CN106844500A - A kind of k core truss community models and decomposition, searching algorithm - Google Patents
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Abstract
The invention provides a kind of k core truss community models, including figure G=(V, E), the subgraph meets：The degree of each edge e >=α * k or side e are comprised in 2 triangles of k；For scheme G arbitrary node u, its core value core (u)=max k | u ∈ Vk‑core}；For figure G in any limit e, its trussness (beam value) λ (e)=max k | e ∈ Ek‑truss}；For any limit e in figure G, its maximal degree δ (e)=min (core (u), core (v))；Wherein, side e=(u, v), the degree of node u is deg (u)=| { v | (u, v) ∈ E } |, and the degree of side e is d (e)=min { deg (u), deg (v) }, the maximal degree for scheming G interior joints is dmax, parameter alpha>0, k >=3.The present invention can comprehensively be excavated to the cohesion subgraph in community model.
Description
Technical field
The invention belongs to scheme the social digging technology neck with community network, more particularly to a kind of k-core-truss communities mould
Type and decomposition, searching algorithm.
Background technology
With the fast development of science and technology, all trades and professions in society all accumulate and acquire substantial amounts of diagram data, example
Such as social graph, the network topology of internet, bank credit network, the protein Internet, highway in online social networks
Transportation network, wireless sensor network, communication network and intelligent grid etc..These diagram datas have two it is more significant
Characteristic：One is the in large scale of them, and the number on summit is all often ten million or even 1,000,000,000 ranks in figure, such as social networks
Facebook collection of illustrative plates, Tencent QQ network and Sina weibo collection of illustrative plates etc.；Two is often all exist in these diagram datas between summit closely
Connected cohesion subgraph (cohesive subgraph) structure.
In recent years, the extensive concern of academia and industrial quarters is caused to the community mining problem in figure and social networks.
In community mining problem, most research work is only devoted to detecting the community structure in artwork.However, much applying
In scene, we concern and find out the community structure comprising query node.For example, in a social networks, we will look into
Community structure where asking certain or several users, and then understand their common interest hobby, or group activity etc.；Again
Such as in telephone communication network, we will inquire about the community that a user is closely connected with it, and then understand its society
Meeting relational network, this application assists in police criminal detection, hits gang crime, terroristic organization etc..These applications are required for
Solve the problems, such as the community search for one or more query node for giving.
On the community search of figure, mainly include two kinds of representational models, k- cores (k-core) and k-truss.k-
The concept of core is proposed first by Seidman.K-core is an induced subgraph, and the degree on the summit in the subgraph is both greater than
Or equal to k, and the subgraph is the clique for possessing this property.In order to solve the k-core resolution problems of big diagram data,
Vladimir and Matjaz take the lead in proposing a linear time algorithm.The algorithm minimum summit of the deletion degree from figure successively,
And summit is organized using a data structure similar to bucket sort, so as to realize that quick k-core is calculated.The algorithm is first
The relatively low summit of core numbers was found before this, and core numbers summit higher was then found successively.Just because of K-core is primarily upon figure
Middle number of degrees node higher, often ignores that some number of degrees are relatively low but the related community in reality.
Relative to k-core, k-truss is a newer concept, and this concept is proposed first by Cohen.Equally
, k-truss is also an induced subgraph, and any a line in the subgraph is all comprised at least in k-2 triangle, and should
Subgraph is the clique for possessing this property.A maximum k- sides connected subgraph also induced subgraph, in the subgraph
All at least there is the disjoint path in k bars side in any two summit, and the subgraph is the clique for possessing this property.It is worth
It is noted that a k-truss is (k-1)-core, otherwise not necessarily set up.As can be seen here, k-truss is a kind of essence
The k-core structures of refining.However, from unlike k-core, the definition of k-truss is the triangle formed based on summit in figure
Shape structure.Therefore, the network (such as bipartite graph or approximate bipartite graph) more rare for those triangles, this definition is not
Properly.Because the structure of cohesion subgraph may still be present in the rare network of this triangle.But, according to k-truss
Definition, we cannot have found this structure, this be k-truss definition a main defect.
The content of the invention
The embodiment of the present invention provides a kind of k-core-truss community models, it is intended to solve k-core and k- in the prior art
Truss models can not comprehensively excavate the technical problem of cohesion subgraph.
