CN109978710A - Overlapping community division method based on K- core iteration factor and community's degree of membership - Google Patents
Overlapping community division method based on K- core iteration factor and community's degree of membership Download PDFInfo
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Abstract
The present invention discloses the overlapping community division method based on K- core iteration factor and community's degree of membership, including the following steps: S1: reading Network data set, generates network structure G and obtains the adjacency information table N of each node of networkij；S2: the K- core iteration factor of each node in network structure G is calculated；S3: the node density of each node in network structure G is calculated, and node density is normalized；S4: in conjunction with K- core iteration factor and node density calculate node influence power, and the maximum node of node influence power is chosen as seed node；S5: carrying out local community as core using seed node and extend to obtain sub- community, so that obtaining first time community divides set；S6: dividing the sub- community in set for first time community and merge, so that obtaining second of community divides set.
Description
Technical field
The present invention relates to overlapping community's partitioning technology fields, in particular to based on K- core iteration factor and community's degree of membership
It is overlapped community division method.
Background technique
The discovery for being overlapped community mainly utilizes the local expansion characteristic of community.In real world, many complicated phases
The relationship of interaction is abstracted into complex network figure often to indicate, node indicates the individual in network, and side indicates between node
There are correlations.Wherein, there are some nodes to belong to different communities simultaneously, this is overlapping community structure, community structure
It can also be expressed as the topological relation of live network to a certain extent.The accurate division application of overlapping community facilitates preferably
Understand network topology structure and function.Prevention and control, public sentiment monitoring in excavation network user group, epidemic transmission etc.
Aspect plays an important role.
But the prior art is to cause time complexity higher, suitable for application in large size using random selection seed node
In network, and it will lead to the problem that community division result is unstable, accuracy rate is not high.
Summary of the invention
Aiming at the problem that randomness that seed node selects during the overlapping community discovery of the prior art, the present invention passes through
Iteration factor thought and node density value are combined to obtain node influence power to select seed node, then pass through node influence
Community's degree of membership is calculated in power, carries out community's expansion according to community's degree of membership selectively addition node, promotes community and divide matter
Amount and accuracy rate.
To achieve the goals above, the present invention the following technical schemes are provided:
Overlapping community division method based on K- core iteration factor and community's degree of membership, including the following steps:
S1: reading Network data set, generates network structure G and obtains the adjacency information table N of each node of networkij；
S2: the K- core iteration factor of each node in network structure G is calculated；
S3: the node density of each node in network structure G is calculated, and node density is normalized；
S4: in conjunction with K- core iteration factor and node density calculate node influence power, and the maximum section of node influence power is chosen
Point is used as seed node；
S5: carrying out local community as core using seed node and extend to obtain sub- community, to obtain the division of first time community
Set；
S6: dividing the sub- community in set for first time community and merge, so that obtaining second of community divides set.
Preferably, in the step S2, the calculation formula of the K- core iteration factor is as follows:
In formula (1), δiIndicate the K- core iteration factor of node i, kiIndicate the core grade of node i,Expression is being counted
Calculate kiWhen the number of iterations, niIt indicatesNumber when secondary iteration interior joint is removed.
Preferably, in the step S3, the calculation formula of the node density is as follows:
In formula (2), ds (i) indicates the density of node i, NiIndicate the adjacent node set of node i, djIndicate node j's
Angle value；
The calculation formula that node density is normalized is as follows:
In formula (3), lo (i) indicates the density of the node i after normalized, and ds (i) indicates the density of node i, ds
(m) density of node m is indicated, V indicates the node set in network structure.
Preferably, in the step S4, the calculation formula of the node influence power is as follows:
NI (i)=δi·lo(i) (4)
In formula (4), NI (i) indicates the node influence power of node i, δiIndicate the K- core iteration factor of node i, lo (i)
The density of node i after indicating normalized.
Preferably, the step S5 the following steps are included:
Step 1: the first seed node is divided into initial community c；
Step 2: traversing the adjacent node set N of initial community cc, and calculate NcBetween middle any node i and community c
Degree of membership f, and be compared with default degree of membership threshold value F, if f >=F, node i is divided into community c；If f < F, node
I is not divided into community c；
Step 3: repeating second step until no node division to community c, sub- community C is obtained1；
Step 4: in the sub- community C of network structure G1Except node in choose the maximum node of node influence power again
As second seed node h2, second step and third step are repeated, sub- community C is obtained2；Until all nodes complete community division,
Set C is divided to obtain first time community.
