CN103761271A - Community partitioning algorithm based on local density - Google Patents

Community partitioning algorithm based on local density Download PDF

Info

Publication number
CN103761271A
CN103761271A CN201410006332.0A CN201410006332A CN103761271A CN 103761271 A CN103761271 A CN 103761271A CN 201410006332 A CN201410006332 A CN 201410006332A CN 103761271 A CN103761271 A CN 103761271A
Authority
CN
China
Prior art keywords
corporations
algorithm
node
community
point
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.)
Pending
Application number
CN201410006332.0A
Other languages
Chinese (zh)
Inventor
马杰良
潘贞贞
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.)
Nanjing University of Information Science and Technology
Original Assignee
Nanjing University of Information Science and Technology
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 Nanjing University of Information Science and Technology filed Critical Nanjing University of Information Science and Technology
Priority to CN201410006332.0A priority Critical patent/CN103761271A/en
Publication of CN103761271A publication Critical patent/CN103761271A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/01—Social networking

Landscapes

  • Business, Economics & Management (AREA)
  • Engineering & Computer Science (AREA)
  • Primary Health Care (AREA)
  • Strategic Management (AREA)
  • Economics (AREA)
  • General Health & Medical Sciences (AREA)
  • Human Resources & Organizations (AREA)
  • Marketing (AREA)
  • Computing Systems (AREA)
  • Health & Medical Sciences (AREA)
  • Tourism & Hospitality (AREA)
  • Physics & Mathematics (AREA)
  • General Business, Economics & Management (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Information Retrieval, Db Structures And Fs Structures Therefor (AREA)

Abstract

A community partitioning algorithm based on local density includes algorithm description, algorithm detection and algorithm simulation. The steps of the algorithm include finding an initial community and an first-order neighbor set thereof, adding nodes into the community in a manner of all adding or single adding, making the community, finding nodes which belong to no community, calculating a community adding rate, adding into the community, submitting the dividing precision, partitioning nodes which are not partitioned correctly into the community, simulating the algorithm, and generating a visual image. The algorithm needs small amount of information, a method is simple, starting from whole information is not required, implement complexity is not required so that processing time of the algorithm is reduced, and the algorithm is finished with a detection algorithm and has the advantages of high efficiency, low complexity and high precision.