The embodiment of the present invention is achieved in that a kind of k-core-truss community models, including one it is undirected, without weight graph
G=(V, E), has a clique in G is schemed, and the subgraph meets：The degree of each edge e >=α * k or side e are comprised in
In k-2 triangle；
For scheme G arbitrary node u, its core value core (u)=max k | u ∈ Vk-core, wherein Vk-coreFor in figure G
K-core communities；
For figure G in any limit e, its trussness λ (e)=max k | e ∈ Ek-truss, wherein Ek-trussFor in figure G
K-truss communities；
For any limit e in figure G, its maximal degree δ (e)=min (core (u), core (v))；
Wherein, the degree of side e=(u, v), node u is deg (u)=| { v | (u, v) ∈ E } |, and the degree of side e is d (e)=min
{ deg (u), deg (v) }, the maximal degree for scheming G interior joints is dmax, parameter alpha>0, k >=3.
Preferably, as α * k>dmaxWhen, the k-core-truss community models are k-truss models.
Preferably, as α * k≤(k-1), the k-core-truss community models are α * k-core models.
Preferably, as α=1/k, whole figure G is k-core-truss communities.
Embodiments of the invention also provide a kind of k-core-truss community models decomposition algorithm, comprise the following steps：
Calculate and record all nodes in figure G=(V, E) core value core (u)=max k | u ∈ Vk-coreAnd core (v)
=max k | v ∈ Vk-core, wherein Vk-coreIt is the k-core communities in figure G；
Calculate and record maximal degree δ (e) of all side e=(u, v) in figure G=(V, E)=min (core (u), core
(v))；
Calculate and record all side e=(u, v) in figure G=(V, E) trussness λ (e)=max k | e ∈
Ek-truss, wherein Ek-trussIt is the k-truss communities in figure G；
The initial value for controlling k is 3；
Will be all while meeting δ (e)<α * k and λ (e)<The side e of two conditions of k is deleted, and obtains K-core-truss communities；
On the basis of the K-core-truss communities for obtaining, k=k+1 is controlled, and repeat previous step, until all sides
All it is deleted；
The all K-core-truss communities for obtaining of output.
Preferably, the time complexity of the k-core-truss community models decomposition algorithm is O (m1.5), wherein m is figure
The side number of G, figure G for it is undirected, without weight graph.
Embodiments of the invention also provide a kind of k-core-truss community models searching algorithm, comprise the following steps：
Calculate and record all nodes in figure G=(V, E) core value core (u)=max k | u ∈ Vk-coreAnd core (v)
=max k | v ∈ Vk-core, wherein Vk-coreIt is the k-core communities in figure G；
Calculate and record maximal degree δ (e) of all side e=(u, v) in figure G=(V, E)=min (core (u), core
(v))；
Calculate and record all side e=(u, v) in figure G=(V, E) trussness λ (e)=max k | e ∈
Ek-truss, wherein Ek-trussIt is the k-truss communities in figure G；
The adjacent side of default node q is searched, and compares λ (e) and δ (e) value of all adjacent sides, choose maximum conduct therein
kmax；
With node q as starting point, using breadth first traversal algorithm by eligible λ (e) >=kmaxOr δ (e) >=α * kmax
Side be added in output queue Q, until searching less than qualified side；
Output queue Q is used as target kmax- core-truss communities.
Preferably, the time complexity of the k-core-truss community models searching algorithm is O (m1.5), wherein m is figure
The side number of G, figure G for it is undirected, without weight graph.
A kind of k-core-truss community models provided in an embodiment of the present invention and decomposition, searching algorithm, by the society
The core value on section model interior nodes and side, maximal degree and trussness data are analyzed, and by breadth first traversal algorithm,
Efficiently solve the problems, such as whole community discoveries or comprising the community search to a query node, can be to the cohesion in community model
Subgraph is excavated comprehensively.
Brief description of the drawings
Fig. 1 is that k-core-truss community models provided in an embodiment of the present invention decompose lower getable k-core-
Truss communities and k-core communities and the contrast schematic diagram of k-truss communities；
Fig. 2 is a kind of algorithm flow of the k-core-truss community models provided in an embodiment of the present invention for community search
Block diagram；
Fig. 3 is a kind of community search of the k-core-truss community models provided in an embodiment of the present invention for query node
Algorithm flow block diagram；
Fig. 4 is λ (e) and δ (e) numerical value the mark figure of each edge in G figures shown in Fig. 1 of the present invention；
Fig. 5 is the maximum 3-core-truss communities figure comprising node 8 in Fig. 1 of the present invention.