Preferably, the degree of membership calculating step includes:
A. calculate node i (i ∈ Nc) adjacent node set NiNNI (i) can be labeled as to the influence power of node i, then NNI
(i) calculation formula is as follows:
In formula (5), NNI (i) indicates the adjacent node set N of node iiTo the influence power of node i, j indicates set NiIn
Any node, NI (j) indicate node j node influence power, NcIndicate the adjacent node set of community c；
B. the adjacent node set N of community c and node i are calculatediIntersection to the influence power of node i；
In formula (6), NNIc(i) influence power of the adjacent node intersection of sets collection to node i of community C and node i is indicated,
Nc(i) node set for belonging to community c in node i adjacent node is indicated, NI (j) indicates the node influence power of node j；
C. subordinating degree function is constructed:
In the present embodiment, the calculation formula of subordinating degree function is following formula:
In formula (7), f (i, c) indicates the degree of membership between node i and community c, NNIc(i) community C and node i are indicated
Adjacent node intersection of sets collection to the influence power of node i, NNI (i) indicates the adjacent node set N of node iiTo node i
Influence power, NIc(i) node i is indicated in the node influence power of community c, and NI (i) indicates node i in the node shadow of network structure
Ring power.
Preferably, the step S6 the following steps are included:
S6-1: isolated community is divided:
Isolated community's interior joint and the adjacent intercommunal degree of membership of son are calculated, this is isolated community and is divided into is subordinate to
It spends maximum corresponding first time community and divides the sub- community of set, so that obtaining second of community divides sub- community；
S6-2: the merging of similar community is carried out:
First time community divides in set, and 2/3rds or more node belongs to other simultaneously in a community Ge Zi if it exists
Certain community Ge Zi, then it is assumed that the two communities are similar community, two similar communities are merged, to obtain second of society
Zoning molecule community, so that obtaining second of community divides set, i.e., final community divides set.
In conclusion by adopting the above-described technical solution, compared with prior art, the present invention at least has beneficial below
Effect:
1. the present invention is by combining to obtain node influence power iteration factor thought and node density value to select to plant
Child node solves the randomness select permeability of seed node.
2. community's degree of membership is calculated by node influence power, society is carried out according to community's degree of membership selectively addition node
Area's expansion promotes stability and accuracy rate that overlapping community divides.
3. the present invention reduces the time of community's division, is applicable to catenet number by quickly selecting seed node
According to concentration.
Detailed description of the invention:
Fig. 1 is a kind of overlapping society based on K- core iteration factor and community's degree of membership according to exemplary embodiment of the present
Limited region dividing method flow diagram.
Fig. 2 is the schematic diagram according to the network structure G of exemplary embodiment of the present.
Specific embodiment
Below with reference to embodiment and specific embodiment, the present invention is described in further detail.But this should not be understood
It is all that this is belonged to based on the technology that the content of present invention is realized for the scope of the above subject matter of the present invention is limited to the following embodiments
The range of invention.
Fig. 1 is a kind of overlapping society based on K- core iteration factor and community's degree of membership according to exemplary embodiment of the present
Limited region dividing method, specifically includes the following steps:
Step S1: reading Network data set, generates network structure and obtains the adjacency information table of each node of network.
In the present embodiment, overlapping community is first read from network and divides data set, generates network structure G and network knot
The adjacency information table N of each node in composition Gij。
G=<V, E>, wherein V indicates that node collection, E indicate side collection.
In formula (1), NijIndicate the adjacency information table of node, eijIndicate the connection side of node i and node j.
Table 1 is overlapped community and divides data set information table
Step S2: the K- core iteration factor of network structure interior joint is calculated.