Description

Corporations' partitioning algorithm based on local consistency
Technical field
The invention belongs to the algorithm field of dividing corporations in complex network, be specifically related to a kind of local message that utilizes and complex network carried out to the corporations' partitioning algorithm based on local consistency of efficient corporations division.
Background technology
In reality, many systems and relation can be carried out abstract representation with complex network, complex network refers generally to the network that node is numerous, annexation is complicated, due to its flexible pervasive descriptive power, can be widely used in each scientific domain complication system is carried out to modeling and analysis, attract in recent years increasing people to study it.Along with the further investigation to network character, physical significance and mathematical characteristic at present, discovery can comprise a plurality of corporations in many complex networks, there is community structure, each corporations be one group have each other compared with large similarity and and between other corporations in its place complex network, have a node cluster of a great difference, that is to say, connection in each corporations between internal node is very tight, and connection between each corporation is relatively sparse; In each corporation, comprise a plurality of nodes, the line between node is called limit, and every limit has directivity, and every limit has its limit weights separately in its direction.Community discovery is to utilize the information of containing in graph topological structure from complex network, to parse its modular community structure, the further investigation of this problem contributes to study in a kind of mode of dividing and rule module, function and the evolution thereof of whole network, organizational principle, topological structure and the dynamics of understanding more exactly complication system, tool is of great significance.
In fact, researchist, in order to get the characteristic of network community structure clear, tests and studies finding the several different methods of community structure in network, to find effective algorithm, finds as far as possible community structure accurately with fewer block of information as far as possible.The discovery scheme of the Newman fast algorithm based on polymerization thought of take is example, its thought is: using each node in complex network as Yi Ge corporations, merge the Liang Ge corporations that make modularity functional value gain maximum, iterative computation, becomes Yi Ge great corporations until whole complex network merges successively.Whole computation process presents with dendrogram, when modularity function Q obtains maximal value, network is divided.The advantage of Newman fast algorithm is that computing velocity is fast, and total time complexity is 0(m (m+n)), wherein m is the limit number in network, n is nodes.Although Newman algorithm can be realized the community discovery in complex network, to have ignored and in complex network, had the features such as the direction on limit between node and weight, the accuracy rate that makes it carry out community discovery is lower.
Up to the present, researchist has also proposed other community discovery algorithms, comprise Zymography, optimal objective function algorithm, based on connecting limit density, betweenness, information center's degree, random walk etc., hierarchical clustering (Hierarchical Clustering) algorithm, W-H algorithm and GN algorithm that the figure in computer realm is cut apart in (Graph Partitioning) algorithm, social science are most representative methods.For example, some corporations' monitoring algorithms have been founded modularity Q and the optimization to Q, but this algorithm is very difficult for the information of obtaining whole network and quantity of information is larger.
Summary of the invention
For addressing the above problem, the invention provides a kind of corporations' partitioning algorithm based on local consistency, efficiently utilize local message that complex network is divided into corporations, break the whole up into parts and simplify the research to complex network, improve Study on Aging Hardening.
For achieving the above object, the invention provides following technical scheme:
Corporations' partitioning algorithm based on local consistency, is characterized in that: comprise that arthmetic statement, algorithm detect and algorithm simulating; Described arthmetic statement is that algorithm is expressed to complicated algorithm with simple language and mathematical formulae, and concrete grammar is:
(a) by concrete network abstract be figure G=(V, the E that a pointed set V and limit collection E form), the node of network is n; If summit with
Figure 227921DEST_PATH_IMAGE002
between have limit to be connected,
Figure 860284DEST_PATH_IMAGE003
, otherwise ; By the nodal scheme of network , calculate LAN that each node and single order adjoint point thereof form; ?
Figure 873874DEST_PATH_IMAGE006
in
Figure 679019DEST_PATH_IMAGE007
maximum point
Figure 466846DEST_PATH_IMAGE001
lAN be made as the initial S of corporations;
(b) by the single order adjoint point collection of the initial S of corporations in whole points join in S, add
Figure 98871DEST_PATH_IMAGE008
if consistency afterwards
Figure 719208DEST_PATH_IMAGE006
will
Figure 123775DEST_PATH_IMAGE008
all add, otherwise optional
Figure 83641DEST_PATH_IMAGE008
in 1 v, its adjoint point set is
Figure 797519DEST_PATH_IMAGE009
if, the rate of joining the Youth League
Figure 577257DEST_PATH_IMAGE010
, during v can join bunch, the node satisfying condition is all joined in this bunch, form one new bunch
Figure 275261DEST_PATH_IMAGE011
, looking for
Figure 292896DEST_PATH_IMAGE011
neighbor node;
(c) repeating step (b), when
Figure 849779DEST_PATH_IMAGE012
time, Stop node adds; And the group at these places, be labeled as the C1 of corporations; Next the corporations looked for, the like mark;
(d) in residue, do not have in the node of mark, find out
Figure 428397DEST_PATH_IMAGE007
maximum point, repeating step (b)-(d);
(e) search the point that is not also classified as corporations, calculate the rate of joining the Youth League of each point
Figure 627297DEST_PATH_IMAGE013
, point is put into
Figure 358493DEST_PATH_IMAGE013
maximum corporations.
By foregoing description method, do not need to get down to Global Information, from partial points or group, by the mode of condensing, progressively expand the scope of corporations, thereby realize corporations, divide.
The method that algorithm detects is: in finding algorithm, there is no the correct node of dividing, propose to detect an index of corporations' dividing precision, make not have correct node division of dividing in correct corporations.
Wherein, the index of detection corporations dividing precision is that average internal connects
Figure 164906DEST_PATH_IMAGE014
;
Figure 919235DEST_PATH_IMAGE014
larger, the inner connection of corporations of division is tightr, and outside connection is more sparse, shows that the corporations that divide are better; In corporations, the inside of any connects
Figure 984143DEST_PATH_IMAGE015
be less than at 0.5 o'clock, recalculate this point
Figure 822042DEST_PATH_IMAGE013
, and it is put into
Figure 986308DEST_PATH_IMAGE013
in maximum corporations.
