to be more than βcAnd the arbitrary value less than or equal to 1, propagate monitoring threshold value P can according to
Family demand is selected to be more than or equal to 0 arbitrary value for being less than or equal to 1.
Especially, the method for the invention, that has activated that node set Q activation number of nodes to be reached pre-sets
Quantitative value L obtained by following methods：
Obtain the X huge groups of UNICOM of wide-scale distribution information in network first, the huge group of UNICOM is included but not
Be confined to participate in the customer group of information forwarding in true propagation, or carry out in a network side seepage flow handle to obtain it is huge
Logical group.Then, it is that the number of nodes of activation for having activated node set Q sets hunting zone section as [Lmin,
Lmax], then carry out dichotomizing search in the section, choose meet to propagate monitoring threshold value P minimum value for it is described in advance
The quantitative value L of setting, wherein hunting zone section minimum value LminWith maximum LmaxIt is non-zero natural number, and Lmin<Lmax。
Preferably, described " dichotomizing search " process is specific as follows：
(1) three variables a, b, c, are set, wherein a, b is respectively directed to the upper bound and the lower bound in the hunting zone section, makes c
=(a+b)/2；Initialize a=Lmin, b=Lmax；
(2), each huge group of UNICOM in the X huge groups of UNICOM is operated as follows：
(2.1) c=(a+b)/2, is calculated, the user that size is c is acquired and gathers；
(2.2) if, the user that size caused by step (2.1) is c gathers at least one user and falls into huge UNICOM's collection
In group, then it is assumed that the Cheng Gongchuanbo monitoring network information is once；
(3), after each described huge group of UNICOM completes the step (2), succeed propagation monitoring letter
The total degree of breath, if propagate monitoring success rateIf P ' >=P, b=c is made, a values are not
Become；If P '<P, makes a=c, and b values are constant.
(4) if, b-a≤1, stopped process, obtain final b values, obtained b user as meet it is default propagate monitoring
Threshold value P optimal set size, makes that " the quantitative value L " pre-set is equal to final b values；Otherwise, step (2) is returned to.
Preferably, X is the integer more than or equal to 100 in described " X huge groups of UNICOM ".
Preferably, the X values are：800th, one of 1000,5000,8000 or 10000.
After such scheme, technical scheme provided by the invention will have the following advantages：
The invention provides a kind of node for only needing limited quantity, just expeditiously can propagate or monitor the network information
Method, step are simple.When network size tends to be infinite, the required nodes of the present invention are almost constant, tend to one often
Number.In addition, the present invention does not need the complete network information, and time complexity is calculated independent of network size, this permission
The information in extensive online social networks easily can also be propagated or monitor even if personal computer.
Brief description of the drawings
Fig. 1 is the method provided by the present invention schematic diagram, is default L=10 user's set in figure.
Fig. 2 is the performance map 2 for the connection group that the embodiment of the present invention 1 provides：Under default v=0.02, propagate (monitoring) and lose
Lose rate 1-P and set sizes L relation.
Fig. 3 is to connect the performance of group and network size N relation on the random network that the embodiment of the present invention 2 provides, and N is
Natural number.
Fig. 4 is to connect the performance of group and network size N relation, N on the scales-free network that the embodiment of the present invention 2 provides
For natural number.
Embodiment
A kind of method propagated the invention provides low-cost or monitor the network information, propagate or supervise for getting one
The connection group of the network information is controlled, improves the propagation efficiency of information and the monitoring efficiency to information.
To enable goal of the invention, feature, the advantage of the present invention more obvious and understandable, below in conjunction with the present invention
Accompanying drawing in embodiment, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that disclosed below
Embodiment be only part of the embodiment of the present invention, and not all embodiments.Based on the embodiment in the present invention, this area
The every other embodiment that is obtained of technical staff, belong to the scope of protection of the invention.
It is described in detail below.
For the information propagation problem on social networks, positive research shows that classical infectious disease transmission (SIR) can be used
Model is portrayed.And the side seepage flow processing in the circulation way and complex network of SIR models is of equal value, pass through this corresponding pass
System, when the ability (two neighboring summit infections relating ability) that information is propagated is that probability of spreading β is more than phase critical point, from
One summit, which is set out, propagates information, and two states only occur in final result, i.e., for information from a summit, it propagates model
Enclose distribution and will appear from bimodal distribution, and show two kinds of completely different phases, one is local phase, and another is global phase.