In the present embodiment, the present invention calculates the K- core iteration factor δ of each node in networki, to solve core node journey
The otherness of degree.The Computation schema of K- core iteration factor is: the k value for defining fringe node in network structure G is 1, from level to level
Into the center of network structure G；First time iteration is to remove the node and side that angle value is 1 in G；If secondary iteration is remaining
Still having angle value in node is 1 node, then repeatedly previous step；Until the angle value of remaining node is both greater than 1, i.e., third time iteration is
Iteration terminates；Similarly, k value successively increases 1 (i.e. k=k++), above-mentioned iterative step is repeated, until sections all in network structure
Point has removed, and calculating terminates.Then the node of every step removal has corresponding K- core iteration factor, and the calculating of K- core iteration factor is public
Formula is as follows:
In formula (2), δiIndicate the K- core iteration factor of node i, kiIndicate that the core grade of node i (can pass through existing K-
Nuclear decomposition algorithm obtains, such as grade is 1,2,3),It indicates calculating kiWhen the number of iterations, niIt indicatesIt is secondary to change
Number when being removed for interior joint.
With reference to Fig. 2, in network structure G, when k value is 1, the node that first time iteration removes is 1,2,3,5,9,
11, the node that second of iteration removes is 4, and the node that third time iteration removes is 6, is less than or equal to 1 section without angle value later
Point, iteration terminate, and core grade is 1, and iteration total degree is 3；The K- core iteration factor of its interior joint 1,2,3,5,9,11 is 1*
(1+1/3), the K- core iteration factor of node 4 are 1* (1+2/3)；The K- core iteration factor of node 6 is 1* (1+3/3).When k value
When being 2, then the node that iteration removes is 7,8,10, and all nodes have all removed at this time, that is, calculating terminates, and core grade is 2, repeatedly
It is 1 for total degree, i.e., the K- core iteration factor of node 7,8,10 is 2* (1+1/1).
Table 2K- core iteration factor computational chart
Step S3: calculate node density, and node density is normalized.
In the present embodiment, the calculation formula of node density is as follows:
In formula (3), ds (i) indicates the density of node i, NiIndicate the adjacent node set of node i, j indicates node, dj
Indicate the angle value (quantity that angle value indicates the side that node is connect with adjacent node) of node j.
In the present embodiment, according to formula (2) it is found that K- core iteration factor δiIt is changed according to the core grade of node,
I.e. K- core iteration factor is not more than twice of core grade, and numerical value is smaller；And resulting node density ds is calculated according to formula (3)
It (i) is the cumulative of node angle value, numerical value is larger；The present invention need to combine K- core iteration factor δiIt is counted with node density ds (i)
It calculates, therefore for convenience of calculating, node density need to be normalized, calculation formula is as follows:
In formula (4), lo (i) indicates the density of the node i after normalized, and ds (i) indicates the density of node i, ds
(m) density of node m is indicated.
Step S4: calculate node influence power, and the maximum node of node influence power is chosen as seed node.
In the present embodiment, the importance of a node is determined by node itself and adjacent all nodes, for seed node
The uncertainty being likely to occur is selected, calculate node influence power is combined by calculate node density and iteration factor, to select
Seed node is taken, the calculation formula of node influence power is as follows:
NI (i)=δi·lo(i) (5)
In formula (5), NI (i) indicates the node influence power of node i, δiIndicate the K- core iteration factor of node i, lo (i)
The density of node i after indicating normalized.
In the present embodiment, the node influence power for calculating gained node is ranked up to obtain set NI, and choose wherein max
The node of NI is labeled as h as the first seed node, the first seed node1.Beneficial effect is: the seed node of selection has most
Big node influence power carries out outside differentially expanding by the seed node, and the community for improving acquisition divides quality.
Step S5: carrying out local community extension by core of seed node, obtains first time community and divides set.
And subordinating degree function is constructed, promote the accuracy rate that community divides.
In the present embodiment, in network node communication process, node influence power is bigger, then shows the influence to other nodes
Power is bigger.
Step 1: by the first seed node (i.e. h1) dividing initial community c, i.e., initial community c only includes seed node h1；
Step 2: traversing the adjacent node set N of initial community cc, and calculate NcBetween middle any node i and community c
Node i is divided into community c if the degree of membership f for calculating resulting node i is greater than or equal to set threshold value F by degree of membership f；If
F is less than F, then node i is not divided into community c
Step 3: repeating second step until no node division to community c, sub- community C is obtained1；
Step 4: in network structure G neutron community C1Except node in choose the maximum section of node influence power again
Point is used as second seed node h2, second step and third step are repeated, sub- community C is obtained2；Until all nodes complete drawing for community
Point, so that obtaining first time community divides set C.