In network, can there are some relatively points (the identical points of company's limit number of He Liangge corporations) of contradictions, these may be put to wrong division like this, the inside by calculation level connect can check post whether by wrong division.
As preferably, algorithm simulating by algorithm simulating, utilizes the visualized graphs of Complex Networks Analysis Software Create evaluation algorithms by MATLAB.
A kind of corporations' partitioning algorithm based on local consistency provided by the invention is compared with traditional corporations' partitioning algorithm, the quantity of information needing is little, method is simple, do not need to get down to Global Information, the complexity of implementing is low, thereby reduced the processing time of algorithm, and algorithm finishes there is detection algorithm, so the beneficial effect that the present invention has is: ageing height, complexity is low, degree of accuracy is high.
Accompanying drawing explanation
Fig. 1, algorithm flow chart of the present invention;
Fig. 2, utilize the visual figure after the present invention divides network corporations of karate club;
Fig. 3, utilize the visual figure after the present invention divides dolphin net corporations;
Fig. 4, utilize the visual figure after the present invention divides football net corporations.
Embodiment
Below with reference to specific embodiment, technical scheme provided by the invention is elaborated, should understands following embodiment and only for the present invention is described, is not used in and limits the scope of the invention.
If Fig. 1 is algorithm flow chart of the present invention, by concrete network abstract be the figure G=(V, E) that a pointed set V and limit collection E form.The node of network is n, can be with an adjacency matrix
Figure 290250DEST_PATH_IMAGE016
represent.If summit with
Figure 84211DEST_PATH_IMAGE002
between have limit to be connected,
Figure 684956DEST_PATH_IMAGE003
, otherwise
Figure 459883DEST_PATH_IMAGE004
.Idiographic flow is as follows:
(1) by the nodal scheme of network
Figure 866594DEST_PATH_IMAGE005
, calculate LAN that each node and single order adjoint point thereof form
Figure 912041DEST_PATH_IMAGE007
; ?
Figure 683688DEST_PATH_IMAGE006
in maximum point
Figure 579149DEST_PATH_IMAGE001
lAN be made as the initial S of corporations.
(2) subsequently point is joined in group, has two kinds of methods:
Method one: integral body adds, by the single order adjoint point collection of S
Figure 246147DEST_PATH_IMAGE008
in whole points join in S, add
Figure 251012DEST_PATH_IMAGE008
if consistency afterwards
Figure 829892DEST_PATH_IMAGE006
will
Figure 516088DEST_PATH_IMAGE008
all add, otherwise forward method two to;
Method two: single adding, the single order adjoint point collection of establishing bunch S is
Figure 457499DEST_PATH_IMAGE008
, optional
Figure 882533DEST_PATH_IMAGE008
in 1 v, its adjoint point set is
Figure 807764DEST_PATH_IMAGE009
if,
Figure 94389DEST_PATH_IMAGE010
, during v can join bunch, the node satisfying condition is all joined in this bunch, form one new bunch
Figure 234514DEST_PATH_IMAGE011
, looking for neighbor node.
(3) repeat flow process (2), when
Figure 42644DEST_PATH_IMAGE012
time, Stop node adds.And the group at these places, be labeled as the C1 of corporations.Next the corporations looked for, the like mark.
(4) in residue, do not have in the node of mark, find out
Figure 70643DEST_PATH_IMAGE007
maximum point, repeats flow process (2)-(4).
(5) finally search the point that is not also classified as corporations, calculate the rate of joining the Youth League of each point
Figure 314542DEST_PATH_IMAGE013
, point is put into the rate of joining the Youth League
Figure 910740DEST_PATH_IMAGE013
maximum corporations.
More than for dividing the main flow process of corporations; After division completes, there is no the correct node of dividing in finding algorithm, propose to detect the index of corporations' dividing precision, the inside by calculation level connects; In corporations, the inside of any connects
Figure 544983DEST_PATH_IMAGE015
be less than at 0.5 o'clock, recalculate this point , and it is put into
Figure 458768DEST_PATH_IMAGE013
in maximum corporations., so just can be there is no correct node division of dividing in correct corporations; Finally by MATLAB by algorithm simulating, by Gephi, algorithm is applied in complex network, generate the visualized graphs of evaluation algorithms.
Be illustrated in figure 2 the visual figure utilizing after the present invention divides network corporations of karate club; Famous karate club network is widely used in corporations' division, and 70 centurial years of 20th century, it had 34 nodes for the initial stage, 78 limits.At viewing duration, between the club supervisor of karate and principal, with regard to whether increasing club tuition fee problem, each stand one's own ground by chance.Final karate club network is divided into two and take separately the corporations of club that the supervisor of club (node 1) and principal's (node 33) be leading nucleus.
Four that with node [9 31 33 34], are formed have been calculated.Calculate the neighbor node of this group, meeting the rate of joining the Youth League
Figure 147238DEST_PATH_IMAGE010
node join in these initial corporations, until algorithm stops.Then in remaining node, the node of degree of finding maximum is 1, and the group of its composition is five that with node [1 234 8], are formed.By above-mentioned same method, obtain its corporations.
Be illustrated in figure 3 the visual figure utilizing after the present invention divides dolphin net corporations; From 1994-2001, Lusseau has studied 62 dolphins that live in New Zealand Doubt ful Sound, by observing the contact situation between them, has built dolphin community network.At his viewing duration, along with leaving of a crucial dolphin, this colony has been divided into two microcommunities.Fig. 2 is the division result to this network with our algorithm.We have obtained 4 community structures, distinguish to some extent with 2 corporations of reality, and this is indicating differentiation result in the future to a certain extent.
In the process of dividing with this algorithm, there is a node 7 and divided by wrong because of the second situation.By detecting, recalculate node 7, and by its correct being divided in corporations.
Be illustrated in figure 4 the visual figure utilizing after the present invention divides football net corporations; In network, 115 nodes represent 115Zhi team, and 613 limits have represented 613 races.These teams are divided into some groups, and each group is comprised of 8～12Zhi team, and the match between the match Yao Bizujian team between interior team is many on the same group.Fig. 3 is the result that we divide, and divides altogether Liao12Ge corporations, with actual the same.
Use algorithm provided by the invention in the process of dividing, have a node 3 to be divided by wrong.This is that in these corporations, the inside of node 3 is connected to 0.25, very little because node [3 4 73 75] forms one four, so be the wrong node of dividing.Node 3 is recalculated, put under in correct corporations.
The disclosed technological means of the present invention program is not limited only to the disclosed technological means of above-mentioned embodiment, also comprises the technical scheme being comprised of above technical characterictic combination in any.