What local mutually represented is that the information is not propagated, and only propagates several steps and just terminates；The overall situation is mutually a Delta function, in nothing
(having) corresponding probability with β into network retains side, strong UNICOM's subgraph size in flow model in porous media.Therefore, information is pushed up from some
Point, which sets out, to be propagated, and its result can only be one of the following two kinds situation：First, information is only propagated as the seldom several steps of number just
Terminate；Second, information can wide-scale distribution, its spread scope is equivalent to the size of maximum UNICOM's subgraph, almost often
Number, the scope is with Initial travel summit without the information of initial vertax only influences to be capable of the probability of spread out.When information is in office
During the phase of domain, that is, when propagating not open, the distribution of its spread scope meets function：
The τ and s*It is constant, in the case of network structure statistical nature is given, τ and s*It is unrelated with network size, only with
Probability of spreading is related.It can be seen that when s is more than s*, P (s) can with s increase and exponential decay occur.If it means that propagate
Scope is more than s*When, global phase can be dropped into during subsequent propagation with almost 1 probability, that is, propagate final scope as maximum
Group of UNICOM.Therefore, if Initial travel summit is chosen to be a scale and is more than s*Group of UNICOM, then finally can be with almost 1
The whole global network of impact probability.
Optimal monitoring summit or Initial travel summit are selected, is substantially to solve same problem.Propagation is letter
Breath blazes abroad, and monitors and refer to receive the information with certain influence power to have blazed abroad.Own by overturning in network
Behind the direction on side, the propagation problem of map network is equivalent to the monitoring problem of former network.On Undirected networks, if not considering mutually
For neighbours summit influence each other power it is variant if, (if variant, it is believed that be directed networkses) Optimal Supervisory Control and propagation
Problem is by with the same solution.
Based on above-mentioned idea, the present invention uses the method that similar SIR is propagated to construct connection group of the size for L.
In the case where network global information is unknown, realize that the purpose of information in infinitely great social networks is propagated or monitored to low-cost.
Embodiment 1：
The present embodiment obtains the structured data of topological network from social network information database.The structured data bag
Include：User's collection, the user concentrate the incidence relation between different user.In the present embodiment using Crescent City
Facebook Network data sets (N=63731).Data set preserves the various record informations of topological network, such as the network information
Multiple users are preserved in database, these users belong to user and collected, and have between all users in network information database
Incidence relation between any two be present in user, the user in network information database can by identity code (ID,
Identity) identify, the incidence relation between user is specially the friends to user according to topological network；
The topological network is expressed as by figure according to the structured data of the topological network.Figure includes described in the present embodiment：
1545686 company sides of two nodes are connected between 63731 nodes and 63731 nodes, the figure includes every
One node corresponds uniquely to a user of user's collection, and two users that incidence relation in the figure be present are corresponding
Node between be connected with a line；
Specific implementation step is as follows：
S.1 it is null set to initialize and activated node set；
S.2 a node is randomly choosed from above-mentioned figure as disseminator, and adds and has activated node set；
S.3 according to preset probable value v (βc≤ v≤1) when to selected node carry out side seepage flow processing, side seepage flow processing bag
Include：Every company side of the node is deleted with 1-v probability, retained with v probability.The company side of reservation is connected
Node be designated as having activated node.
S.4 one is randomly selected in node set has been activated never turns into the node of disseminator as new disseminator, root
Its adjacent node is S.3 activated according to step, and the node activated is added and has activated node set.
If S.5 having activated number of nodes reaches the size L pre-set, stopped process.Otherwise, step is returned to S.4.Until
Process when number of nodes reaches the quantitative value L pre-set that activated for having activated node set stops.
Table 1 is shown under different preset probable value v, βcValue is 0.009, reach propagation monitoring threshold value P >=
When 0.99, under different probability of spreading β, the connection group that the present embodiment is elected is as the number of nodes L values for propagating needs
(in Undirected networks, monitoring is of equal value with propagating).The P is in selected gather, at least one node falls into given letter
The probability of the huge group of UNICOM of breath.As can be seen that in the case where not knowing the information of global network, seldom section can be used completely
Point, efficiently realize global propagation and the monitoring network information.
The accompanying drawing 2 of the present embodiment is shown when pre-setting v=β=0.02,1-P and set sizes L relation.It can see
Go out, 1-P exponential decays with set sizes L growth, illustrate when set sizes are sufficiently large really can with close to 1 it is general
Rate propagates/monitor the network information.