In the present embodiment, steps are as follows for the calculating of degree of membership between node and community:
A. calculate node i (i ∈ Nc) adjacent node set NiNNI (i) can be labeled as to the influence power of node i, then NNI
(i) calculation formula is as follows:
In formula (6), NNI (i) indicates the adjacent node set N of node iiTo the influence power of node i, j indicates set NiIn
Any node, NI (j) indicate node j node influence power, NcIndicate the adjacent node set of community c.
B. the adjacent node set N of community c and node i are calculatediIntersection to the influence power of node i.
In the present embodiment, node i is community c adjacent node set NcIn any node, then the adjacent node of node i has
For a part in community c, this part of nodes can be labeled as set Nc(i), the section for belonging to community C in node i adjacent node is indicated
Point set, i.e. Nc(i)=NiThe community ∩ c.The adjacent node set N of community c and node iiIntersection to the influence power of node i, meter
It is as follows to calculate formula:
In formula (7), NNIc(i) influence power of the adjacent node intersection of sets collection to node i of community c and node i is indicated,
Nc(i) node set for belonging to community c in node i adjacent node is indicated, NI (j) indicates the node influence power of node j.
In the present embodiment, when community c is as separate network structure chart, K- core iteration factor of the node i relative to community c
It is denoted asSimilarly, node density ds of the node i relative to community cc(i), node i is close relative to normalized node in community c
Degree is loc(i), node i is NI relative to the node influence power of community cc(i)。
C. subordinating degree function is constructed.
In the present embodiment, the calculation formula of subordinating degree function is following formula:
In formula (8), f (i, c) indicates the degree of membership between node i and community c, NNIc(i) community c and node i are indicated
Adjacent node intersection of sets collection to the influence power of node i, NNI (i) indicates the adjacent node set N of node iiTo node i
Influence power, NIc(i) node influence power of the node i in community c is indicated, NI (i) indicates node i in the node of network structure
Influence power.
Step S6: dividing the sub- community in set for first time community and merge, and obtains second of community and divides set.
In the present embodiment, setting is respectively less than when the community that seed node is formed is adjacent the degree of membership f between node
When degree of membership threshold value F, then the community that the seed node is formed being denoted as isolated community, i.e., isolated community only includes a node,
Its node and the degree of membership f of other communities are less than the degree of membership threshold value F of setting.
Step S6-1: isolated community is divided.
Isolated community's interior joint and adjacent intercommunal degree of membership f are calculated, this is isolated community and is divided into degree of membership
The corresponding sub- community maxf.Such as isolate community's interior joint and adjacent sub- community C1Between degree of membership be f1, with adjacent sub- society
Area C2Between degree of membership be f2, and f1> f2, then by isolated community and adjacent sub- community C1It merges, to obtain second
Community divides sub- community R1；If f1=f2, then isolated community is divided into adjacent sub- community C1And C2In, to obtain second of society
Zoning molecule community.
Step S6-2: the merging of similar community is carried out.
In the present embodiment, first time community divide set in, if it exists in a community Ge Zi 2/3rds or more node
Belong to some other sub- community simultaneously, then it is assumed that the two communities are similar community；The community Liang Ge is merged until discontented
Until the condition of the similar community of foot, so that obtaining second of community divides sub- community.Such as sub- community C1Interior joint collection is combined into S1,
Node number is P1；Sub- community C2Interior joint collection is combined into S2, and node number is P2 (P1 < P2)；S3=S1 ∩ S2 is then defined, is saved
Point number is P3；If the community P3/P1 >=2/3, Ze Zi C1With sub- community C2For similar community, it is merged into new community R2。
In the present embodiment, by above-mentioned steps, to all carry out community's division to the node in network structure G, obtain
Set R, i.e., final community division result are divided to second of community.
