CN110300016B - Network information diffusion source inference method based on differential pre-solution set - Google Patents

Network information diffusion source inference method based on differential pre-solution set Download PDF

Info

Publication number
CN110300016B
CN110300016B CN201910397763.7A CN201910397763A CN110300016B CN 110300016 B CN110300016 B CN 110300016B CN 201910397763 A CN201910397763 A CN 201910397763A CN 110300016 B CN110300016 B CN 110300016B
Authority
CN
China
Prior art keywords
node
diffusion
source
information
network
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.)
Active
Application number
CN201910397763.7A
Other languages
Chinese (zh)
Other versions
CN110300016A (en
Inventor
周川
胡玥
谭建龙
郭莉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Institute of Information Engineering of CAS
Original Assignee
Institute of Information Engineering of CAS
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Institute of Information Engineering of CAS filed Critical Institute of Information Engineering of CAS
Priority to CN201910397763.7A priority Critical patent/CN110300016B/en
Publication of CN110300016A publication Critical patent/CN110300016A/en
Application granted granted Critical
Publication of CN110300016B publication Critical patent/CN110300016B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/142—Network analysis or design using statistical or mathematical methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network

Landscapes

  • Engineering & Computer Science (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Physics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Pure & Applied Mathematics (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Algebra (AREA)
  • Information Retrieval, Db Structures And Fs Structures Therefor (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention provides a network information diffusion source inference method based on a differential pre-solution set, which belongs to the field of information technology processing and adopts G ═ V, E to represent the connection between network nodesWherein V represents a network node set, E represents a network edge set, a difference pre-solution set S is selected from the network node set, diffusion source characteristics are established, cascade information is collected, and the modulus I of an index set is judgedcIf the size of the node I is larger than a preset value, extracting a feature vector of the cascade C, adjusting the diffusion source feature of each node V belonging to V, calculating norms of all the nodes V belonging to V one by one, finding the node with the minimum norm and deducing the node as a source. The method can be used for actively optimizing and selecting the data source, so that the quality of input data is improved, and the accuracy of source inference is greatly improved.