Claims (4)

1. the corporations' partitioning algorithm based on local consistency, is characterized in that: comprise that arthmetic statement, algorithm detect and algorithm simulating; Described arthmetic statement is that algorithm is expressed to complicated algorithm with simple language and mathematical formulae, and concrete grammar is:
(a) by concrete network abstract be figure G=(V, the E that a pointed set V and limit collection E form), the node of network is n; If summit
Figure 153770DEST_PATH_IMAGE001
with
Figure 205908DEST_PATH_IMAGE002
between have limit to be connected, , otherwise
Figure 865877DEST_PATH_IMAGE004
; By the nodal scheme of network
Figure 305473DEST_PATH_IMAGE005
, calculate LAN that each node and single order adjoint point thereof form; ?
Figure 290746DEST_PATH_IMAGE006
in
Figure 538188DEST_PATH_IMAGE007
maximum point
Figure 999125DEST_PATH_IMAGE001
lAN be made as the initial S of corporations;
(b) by the single order adjoint point collection of the initial S of corporations
Figure 52532DEST_PATH_IMAGE008
in whole points join in S, add
Figure 626733DEST_PATH_IMAGE008
if consistency afterwards
Figure 107393DEST_PATH_IMAGE006
will all add, otherwise optional in 1 v, its adjoint point set is
Figure 75852DEST_PATH_IMAGE009
if, the rate of joining the Youth League , during v can join bunch, the node satisfying condition is all joined in this bunch, form one new bunch
Figure 959680DEST_PATH_IMAGE011
, looking for
Figure 292572DEST_PATH_IMAGE011
neighbor node;
(c) repeating step (b), when
Figure 2014100063320100001DEST_PATH_IMAGE012
time, Stop node adds; And the group at these places, be labeled as the C1 of corporations; Next the corporations looked for, the like mark;
(d) in residue, do not have in the node of mark, find out
Figure 957210DEST_PATH_IMAGE007
maximum point, repeating step (b)-(d);
(e) search the point that is not also classified as corporations, calculate the rate of joining the Youth League of each point
Figure 435465DEST_PATH_IMAGE013
, point is put into
Figure 702498DEST_PATH_IMAGE013
maximum corporations.
2. a kind of corporations' partitioning algorithm based on local consistency according to claim 1, it is characterized in that: the method that described algorithm detects is: in finding algorithm, there is no the correct node of dividing, propose to detect the index of corporations' dividing precision, make not have correct node division of dividing in correct corporations.
3. a kind of corporations' partitioning algorithm based on local consistency according to claim 2, is characterized in that: the described index that detects corporations' dividing precision is that average internal connects ;
Figure 39118DEST_PATH_IMAGE014
larger, the inner connection of corporations of division is tightr, and outside connection is more sparse, shows that the corporations that divide are better; In corporations, the inside of any connects
Figure 485012DEST_PATH_IMAGE015
be less than at 0.5 o'clock, recalculate this point
Figure 177025DEST_PATH_IMAGE013
, and it is put into
Figure 914037DEST_PATH_IMAGE013
in maximum corporations.
4. a kind of corporations' partitioning algorithm based on local consistency according to claim 1, is characterized in that: described algorithm simulating by algorithm simulating, utilizes the visualized graphs of Complex Networks Analysis Software Create evaluation algorithms by MATLAB.
CN201410006332.0A 2014-01-07 2014-01-07 Community partitioning algorithm based on local density Pending CN103761271A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201410006332.0A CN103761271A (en) 2014-01-07 2014-01-07 Community partitioning algorithm based on local density