Specific embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
In k-core-truss community models provided in an embodiment of the present invention, what we discussed is undirected, without weight graph G=
(V, E), the degree of note node u is deg (u)=| { v | (u, v) ∈ E } |, and the degree of side e is d (e)=min { deg (u), deg (v) },
The maximal degree of node is d in figure Gmax.On this basis, we define k-core-truss community models and are：
Given above-mentioned figure G, parameter alpha>0, while integer k >=3, we define a kind of cohesive of broad sense
Subgraph, referred to as k-core-truss communities, are denoted as CTk, and if only if, and this subgraph meets following two properties：(1) it is every
The degree of bar side e is more than or equal to α * k, or is at least comprised in k-2 triangle；(2) clique of property (1) is met.
Further, in the k-core-truss community models of the definition：
For any node u in figure G, its core value is designated as core (u), wherein core (u)=max k | u ∈
Vk-core}；Wherein Vk-coreRepresent the k-core communities in figure G.
For any limit e in figure G, its trussness is designated as λ (e), wherein λ (e)=max k | e ∈
Ek-truss}；Wherein Ek-trussRepresent the k-truss communities in figure G.
For any limit e=(u, v) in figure G, its maximal degree is designated as δ (e), wherein δ (e)=min (core (u),
core(v))。
According to defined k-core-truss community models, it is known that the model has nesting and hierarchical structure, i.e.,：It is induced subgraph, it is possible to be made up of multiple connection block, these are all the first two models for remaining
Characteristic.But its more embodiment be trade off, it is flexible and controllable.By setup parameter α, this model can balance k-core moulds
Type and k-truss models, and it is at least a min { α * k, k-1 }-core.When α is sufficiently large, i.e. α * k>dmax(figure midpoint
Maximal degree) when, this model is just equivalent to k-truss；As α * k≤(k-1), the model is a α * k-core；At other
In the case of, the model is the mixture of k-core and k-truss.
Can be by changing the size of parameter alpha in k-core-truss models provided in an embodiment of the present invention so that whole
Search community is more flexible, and when α values are smaller, such as α=1/k, k-core-truss search community are exactly connected graph G sheets
Body, because the side of all δ (e) >=1 will be all comprised in Search Results.When taking α * k>dmaxWhen, whole k-core-
Community search result under truss is exactly a k-truss community, because any a line can meet δ (e) in figure>α*
K, in other cases, k-core-truss communities are exactly a Search Results for mixing k-core and k-truss communities.This hair
In bright embodiment, the value of α can be set according to actual demand.
As shown in figure 1, we can contrast tri- kinds of models of k-core, k-truss and k-core-truss in community discovery
On difference, the most notably subgraph of right-hand component, if with k-core models, can only find by 8,9,10,11,
12,13 } the 3-core communities of 6 nodes composition, and if with k-truss models, can only find { 5,6,7,8,9 } this 5
The 3-truss communities of individual node composition.It is proposed that k-core-truss model under, it can be found that 5,6,7,8,9,
10,11,12,13 } 9 communities of point, and the relation between node more comprehensively embodies in this community.Community specifically related to is searched
Rope algorithm can be described in detail below.
The community search algorithm of the figure G of the embodiment of the present invention typically solves the problems, such as two classes：(1) all societies in figure are found out
Area；(2) query node, the maximum community where finding out the node are given.According to this two classes problem, it is proposed that problem
It is defined as follows
(1) figure G=(V, E) and parameter alpha are given, for all possible k (k >=3), all of k-core-truss is found out
Community；
(2) figure G=(V, E), parameter alpha and node q are given, all k-core-truss communities comprising node q are found out, and
And k values are maximum.
Define regarding to the issue above, embodiments of the invention will be described the decomposition and search of k-core-truss community models
Algorithm.
As shown in Fig. 2 for solve problem (1), the technical solution adopted by the present invention is the synchronization point of core and truss
Solution.Will scheme to be unsatisfactory for condition in G：Leave out on the side of δ (e) >=α * k or λ (e) >=k, it is notable that the side of deletion will be simultaneously
Two above-mentioned conditions are unsatisfactory for, in other words, when side e meets δ (e) simultaneously<α * k and λ (e)<During two conditions of k, side e needs
Delete, i.e. e is not belonging to our k-core-truss to be looked for, comprises the following steps that：
Step S10, calculate and record all nodes in figure G=(V, E) core value core (u)=max k | u ∈ Vk-core}
With core (v)=max k | v ∈ Vk-core, wherein Vk-coreIt is the k-core communities in figure G；
Step S20, calculates and records maximal degree δ (e)=min (core of all side e=(u, v) in figure G=(V, E)
(u),core(v))；
Step S30, calculate and record all side e=(u, v) in figure G=(V, E) trussness λ (e)=max k | e
∈Ek-truss, wherein Ek-trussIt is the k-truss communities in figure G；
Step S40, the initial value for controlling k is 3；
Step S50, will be all while meeting δ (e)<α * k and λ (e)<The side e of two conditions of k is deleted, and obtains k-core-
Truss communities；Here k is initial value 3；
Step S60, on the basis of the k-core-truss communities for obtaining in a previous step, controls k=k+1, and repeat
Previous step, until all sides are all deleted；
Step S70, exports all K-core-truss communities for obtaining.