Description

Network information diffusion source inference method based on differential pre-solution set
Technical Field
The invention relates to the field of information technology processing, in particular to a network information diffusion source inference method based on a differential pre-solution set.
Background
An important characteristic of the complex network is that the information can be spread in a cascading manner, and the rapid and explosive diffusion of the information is realized. The inference of the source of network information diffusion (hereinafter referred to as "source inference") aims to infer the initial node of diffusion according to the observed partial diffusion cascade information (such as partial node information participating in the information diffusion and the participation time thereof, and the like), i.e. to find out who initiated the diffusion originally. The technology can be widely applied to public opinion confrontation, hidden danger elimination and other aspects, such as rumor disseminator discovery on a social network, Trojan horse spread source detection in a computer network, infectious disease transmission source inference among people and the like.
The existing source inference method is generally carried out under the assumption of a certain random dynamic model. The most widely used models here are the SI model, SIS model and SIR model [1], where S represents the susceptable susceptibility state, I represents the infested infected state and R represents the recovered immune state. A representative source inference method is as follows:
heuristic algorithms based on centrality measures [2 ]. The method selects the node with higher centrality measurement as the source node. The most representative centrality measure here is the centrality of compactness, and the intuitive idea is that the smaller the sum of the distances from a node to all infected nodes is, the more likely this node is to be the source of the spread. The method is heuristic and does not consider the information of the time of participation of the nodes in diffusion and the like.
Optimization method based on maximum likelihood [3 ]. The method defines the source inference problem as finding the node that maximizes the likelihood of the observed partial diffusion cascade occurring and treats that node as the source node. The method utilizes the basic idea of maximum likelihood and provides a benchmark optimization framework for the source inference problem. The method [3] converts the optimization problem into the counting problem of the generation path by using the memoryless of exponential distribution and the annullessness of a tree structure.
In addition, the Monte Carlo sampling method [4], the BP algorithm [5], the DMP algorithm [6], the spectrum method [7] and other methods provide different solving technical schemes for deducing problems from the source from different modeling perspectives.
In the prior art, input data (i.e., the partial cascade information) faced by the source inference is passively acquired, and no optimization selection is performed on the source of the data, and the improvement of the source inference performance is usually greatly restricted by the quality of the data. The existing methods can be called as pure 'after-the-fact' methods, namely after cascade expansion is carried out, according to observable and passively taken part of diffusion cascade information, a metric or a model is designed to search a source.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a network information diffusion source inference method based on a differential pre-solution set, which can be used for actively optimizing and selecting data sources, improving the quality of input data and greatly improving the accuracy of source inference.
In order to solve the technical problems, the invention adopts the following technical scheme:
a network information diffusion source inference method based on a differential pre-solution set comprises the following steps:
representing the connection relation between the network nodes by G ═ V, E, wherein V represents a network node set, and E represents a network edge set; selecting a subset from V as a differential pre-solution set S, where S: is ═ s1,…,sKIs G inThe first K nodes with the highest degree;
estimating the diffusion time t (V, S) of each node V ∈ V to all nodes in S according to the difference pre-solution set Sk) Where K is 1,2, …, K, establishing a diffusion source signature based on the diffusion time
Figure GDA0002635416950000021
For a first order concatenated data set
Figure GDA0002635416950000022
Each data ClCs is expressed as
Figure GDA00026354169500000214
ulIs ClThe originating node of (a) is,
Figure GDA0002635416950000024
is ClV. oflIs ulThe first-order child node of (1),
Figure GDA0002635416950000025
representing a node vlParticipate in ClThe time of (a) is,
Figure GDA0002635416950000026
representing a node vlDoes not participate in ClOr participated in but not observed; collecting cascade information by differential pre-solution set S
Figure GDA0002635416950000027
Wherein
Figure GDA0002635416950000028
Representing a node skThe time of participation in the cascade C,
Figure GDA0002635416950000029
representing a node skDoes not participate in cascade C;
set of judgment indicators
Figure GDA00026354169500000210
Modulo IcIf the magnitude of | is greater than a preset value, extracting the feature vector of the cascade C
Figure GDA00026354169500000211
Wherein k is more than or equal to 11<k2<…<kI≤K；
According to index set ICThe diffusion source characteristics of each node V E V are adjusted according to the information of the node V E V, and the adjusted diffusion source characteristics
Figure GDA00026354169500000212
Calculating the norm | h' (V) -h (C) | one by one for all the nodes V e V2And finding the node with the minimum norm is inferred as the source.