In the present invention, the accuracy that overlapping community divides is calculated using expanded mode lumpiness function EQ:
In formula (9), M indicates that network data concentrates the quantity on side；QuIndicate the number of the affiliated community node u；QvIndicate section
The number of the affiliated community point v；NuvIndicate whether there is side between node u and node v, if there is side NuvIt is 1, is otherwise 0；duIndicate section
The angle value of point u；dvIndicate the angle value of node v；RTIndicate that T second of communities divide sub- community.EQ value is bigger to be indicated finally
It is more accurate that community divides set.
Table 3: EQ of each algorithm in real data set compares
| Network | This algorithm | OCDEDC | OMKLP | QLFM | LFM | COPRA |
| Karate | 0.4239 | 0.4302 | 0.3679 | 0.3565 | 0.3323 | 0.3239 |
| Lesmis | 0.5118 | 0.4819 | 0.4338 | 0.4893 | 0.4617 | 0.4997 |
| Dolphins | 0.5198 | 0.516 | 0.5191 | 0.4002 | 0.3724 | 0.5006 |
| Polbooks | 0.5353 | 0.5171 | 0.4842 | 0.4725 | 0.4635 | 0.4715 |
| Football | 0.5969 | 0.5754 | — | 0.3654 | 0.3231 | 0.3421 |
| 0.3674 | 0.1756 | 0.3079 | 0.1337 | 0.1512 | 0.3556 | |
| Polblogs | 0.3089 | 0.0501 | 0.1963 | 0.3156 | 0.2783 | 0.3159 |
| Netscience | 0.9413 | 0.9093 | 0.9109 | 0.8786 | 0.8381 | 0.7255 |
| Blogs | 0.7805 | 0.6546 | — | 0.7214 | 0.5283 | — |
| PGP | 0.4428 | 0.6546 | 0.7008 | 0.6762 | 0.4243 | 0.5793 |
| Internet | 0.4561 | — | 0.1853 | 0.2316 | 0.2163 | 0.1352 |
Table 4: the runing time (unit: ms) of each algorithm compares
| Network | This algorithm | OCDEDC | QLFM | LFM |
| Karate | 60 | 68 | 31 | 25 |
| Lesmis | 72 | 187 | 46 | 26 |
| Dolphins | 80 | 479 | 52 | 44 |
| Polbooks | 149 | 1,904 | 67 | 52 |
| Football | 157 | 2,496 | 50 | 202 |
| 10,251 | 45,633 | 14,161 | 67,864 | |
| Polblogs | 46,249 | 898,691 | 65,783 | 297,114 |
| Netscience | 2,182 | 15,740 | 193 | 736 |
| Blogs | 68,543 | 151,884 | 5,335 | 523,976 |
| PGP | 45,864 | 2,656,088 | 98,911 | 1,106,265 |
| Internet | 2,324,148 | — | 8,354,378 | 2,457,521 |
As can be seen from Table 3, this algorithm is compared with other algorithms, and community has divided accuracy in multiple data sets
It improves.As can be seen from Table 4, lesser complex network (network of the number of nodes less than 1000: Karate, Lesmis,
Dolphins, Polbooks, Football) in, since this algorithm will calculate the community of adjacent node when carrying out local expansion
Degree of membership so time loss is higher than other algorithms, but in the practical application of smaller network, can be ignored；Larger
Complex network (number of nodes be greater than 1000 network: Email, Polblogs, Netscience, Blogs, PGP,
Internet in), although this algorithm will calculate community's degree of membership of adjacent node, community's degree of membership of each adjacent node
It only needs to calculate once, compared to the multiple calculating of other local expansion classes overlapping community discovery algorithm, reduces and calculate the time, because
In biggish complex network, time loss can be greatly reduced in this algorithm for this, so that time efficiency is higher.Therefore originally
Invention (number of nodes is greater than 1000) suitable for catenet data set, can be improved arithmetic speed, when reducing community's division
Between,.
Claims (7)
1. the overlapping community division method based on K- core iteration factor and community's degree of membership, which is characterized in that including following
Step:
S1: reading Network data set, generates network structure G and obtains the adjacency information table N of each node of networkij；
S2: the K- core iteration factor of each node in network structure G is calculated；
S3: the node density of each node in network structure G is calculated, and node density is normalized；
S4: it in conjunction with K- core iteration factor and node density calculate node influence power, and chooses the maximum node of node influence power and makees
For seed node；
S5: carrying out local community as core using seed node and extend to obtain sub- community, so that obtaining first time community divides set；
S6: dividing the sub- community in set for first time community and merge, so that obtaining second of community divides set.