Table 1
| β=0.012 | β=0.014 | β=0.016 | β=0.018 | β=0.020 | β=0.022 | β=0.024 | β=0.026 | β=0.028 | |
| V=0.02 | 34 | 20 | 14 | 10 | 8 | 7 | 6 | 5 | 5 |
| V=0.04 | 54 | 35 | 25 | 19 | 15 | 13 | 11 | 9 | 8 |
| V=0.06 | 61 | 39 | 29 | 23 | 19 | 16 | 13 | 12 | 10 |
| V=0.08 | 67 | 43 | 31 | 25 | 20 | 17 | 15 | 13 | 12 |
Embodiment 2：
The present embodiment produces artificial network by given node degree series using computer.The artificial network according to
The difference of degree series, including two kinds of network structure data：Random network (degree series are Poisson distribution) and scales-free network (degree
Sequence is distributed for power-law)；
The topological network is expressed as by figure according to the structured data of the topological network.Figure described in the present embodiment
Node scale N chooses following 19 kinds, and from small to large respectively 1000,2000,3000,4000,5000,6000,7000,
8000,9000,10000,20000,30000,40000,50000,60000,70000,80000,90000,100000.It is described
Each node that figure includes uniquely represents a user, is represented in the figure per a line and has the two of incidence relation
Individual user；
Specific implementation step is as follows：
S.1 it is null set to initialize and activated node set；
S.2 a node is randomly choosed from above-mentioned figure as disseminator；And add and activated node set；
S.3 according to preset probable value v (βc≤ v≤1) when to selected node carry out side seepage flow processing, the βcAccording to
The predetermined percolation threshold of structured data of the topological network.Side seepage flow processing includes：Every possessed the node
Even side is deleted with 1-v probability, is retained with v probability.The node that the company side of reservation is connected is designated as having activated section
Point, and add and activated node set.
S.4 one is randomly selected in node set has been activated never turns into the node of disseminator as new disseminator, root
Its adjacent node is activated according to step S3, and the node of activation is added and has activated node set.
If it is the natural number of non-zero, stopped process S.5 to have activated number of nodes to reach the size L, the L pre-set.
Otherwise, step is returned to S.4.
On random network, the present embodiment chooses v=β=0.12, βc=0.1, propagate monitoring threshold value P >=0.99 when
The impact of performance and network size N relation are as shown in Figure 3.With on scales-free network, the present embodiment choose v=β=0.05,
βc=0.045, propagate monitoring threshold value P >=0.99 when the impact of performance and network size N relation as shown in Figure 4.From figure
In as can be seen that when 1/N tends to 0, i.e., when network tends to infinity, huge group of UNICOM tends to one often in statistical significance
Number is (shown in subgraph).Meet P needed for algorithm proposed by the present invention>0.99 node number is almost constant, tends to one often
Number.The P is in selected gather, at least one node falls into the probability of the huge group of UNICOM of given information.
Claims (9)
1. a kind of low-cost is propagated or the method for the monitoring network information, including：The topology data of network is expressed as figure；Institute
Stating figure includes N number of node, and each node corresponds uniquely to a user in the network；The figure also includes the net
Any two has the company side being connected between two nodes corresponding to the user of incidence relation in network；Wherein N is non-zero
Natural number；Given probability of spreading β and propagate monitoring threshold value P condition, wherein, probability of spreading β spans are βc＜ β≤1,
The βcFor the predetermined percolation threshold of structured data according to the topological network, propagating monitoring threshold value P spans is
0≤P≤1；
Characterized in that, comprise the following steps that：
S.1, set initialization and activate node set Q as empty set；
S.2 a node, is randomly choosed from the figure as disseminator, and the node is added and has activated node set Q；
S.3, according to preset probable value v, to the step, S.2 selected node carries out side seepage flow processing so as to activate the node
Adjacent node, and by the adjacent node activated add activated node set Q；The v meets βc≤v≤1；
S.4 one, is randomly selected in node set Q has been activated never as disseminator node as new disseminator, according to
Step S.3 preset probable value v and according to step S.3 to carrying out the processing of side seepage flow as the node of new disseminator so as to swash
The adjacent node of the node living as new disseminator, and using as the neighbour activated of the node of new disseminator
Connect node addition and activate node set Q；
If process when number of nodes reaches the quantitative value L pre-set that activated S.5, activated in node set Q stops, its
Middle L is the non-zero natural number less than N；Otherwise, step is returned to S.4；The L user finally obtained believes as propagating or monitoring network
User's set of breath.
2. a kind of low-cost according to claim 1 is propagated or the method for the monitoring network information, it is characterised in that：The step
Suddenly S.3 in the side seepage flow processing procedure include：To the step every company side that S.2 selected node is possessed with 1-v's
Probability is deleted, and is retained with v probability；The adjacent node that the company side of reservation is connected is designated as having activated node.