Further, the diffusion time t (v, S) of all the nodes v to S is estimated by using a diffusion modelk) The diffusion model is: each directed edge E ═ u in the information edge E1,u2) The time of diffusion obeys exponential distribution Exp (lambda)e) If the log information is propagated through the history on a certain edge to be an empty set, removing the edge from the E; if log information is propagated through the history on an edge little enough, then the average of the parameters on other edges is used to estimate λ on that edgee。
Further, said λeCascading data sets according to a first order
Figure GDA00026354169500000213
Is estimated by adding/averaging/inverting the information in (1).
Further, the diffusion time t (v, s) is estimatedk) The method comprises simulating the set number of times from v to skThe desired diffusion time was then averaged.
Further, if modulo | IcIf the | is less than the preset value, the source inference is directly carried out by adopting the traditional method, wherein the traditional method comprises a heuristic algorithm based on centrality measurement, an optimization method based on maximum likelihood and Monte Carlo samplingMethod, BP algorithm, DMP algorithm, spectral method.
Further, the preset value is 3, but the value is not limited, and is set according to actual needs.
A system for network information diffusion source inference based on a differential pre-solution set includes a memory storing a computer program configured to be executed by the processor to perform the steps of any of the above methods and a processor.
A computer-readable storage medium comprising a computer program which, when executed by a processor of a server, causes the server to perform the steps of any of the methods described above.
The method actively optimizes and selects the data source, extracts the characteristics of each node in the network as a diffusion source by introducing the concept of differential pre-solution set, converts the source inference problem into the characteristic matching problem, reduces the complexity and greatly improves the source inference precision. This is a method combining "a priori" and "a posteriori"; before the cascade expansion distribution, optimizing and selecting some nodes to collect information in real time; after the cascade diffusion, the diffusion source inference is carried out by utilizing the collected information.
Drawings
FIG. 1 is a flow chart of a method for inferring a network information diffusion source based on a differential pre-solution set.
Detailed Description
In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.
The method aims to establish a novel diffusion source inference whole scheme for the network G ═ (V, E). Here, V denotes a network node set, and E denotes a network edge set, which is used to describe the connection relationship between nodes. Without loss of generality, it is assumed that G is a directed fully connected graph, and the direction of an edge represents the direction of information diffusion. In addition to the network topology, a certain amount of first-order concatenated data sets are required
Figure GDA0002635416950000035
Training the model as input, concatenating data C for each first orderlCan be expressed as
Figure GDA0002635416950000031
Wherein v islIs ClThe originating node of (a) is,
Figure GDA0002635416950000032
is ClV. oflIs ulThe first-order child node of (1),
Figure GDA0002635416950000033
representing a node vlParticipate in ClTime of (d). If it is
Figure GDA0002635416950000034
Representing a node vlDoes not participate in ClOr participated in but not observed. The method comprises two modules of diffusion source feature extraction and diffusion source inference, wherein the diffusion source feature extraction is an offline module, and the diffusion source inference is an online module. The specific implementation steps of the diffusion source feature extraction are as follows:
1. selecting a set of differential pre-solutions
The difference pre-solution set S is a subset of the node set V, and the size K < | V |, where the value K can be adjusted according to budget and demand (generally, the larger the value K, the higher the accuracy of the model, but the corresponding computational complexity will also increase). The nodes in the differential pre-solution set S are nodes to be observed in real time, and the time of participating in cascade diffusion needs to be recorded. In order to make the differential pre-solution set S collect the diffusion information as much as possible and ensure the validity of the information, the differential pre-solution set S is taken here: is ═ s1,…,sKAnd the nodes are the first K nodes with the highest incoming degree in the network G (V, E).
2. Establishing a diffuse source signature for each node
This step establishes the diffuse source signature for each node V e V, according to the differential pre-solution set S selected in the previous step.
1) Suppose information follows each directed edge e ═ u1,u2) The time of diffusion obeys exponential distribution Exp (lambda)e) Here λ iseData sets can be cascaded according to a first order
Figure GDA00026354169500000411
Is estimated by adding/averaging/inverting the information in (1). If the log information is propagated through the history on a certain edge as an empty set, the edge can be removed from the E; if log information is propagated particularly rarely through the history on a certain edge, the average of the parameters on other edges can be used to estimate λ on that edgee。
2) Estimating the diffusion time t (v, S) of all the nodes from the node v to the node S by using the diffusion model obtained in the step 1)k) (where K is 1,2, …, K). Specifically, the simulation is performed 100 times from v to skThe required diffusion time, then the 100 results are averaged and noted as t (v, s)k)。