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201410006332.0A CN103761271A (en) 2014-01-07 2014-01-07 Community partitioning algorithm based on local density

Publications (1)

Publication Number Publication Date
CN103761271A true CN103761271A (en) 2014-04-30

Family

ID=50528508

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201410006332.0A Pending CN103761271A (en) 2014-01-07 2014-01-07 Community partitioning algorithm based on local density

Country Status (1)

Country Link
CN (1) CN103761271A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10572501B2 (en) 2015-12-28 2020-02-25 International Business Machines Corporation Steering graph mining algorithms applied to complex networks
CN111935748A (en) * 2020-08-18 2020-11-13 国网河南省电力公司信息通信公司 Virtual network resource allocation method with high reliability and load balance

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100185935A1 (en) * 2009-01-21 2010-07-22 Nec Laboratories America, Inc. Systems and methods for community detection
CN102779142A (en) * 2011-06-28 2012-11-14 安徽大学 Quick community discovery method based on community closeness

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100185935A1 (en) * 2009-01-21 2010-07-22 Nec Laboratories America, Inc. Systems and methods for community detection
CN102779142A (en) * 2011-06-28 2012-11-14 安徽大学 Quick community discovery method based on community closeness

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
幸后旺: "复杂网络社团结构划分算法研究", 《中国优秀硕士学位论文 基础科学辑》 *
熊站营: "基于增量和密度的动态网络社团检测算法", 《中国优秀硕士学位论文全文数据库 信息科技辑》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10572501B2 (en) 2015-12-28 2020-02-25 International Business Machines Corporation Steering graph mining algorithms applied to complex networks
CN111935748A (en) * 2020-08-18 2020-11-13 国网河南省电力公司信息通信公司 Virtual network resource allocation method with high reliability and load balance
CN111935748B (en) * 2020-08-18 2023-06-23 国网河南省电力公司信息通信公司 Virtual network resource allocation method with high reliability and load balance

Similar Documents

Publication Publication Date Title
CN102929942B (en) The overlapping community discovery method of a kind of community network based on integrated study
Yu et al. Geo-friends recommendation in gps-based cyber-physical social network
Li et al. Quantitative function for community detection
CN104102745B (en) Complex network community method for digging based on Local Minimum side
CN109919108A (en) Remote sensing images fast target detection method based on depth Hash auxiliary network
CN106557574B (en) Target address matching method and system based on tree structure
CN107103754A (en) A kind of road traffic condition Forecasting Methodology and system
CN103455610B (en) Network community detecting method based on multi-objective memetic computation
CN104679818A (en) Video keyframe extracting method and video keyframe extracting system
CN106600065A (en) Individualized learning path extraction and jointing method and system based on directed hypergraph
CN109921938A (en) Fault detection method under a kind of cloud computing environment
CN106203494A (en) A kind of parallelization clustering method calculated based on internal memory
CN105320764A (en) 3D model retrieval method and 3D model retrieval apparatus based on slow increment features
CN104992259A (en) Complex network survivability and key node analysis method based on community structure
CN110765582A (en) Self-organization center K-means microgrid scene division method based on Markov chain
CN103617163A (en) Quick target association method based on clustering analysis
CN102819611A (en) Local community digging method of complicated network
CN102496033B (en) Image SIFT feature matching method based on MR computation framework
CN110716998B (en) Fine scale population data spatialization method
CN102364490A (en) Automatic synchronization recognition method based on hierarchical analyzing model
CN108536825A (en) A method of whether identification source of houses data repeat
CN103761271A (en) Community partitioning algorithm based on local density
CN104657442A (en) Multi-target community discovering method based on local searching
CN110442800A (en) A kind of semi-supervised community discovery method of aggregators attribute and graph structure
He et al. Genetic algorithm with ensemble learning for detecting community structure in complex networks

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20140430

RJ01 Rejection of invention patent application after publication