3. a kind of low-cost according to claim 1 or 2 is propagated or the method for the monitoring network information, it is characterised in that：Institute
State step S.5 described in " the quantitative value L " pre-set acquisition process is as follows：Wide-scale distribution in the network is obtained first to believe
X huge groups of UNICOM of breath, then set a hunting zone for the number of nodes of activation for having activated node set Q
Section is [Lmin,Lmax], then dichotomizing search is carried out in the section, choose meet to propagate monitoring threshold value P minimum value make
For the quantitative value L pre-set, wherein the hunting zone section minimum value LminWith maximum LmaxIt is non-zero nature
Number, and Lmin<Lmax。
4. a kind of low-cost according to claim 3 is propagated or the method for the monitoring network information, it is characterised in that：It is described
" dichotomizing search " is carried out as follows：
(1) three variables a, b, c, are set, wherein a, b is respectively directed to the upper bound and the lower bound in hunting zone section, makes c=(a+b)/2；
Initialize a=Lmin, b=Lmax；
(2), each huge group of UNICOM in the X huge groups of UNICOM is operated as follows：
(2.1) c=(a+b)/2, is calculated, the user that size is c is acquired and gathers；
(2.2) if, the user that size caused by step (2.1) is c gather at least one user and fall into huge group of UNICOM,
Then think the Cheng Gongchuanbo monitoring network information once；
(3), after each described huge group of UNICOM completes the step (2), succeed propagate monitoring information
Total degree, if propagate monitoring success rateIf P ' >=P, b=c is made, a values are constant；If P '<
P, makes a=c, and b values are constant；
(4) if, b-a≤1, stopped process, obtain final b values, obtained b user as meet it is default propagate monitoring threshold value P
Optimal set size, make that " the quantitative value L " pre-set is equal to final b values；Otherwise, step (2) is returned to.
5. a kind of low-cost according to claim 3 is propagated or the method for the monitoring network information, it is characterised in that：" the X
X is the integer more than or equal to 100 in individual huge group of UNICOM ".
6. a kind of low-cost according to claim 5 is propagated or the method for the monitoring network information, it is characterised in that：The X
Value is：800th, one of 1000,5000,8000 or 10000.
7. a kind of low-cost according to claim 3 is propagated or the method for the monitoring network information, it is characterised in that：It is described huge
Group of big UNICOM includes participating in the customer group of information forwarding in true propagation, or carries out side seepage flow in a network and handle what is obtained
Huge group of UNICOM.
8. a kind of low-cost monitoring according to claim 1 or 2 and the method for promoting information propagation in social networks, it is special
It is described two that sign is that the incidence relation in " any two has the user of incidence relation in the network " includes
The friends of user.
9. a kind of low-cost monitoring according to claim 1 or 2 and the method for promoting information propagation in social networks, it is special
Sign is that the incidence relation in " any two has the user of incidence relation in the network " includes two users
Between relation between existing follower and the person of being concerned.
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| CN106022937A (en) * | 2016-05-27 | 2016-10-12 | 北京大学 | Deduction method of social network topological structure |
| CN106055627A (en) * | 2016-05-27 | 2016-10-26 | 西安电子科技大学 | Recognition method of key nodes of social network in topic field |
| US20170026332A1 (en) * | 2014-04-04 | 2017-01-26 | Carii, Inc. | Methods, systems, and computer-readable media for providing community-based information networks |
| CN106411904A (en) * | 2016-10-10 | 2017-02-15 | 华侨大学 | Network risk control method based on microstate prediction |
| CN106557985A (en) * | 2016-11-21 | 2017-04-05 | 云南大学 | A kind of social network information propagating source method for solving based on random walk |
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2017
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Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101901251A (en) * | 2010-06-28 | 2010-12-01 | 吉林大学 | Method for analyzing and recognizing complex network cluster structure based on markov process metastability |
| US20170026332A1 (en) * | 2014-04-04 | 2017-01-26 | Carii, Inc. | Methods, systems, and computer-readable media for providing community-based information networks |
| CN105528407A (en) * | 2015-12-04 | 2016-04-27 | 杭州师范大学 | Method and apparatus for obtaining L users having optimum communication influence |
| CN106022937A (en) * | 2016-05-27 | 2016-10-12 | 北京大学 | Deduction method of social network topological structure |
| CN106055627A (en) * | 2016-05-27 | 2016-10-26 | 西安电子科技大学 | Recognition method of key nodes of social network in topic field |
| CN106411904A (en) * | 2016-10-10 | 2017-02-15 | 华侨大学 | Network risk control method based on microstate prediction |
| CN106557985A (en) * | 2016-11-21 | 2017-04-05 | 云南大学 | A kind of social network information propagating source method for solving based on random walk |
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