3) So far, the diffusion source characteristics h (v) of the node v are the following K-dimensional vectors
Figure GDA0002635416950000041
4) As with 2) and 3) establish a diffuse source signature for each node in V.
After the on-line module for extracting the characteristics of the diffusion source is prepared, the on-line module for deducing the diffusion source can be started. For a complete cascade C of in-line diffusions, the goal is to solve the set S: is ═ s1,…,sKActively collect the cascade information and further deduce its diffusion origin. This collected concatenation information is noted as
Figure GDA0002635416950000042
Wherein
Figure GDA0002635416950000043
Representing a node skTime to participate in cascade C if
Figure GDA0002635416950000044
Representing a node skDoes not participate in cascade C. After the diffusion source feature extraction, the specific implementation steps of the diffusion source inference are as follows:
3. extraction cascade
Figure GDA0002635416950000045
Is characterized by
Introduction mark
Figure GDA0002635416950000046
Index set ICIndicating which nodes in the differential pre-solution set S are participating in the cascade C. If set ICIs small in modulus (ratio | I)C|<3) Then the method is skipped from the following steps and the used method (such as the heuristic algorithm based on centrality measurement [2] is directly adopted]) And performing source inference. Otherwise (| I)C| ≧ 3), the following steps are continued. It is noted here that if the cascade is small, generally, the cascade does not cause much harm, so the significance of performing source inference on the cascade is not large; if the cascade is larger, the selection mode of the differential pre-solution set S is combined, and the set ICGenerally, the size is larger, and the method can be used in the field and has the effect naturally. Next assume | ICI is not less than 3 and does not mark IC＝{k1,k2,…,kIWherein 1 is less than or equal to k1<k2<…<kIK is less than or equal to K. Defining a cascade
Figure GDA0002635416950000047
Figure GDA0002635416950000048
The feature vector h (C) of (2) is:
Figure GDA0002635416950000049
4. cascade connection
Figure GDA00026354169500000410
Source inference of
According to the above ICIn this step, the characteristics of each node in V obtained in step 2 above are first adjusted. Taking the node V epsilon V, the adjusted diffusion source characteristic h' (V) is the following vector in dimension I-1:
Figure GDA0002635416950000051
it is because of the way h' (v) is defined that S is defined as the differential pre-solution set in step 1. Next, for all the nodes V e V, calculate | h' (V) -h (C) | one by one2. The smaller the norm is, the more likely the corresponding v node is to be a source of diffusion, and the node with the minimum norm is inferred as the source.
To verify the effectiveness of the proposed method, a simulation experiment was performed on a social network G with 114 nodes, 613 edges. First using a stochastic model (where all λ's are assumed to bee1) generating a first order concatenated data set
Figure GDA0002635416950000052
Then, according to the training data, establishing a feature h (v) for each node v in the social network G through the above steps 1 and 2, wherein the parameter K involved is an adjusted parameter, which is 5,10,15,20,25, 30. Next, a model test data set is generated as
Figure GDA0002635416950000053
Where n is 1,2, …,1000 and each cascade C(n)The sources of (a) are all randomly chosen. And performing source inference on the 1000 cascade data of the source to be inferred through the steps 3 and 4 respectively. To evaluate the effectiveness of the proposed method, inference accuracy (the ratio of the source inference correct data in 1000 test data) and error distance (the average distance between the inference source and the true source over G, i.e. the average hop number) are used. It is clear that the higher the inference accuracy the better, the lower the error distance the better. The results of the experiment are as follows:
size of differential pre-solution set K 5 10 15 20 25 30
Rate of accuracy of inference 4.8％ 8.8％ 11.4％ 13.0％ 13.3％ 13.9％
Distance of error 1.93 1.67 1.58 1.52 1.48 1.46
The experimental result shows that with the increase of the difference pre-solution set K, the performance of the source inference method is better and better, and compared with the inference accuracy rate which is often less than 10% of the traditional source inference method, the result of the method is greatly improved.
The invention introduces the following documents:
[1]Wenyu Zang,Peng Zhang,Chuan Zhou,and Li Guo.Locating Multiple Sources in Social Networks under the SIR Model:A Divide-and-Conquer Approach.Journal of Computational Science,Vol.10,September 2015,Pages 278-287.
[2]Comin Henrique,Fontoura Costa,and Luciano.Identifying the starting point of a spreading process in complex networks.Physical Review E,84(5):056105,2011.
[3]Shah Devavrat and Zaman Tauhid.Rumors in a network:Who’s the culprit？IEEE Transactions on Information Theory,57(8):5163–5181,2011.
[4]Ameya Agaskar and Yue Lu.A fast monte carlo algorithm for source locating on graphs.In SPIE,2013.
[5]Fabrizio Altarelli,Alfredo Braunstein,and Luca Dall Asta.Bayesian inference of epidemics on networks via belief propagation.In arXiv,2013.
[6]Lokhov Andrey,M′ezard Marc,Ohta Hiroki,and Zdeborova′Lenka.Inferring the origin of an epidemy with dynamic message-passing algorithm.arXiv preprint arXiv:1303.5315,2013.
[7]Fioriti Vincenzo and Chinnici Marta.Predicting the sources of an outbreak with a spectral technique.arXiv preprint arXiv:1211.2333,2012.
the above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person skilled in the art can modify the technical solution of the present invention or substitute the same without departing from the spirit and scope of the present invention, and the scope of the present invention should be determined by the claims.