2. the overlapping community division method based on K- core iteration factor and community's degree of membership as described in claim 1, feature
It is, in the step S2, the calculation formula of the K- core iteration factor is as follows:
In formula (1), δiIndicate the K- core iteration factor of node i, kiIndicate the core grade of node i,It indicates calculating ki
When the number of iterations, niIt indicatesNumber when secondary iteration interior joint is removed.
3. the overlapping community division method based on K- core iteration factor and community's degree of membership as described in claim 1, feature
It is, in the step S3, the calculation formula of the node density is as follows:
In formula (2), ds (i) indicates the density of node i, NiIndicate the adjacent node set of node i, djIndicate the degree of node j
Value；
The calculation formula that node density is normalized is as follows:
In formula (3), lo (i) indicates the density of the node i after normalized, and ds (i) indicates the density of node i, ds (m) table
Show the density of node m, V indicates the node set in network structure.
4. the overlapping community division method based on K- core iteration factor and community's degree of membership as described in claim 1, feature
It is, in the step S4, the calculation formula of the node influence power is as follows:
NI (i)=δi·lo(i) (4)
In formula (4), NI (i) indicates the node influence power of node i, δiIndicate the K- core iteration factor of node i, lo (i) expression is returned
One changes the density of treated node i.
5. the overlapping community division method based on K- core iteration factor and community's degree of membership as described in claim 1, feature
Be, the step S5 the following steps are included:
Step 1: the first seed node is divided into initial community c；
Step 2: traversing the adjacent node set N of initial community cc, and calculate NcBeing subordinate between middle any node i and community c
F is spent, and is compared with default degree of membership threshold value F, if f >=F, node i is divided into community c；If f < F, node i is not
It is divided into community c；
Step 3: repeating second step until no node division to community c, sub- community C is obtained1；
Step 4: in the sub- community C of network structure G1Except node in choose the maximum node of node influence power again as
Two seed node h2, second step and third step are repeated, sub- community C is obtained2；Until all nodes complete the division of community, to obtain
Set C is divided to first time community.
6. the overlapping community division method based on K- core iteration factor and community's degree of membership as claimed in claim 5, feature
It is, the degree of membership calculates step and includes:
A. calculate node i (i ∈ Nc) adjacent node set NiNNI (i) can be labeled as to the influence power of node i, then NNI (i)
Calculation formula is as follows:
In formula (5), NNI (i) indicates the adjacent node set N of node iiTo the influence power of node i, j indicates set NiIn appoint
One node, NI (j) indicate the node influence power of node j, NcIndicate the adjacent node set of community c；
B. the adjacent node set N of community c and node i are calculatediIntersection to the influence power of node i；
In formula (6), NNIc(i) influence power of expression community C and the adjacent node intersection of sets collection of node i to node i, Nc(i)
Indicate the node set for belonging to community c in node i adjacent node, NI (j) indicates the node influence power of node j；
C. subordinating degree function is constructed:
In the present embodiment, the calculation formula of subordinating degree function is following formula:
In formula (7), f (i, c) indicates the degree of membership between node i and community c, NNIc(i) adjoining of community C and node i are indicated
Influence power of the intersection of node set to node i, the adjacent node set N of NNI (i) expression node iiTo the influence power of node i,
NIc(i) node i is indicated in the node influence power of community c, and NI (i) indicates node i in the node influence power of network structure.
7. the overlapping community division method based on K- core iteration factor and community's degree of membership as described in claim 1, feature
Be, the step S6 the following steps are included:
S6-1: isolated community is divided:
Isolated community's interior joint and the adjacent intercommunal degree of membership of son are calculated, this is isolated community and is divided into degree of membership most
Big corresponding first time community divides the sub- community of set, so that obtaining second of community divides sub- community；
S6-2: the merging of similar community is carried out:
First time community divide set in, if it exists in a community Ge Zi 2/3rds or more node simultaneously belong to it is some other
Sub- community, then it is assumed that the two communities are similar community, and two similar communities are merged, and are drawn to obtain second of community
Molecule community, so that obtaining second of community divides set, i.e., final community divides set.
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