Further, in the present embodiment, the step S30 can simultaneously be carried out with step S10 or step S20, step S30
Can also be in the made above of step S10, or in the made above of step S20.
In the present embodiment, we using step S10, step S20 and step S30 as initialization step, by calculate core value,
The maximal degree and trussness values on side, then by breadth first traversal algorithm (BFS) in step S50, since k=3, will
It is all while meeting δ (e)<α * k and λ (e)<Two edge contracts of condition of k.Result after deletion is exactly 3-core-truss societies
Area.We continue to search for 4-core-truss, so in step S60, after plus 1 by k, coming back to step S50.Note, this
Secondary circulation is carried out on the result i.e. 3-core-truss drawn in step S60, rather than again to figure G operate.Such as
Fig. 1, community search is carried out using the algorithm of the embodiment of the present invention to the G figures in Fig. 1, and we can obtain 2 3-core-
Truss communities：{ 5,6,7,8,9,10,11,12,13 } and { 18,19,20 } and 1 4-core-truss community：14,15,16,
17}.In the present embodiment, it is preferable that parameter alpha=1.
May certify that, the time complexity of the algorithm is O (m1.5), wherein m is the side number of figure G, and mainly algorithm is being calculated
O (m are needed during the trussness values on all sides1.5) time.
As shown in figure 3, for solve problem (2), according to the definition to k-core-truss, for the society being eventually found
Area, the δ (e) or λ (e) on side e=(u, v) is bigger, and the k values of the k-core-truss where showing the side are bigger, node u or v
The k values of the k-core-truss at place are also bigger.We are the query node q given for, to find out the maximum k comprising q
The k-core-truss of value, the maximal degree and trussness values that we can first find out all sides comprising q is compared, and obtains
To kmaxValue, i.e. q is present in a kmaxIn-core-truss communities, we can find out this community by DFS again.
Comprise the following steps that：
Step S100, calculate and record all nodes in figure G=(V, E) core value core (u)=max k | u ∈ Vk-core}
With core (v)=max k | v ∈ Vk-core, wherein Vk-coreIt is the k-core communities in figure G；
Step S200, calculates and records maximal degree δ (e)=min (core of all side e=(u, v) in figure G=(V, E)
(u),core(v))；
Step S300, calculate and record all side e=(u, v) in figure G=(V, E) trussness λ (e)=max k | e
∈Ek-truss, wherein Ek-trussIt is the k-truss communities in figure G；
Step S400, searches the adjacent side of default node q, and compares λ (e) and δ (e) value of all adjacent sides, chooses therein
Maximum is used as kmax；
Step S500, with node q as starting point, using breadth first algorithm by eligible λ (e) >=kmaxOr δ (e) >=
The side of α * k is added in output queue Q, until searching less than qualified side；
Step S600, output queue Q is used as target kmax- core-truss communities.
Similarly, in the present embodiment, the step S300 can simultaneously be carried out with step S100 or step S200, step
S300 can also be in the made above of step S100, or in the made above of step S200.
By taking the example of Fig. 1 as an example, such as the maximum k-core-truss communities where finding node 8, step S100- steps
Rapid S300 as initialization step, by calculating core value, the maximal degree on side and trussness values, then by the maximum of each edge
Degree and trussness are marked on the diagram, as shown in Figure 4., in step S400, compare the trussness values of all adjacent sides of q
With δ (e)/α, it is preferred in the present embodiment, it is described to put α=1.
The adjacent side of node 8 includes side (5,8), side (6,8), side (7,8), side (8,9), side (8,11), and side (8,13) obtain
kmax=3.Then according to step S500, with q as starting point, BFS traversal obtains the maximum 3-core-truss societies comprising node 8
Area：{ 5,6,7,8,9,10,11,12,13 }, as shown in Figure 5.
May certify that, the time complexity of the algorithm is also O (m1.5), wherein m is the side number of figure G, and mainly algorithm is in meter
O (m are needed during the trussness values for calculating all sides1.5) time.
The community search algorithm based on k-core-truss that the above embodiment of the present invention is provided can solve the problem that whole societies
Area finds and comprising the community search problem to a query node, and time complexity is O (m1.5), m is the quantity on figure G sides,
Community model of the invention and algorithm efficiently solve k-core models and k-truss models etc. and can not find more comprehensively society
The problem in area.
Presently preferred embodiments of the present invention is the foregoing is only, is not intended to limit the invention, it is all in essence of the invention
Any modification, equivalent and improvement made within god and principle etc., should be included within the scope of the present invention.
Claims (8)
1. a kind of k-core-truss community models, it is characterised in that including one it is undirected, without weight graph G=(V, E), in G is schemed
With a clique, the subgraph meets：The degree of each edge e >=α * k or side e are comprised in k-2 triangle；
For scheme G arbitrary node u, its core value core (u)=max k | u ∈ Vk-core, wherein Vk-coreIt is the k- in figure G
Core communities；
For figure G in any limit e, its beam value λ (e)=max k | e ∈ Ek-truss, wherein Ek-trussIt is the k-truss in figure G
Community；
For any limit e in figure G, its maximal degree δ (e)=min (core (u), core (v))；
Wherein, the degree of side e=(u, v), node u is deg (u)=| { v | (u, v) ∈ E } |, and the degree of side e is d (e)=min { deg
(u), deg (v) }, the maximal degree for scheming G interior joints is dmax, parameter alpha>0, k >=3.
2. k-core-truss community models as claimed in claim 1, it is characterised in that as α * k>dmaxWhen, the k-
Core-truss community models are k-truss models.
3. k-core-truss community models as claimed in claim 1, it is characterised in that as α * k≤(k-1), the k-
Core-truss community models are α * k-core models.
4. k-core-truss community models as claimed in claim 1 the, it is characterised in that during parameter alpha=1/k, entirely
Figure G is k-core-truss models.
5. a kind of k-core-truss community models decomposition algorithm, it is characterised in that comprise the following steps：
Calculate and record all nodes in figure G=(V, E) core value core (u)=max k | u ∈ Vk-coreAnd core (v)=
max{k|v∈Vk-core, wherein Vk-coreIt is the k-core communities in figure G；
Calculate and record maximal degree δ (the e)=min (core (u), core (v)) of all side e=(u, v) in figure G=(V, E)；
Calculate and record all side e=(u, v) in figure G=(V, E) trussness λ (e)=max k | e ∈ Ek-truss, wherein
Ek-trussIt is the k-truss communities in figure G；
The initial value for controlling k is 3；
Will be all while meeting δ (e)<α * k and λ (e)<The side e of two conditions of k is deleted, and obtains 3-core-truss communities；
On the basis of the K-core-truss communities for obtaining in a previous step, k=k+1 is controlled, and repeat previous step, until
All sides are all deleted；
The all K-core-truss communities for obtaining of output, wherein k >=3.
6. k-core-truss community models decomposition algorithm as claimed in claim 5, it is characterised in that the k-core-
The time complexity of truss community model algorithms is O (m1.5), wherein m is the side number of figure G, figure G for it is undirected, without weight graph.
7. a kind of k-core-truss community models searching algorithm, it is characterised in that comprise the following steps：
Calculate and record all nodes in figure G=(V, E) core value core (u)=max k | u ∈ Vk-coreAnd core (v)=
max{k|v∈Vk-core, wherein Vk-coreIt is the k-core communities in figure G；
Calculate and record maximal degree δ (the e)=min (core (u), core (v)) of all side e=(u, v) in figure G=(V, E)；
Calculate and record all side e=(u, v) in figure G=(V, E) trussness λ (e)=max k | e ∈ Ek-truss, wherein
Ek-trussIt is the k-truss communities in figure G；
Search the adjacent side of default node q, and relatively more all adjacent sides λ (e) and δ (e)/α values, selection maximum conduct therein
kmax；
With node q as starting point, using breadth first algorithm by eligible λ (e) >=kmaxOr δ (e) >=α * kmaxSide add
To in output queue Q, until searching less than qualified side；
Output queue Q is used as target kmax- core-truss communities.
8. k-core-truss community models searching algorithm as claimed in claim 7, it is characterised in that the k-core-
The time complexity of truss community model algorithms is O (m1.5), wherein m is the side number of figure G, figure G for it is undirected, without weight graph.
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| CN109885669A (en) * | 2019-01-30 | 2019-06-14 | 中国地质大学（武汉） | A kind of text key word acquisition methods and system based on complex network |
| CN110334159A (en) * | 2019-05-29 | 2019-10-15 | 苏宁金融服务(上海)有限公司 | Information query method and device based on relation map |
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| CN112818178A (en) * | 2019-10-30 | 2021-05-18 | 华东师范大学 | Fast and efficient community discovery method and system based on (k, p) -core |
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