Claims (8)

1. A network information diffusion source inference method based on a differential pre-solution set comprises the following steps:
denoting G ═ V, E connection between network nodesWherein V represents a set of network nodes and E represents a set of network edges; selecting a subset from V as a differential pre-solution set S, where S: is ═ s1,…,sKThe nodes are the first K nodes with the highest incoming degree in G;
estimating the diffusion time t (V, S) of each node V ∈ V to all nodes in S according to the difference pre-solution set Sk) Where K is 1,2, …, K, establishing a diffusion source signature based on the diffusion time
Figure FDA0002640491770000011
For a first order concatenated data set
Figure FDA0002640491770000012
Each data ClCs is expressed as
Figure FDA0002640491770000013
ulIs ClThe originating node of (a) is,
Figure FDA0002640491770000014
is ClV. oflIs ulThe first-order child node of (1),
Figure FDA0002640491770000015
representing a node vlParticipate in ClThe time of (a) is,
Figure FDA0002640491770000016
representing a node vlDoes not participate in ClOr participated in but not observed; collecting cascade information by differential pre-solution set S
Figure FDA0002640491770000017
Wherein
Figure FDA0002640491770000018
Representing a node skThe time of participation in the cascade C,
Figure FDA0002640491770000019
representing a node skDoes not participate in cascade C;
set of judgment indicators
Figure FDA00026404917700000110
Modulo IcIf the magnitude of | is greater than a preset value, extracting the feature vector of the cascade C
Figure FDA00026404917700000111
Wherein k is more than or equal to 11<k2<…<kI≤K；
According to index set ICThe diffusion source characteristics of each node V E V are adjusted according to the information of the node V E V, and the adjusted diffusion source characteristics
Figure FDA00026404917700000112
Calculating the norm | h' (V) -h (C) | one by one for all the nodes V e V2And finding the node with the minimum norm is inferred as the source.
2. The method of claim 1, wherein the diffusion time t (v, s) of all of nodes v to s is estimated using a diffusion modelk) The diffusion model is: each directed edge E ═ u in the information edge E1,u2) The time of diffusion obeys exponential distribution Exp (lambda)e) If the log information is propagated through the history on an edge as an empty set, the edge is removed from E.
3. The method of claim 2, wherein λ iseCascading data sets according to a first order
Figure FDA00026404917700000113
Is estimated by adding/averaging/inverting the information in (1).
4. The method of claim 1, wherein the diffusion time t (v, s) is estimatedk) The method comprises simulating the set number of times from v to skThe desired diffusion time was then averaged.
5. The method of claim 1, wherein if modulo IcIf the | is less than the preset value, the source is deduced directly by adopting a traditional method, wherein the traditional method comprises a heuristic algorithm based on centrality measurement, an optimization method based on maximum likelihood, a Monte Carlo sampling method, a BP algorithm, a DMP algorithm and a spectrum method.
6. The method of claim 1, wherein the predetermined value is 3.
7. A system for inference of network information diffusion sources based on differential pre-solution set, comprising a memory and a processor, wherein the memory stores a computer program configured to be executed by the processor for performing the steps of the method according to any of the preceding claims 1 to 6.
8. A computer-readable storage medium, comprising a computer program which, when executed by a processor of a server, causes the server to perform the steps of the method of any of claims 1-6.
CN201910397763.7A 2019-05-14 2019-05-14 Network information diffusion source inference method based on differential pre-solution set Active CN110300016B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910397763.7A CN110300016B (en) 2019-05-14 2019-05-14 Network information diffusion source inference method based on differential pre-solution set

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910397763.7A CN110300016B (en) 2019-05-14 2019-05-14 Network information diffusion source inference method based on differential pre-solution set

Publications (2)

Publication Number Publication Date
CN110300016A CN110300016A (en) 2019-10-01
CN110300016B true CN110300016B (en) 2020-12-04

Family

ID=68026837

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910397763.7A Active CN110300016B (en) 2019-05-14 2019-05-14 Network information diffusion source inference method based on differential pre-solution set

Country Status (1)

Country Link
CN (1) CN110300016B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106972952A (en) * 2017-02-28 2017-07-21 浙江工业大学 A kind of Information Communication leader's Node extraction method based on internet pricing correlation
CN106992966A (en) * 2017-02-28 2017-07-28 浙江工业大学 A kind of spreading network information implementation method for true and false message
CN108334953A (en) * 2018-01-09 2018-07-27 浙江工业大学 One kind being based on the newer social networks degree of belief learning method of weight

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106972952A (en) * 2017-02-28 2017-07-21 浙江工业大学 A kind of Information Communication leader's Node extraction method based on internet pricing correlation
CN106992966A (en) * 2017-02-28 2017-07-28 浙江工业大学 A kind of spreading network information implementation method for true and false message
CN108334953A (en) * 2018-01-09 2018-07-27 浙江工业大学 One kind being based on the newer social networks degree of belief learning method of weight

Also Published As

Publication number Publication date
CN110300016A (en) 2019-10-01

Similar Documents

Publication Publication Date Title
Li et al. Federated recommendation system via differential privacy
CN111222029B (en) Method for selecting key nodes in network public opinion information dissemination
CN106972952B (en) Information propagation leader node extraction method based on network degree correlation
CN113422695B (en) Optimization method for improving robustness of topological structure of Internet of things
CN108122168A (en) Seed node screening technique and device in social activity network
CN107784327A (en) A kind of personalized community discovery method based on GN
CN111915294A (en) Safety, privacy protection and tradable distributed machine learning framework based on block chain technology
US20140095616A1 (en) Method and system for sampling online social networks
CN107566249A (en) A kind of method for training the model for predicting social network user forwarding message
CN107222410B (en) Method, device, terminal and computer readable storage medium for link prediction
CN110300016B (en) Network information diffusion source inference method based on differential pre-solution set
US20190197633A1 (en) Social media account filtering method and apparatus
CN110247805A (en) A kind of method and device for propagating key node based on the identification that K shell decomposes
Kanda et al. Estimation of data propagation time on the bitcoin network
CN109547265A (en) Complex network local immunity method and system based on random walk sampling
Zhang et al. Glasu: A communication-efficient algorithm for federated learning with vertically distributed graph data
CN110362754B (en) Online social network information source detection method based on reinforcement learning
Lawrence et al. Maximum likelihood estimation of internal network link delay distributions using multicast measurements
Clegg et al. Likelihood-based assessment of dynamic networks
Krishnamurthy et al. Segregation in social networks: Markov bridge models and estimation
Nicola et al. Efficient importance sampling heuristics for the simulation of population overflow in Jackson networks
CN110738418A (en) Detection method of weakly connected overlapping communities
CN116032828B (en) Medium number centrality approximate calculation method and device
CN112579831B (en) Network community discovery method, device and storage medium based on SimRank global matrix smooth convergence
CN115442243B (en) Sequential network node centrality evaluation method and device based on sequential path tree

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant