CN107040467A - A kind of searching algorithm of complex network topologies Centroid - Google Patents
A kind of searching algorithm of complex network topologies Centroid Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L45/00—Routing or path finding of packets in data switching networks
- H04L45/02—Topology update or discovery
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L45/00—Routing or path finding of packets in data switching networks
- H04L45/12—Shortest path evaluation
- H04L45/122—Shortest path evaluation by minimising distances, e.g. by selecting a route with minimum of number of hops
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L45/00—Routing or path finding of packets in data switching networks
- H04L45/48—Routing tree calculation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04J3/0635—Clock or time synchronisation in a network
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
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Abstract
The invention belongs to technical field of network security, a kind of disclosed searching algorithm of complex network topologies Centroid, its step is as follows：Network topology structure is obtained；Node non-directed graph is obtained；Node traverses degree is solved；Network traverser degree is solved；Network topology Centroid is solved.The network topology Centroid that the present invention is used is that the importance to node from network information diffusion velocity and time efficiency is measured, both the oretical Foundation Stone can be provided for complex network defence, or the precision time service of complex network information system provides solution.Therefore present invention is particularly suitable for the key node of complex network defence and network information system precision time service solution.
Description
Technical field
The invention belongs to technical field of network security, and in particular to a kind of search of complex network topologies Centroid is calculated
Method.
Background technology
The central research of complex network is an important branch of network safety filed, and the importance of network node can lead to
The centrality of node is crossed to weigh.Spend centrality, close to centrality, Betweenness Centrality and eigenvector centrality isometry method
The importance primarily focused on from the connectivity pair node of network is described, and Network Central Node defined in the present invention is then
It is that the importance of node is measured in the speed and time efficiency spread from the network information.
The propagation of network topology Centroid searching algorithm and internet worm, the diffusion of network public-opinion and ntp server
It is layered time service principle consistent, therefore Network Central Node theory both can provide the oretical Foundation Stone for complex network defence, also may be used
Solution is provided with the precision time service for complex network information system.
Complex network defence the oretical Foundation Stone Network Central Node be whole network key node and critical path must
Through part, it should which targetedly the fragility and weak link to Network Central Node are on the defensive.
Network information system precision time service solution is not increasing network hardware equipment and is not changing network topology structure
In the case of, heart node configuration NTP (network time server) master server, reduces master server to the whole network point in a network
The number of plies of layer time service, so as to reach the most precision time service to whole network.
With the complex network Centroid Solve problems of network information diffusion velocity and time efficiency node metric importance
It is very difficult, challenging, in the document currently published, not yet sees correlative study achievement.
The content of the invention
The present invention proposes a kind of complex network with network information diffusion velocity and time efficiency node metric importance
The searching algorithm of Centroid, both can provide the oretical Foundation Stone, or complex network information system for complex network defence
Precision time service provide solution.
For achieving the above object, the present invention is adopted the following technical scheme that：
A kind of searching algorithm of complex network topologies Centroid, is comprised the following steps that：
Step 1, network topology structure are obtained
Objective network is scanned, mobile host computers are found, network topology structure is obtained；
Step 2, node non-directed graph are obtained
Each node of the objective network topological structure that step 1 is obtained and connective with simple Connected undigraph G=(V, E)
Expression, wherein V and E are respectively the set on node and side；
Step 3, node traverses degree are solved
Shortest paths of the solution node v ∈ V to other nodes in the simple Connected undigraph G=(V, E) obtained to step 2
Footpath, the maximum for choosing shortest path is node traverses degree；If node v1,v2∈ V are P in figure G shortest path lengthL(v1,
v2), then node v is in figure G node traverses degree：Nd(v)=maxu∈V(PL(u,v))；
Step 4, network traverser degree are solved
According to step 3, the node traverses degree of each node v in simple Connected undigraph G=(V, E) is solved, node is chosen
The minimum value of traversal degree is network traverser degree；Figure G network traverser degree be：Nd=minv∈V(Nd(v))；
Step 5, network topology Centroid are solved
According to step 4, if node v ∈ V node traverses degree is equal to network traverser degree, i.e. Nd(v)=Nd, then predicate node v
For Network Central Node.
Due to using technical scheme as described above, the present invention has following superiority：
A kind of searching algorithm of complex network topologies Centroid, using following steps：Network topology structure is obtained；Node
Non-directed graph is obtained；Node traverses degree is solved；Network traverser degree is solved；Network topology Centroid is solved.The net that the present invention is used
Network topology Centroid is that importance to node from network information diffusion velocity and time efficiency is measured, both can be with
The oretical Foundation Stone is provided for complex network defence, or the precision time service of complex network information system provides solution.Cause
Present invention is particularly suitable for the key node of complex network defence and network information system precision time service solution for this.
Brief description of the drawings
Fig. 1 is implementation process figure of the invention；
Fig. 2 is the network topology structure schematic diagram of Complex Information System.
Embodiment
Fig. 1 is a kind of searching algorithm of complex network topologies Centroid of the present invention, and its step is as follows：
Step 1, network topology structure are obtained
Objective network is scanned, mobile host computers are found, network topology structure is obtained；
Step 2, node non-directed graph are obtained
Each node of the objective network topological structure that step 1 is obtained and connective with simple Connected undigraph G=(V, E)
Expression, wherein V and E are respectively the set on node and side；
Step 3, node traverses degree are solved
Shortest paths of the solution node v ∈ V to other nodes in the simple Connected undigraph G=(V, E) obtained to step 2
Footpath, the maximum for choosing shortest path is node traverses degree.If node v1,v2∈ V are P in figure G shortest path lengthL(v1,
v2), then node v is in figure G node traverses degree：Nd(v)=maxu∈V(PL(u,v))；
Step 4, network traverser degree are solved
According to step 3, the node traverses degree of each node v in simple Connected undigraph G=(V, E) is solved, node is chosen
The minimum value of traversal degree is network traverser degree.Figure G network traverser degree be：Nd=minv∈V(Nd(v))；
Step 5, network topology Centroid are solved
According to step 4, if node v ∈ V node traverses degree is equal to network traverser degree, i.e. Nd(v)=Nd, then predicate node v
For network topology Centroid.
The concept of Netcentricity
Define 1 node traverses degree：In network, the maximum of the shortest path (fewest number of hops) of node to each other node
Value.
Define 2 network traverser degree：The minimum value of all node traverses degree in network.
Define 3 network topology Centroids：The node that node traverses degree is equal to network traverser degree is referred to as network topology center
Node.
Prove that 1 network topology has Centroid, but the topological Centroid of some networks is not exclusive.
Prove：According to defining 1,2 and 3, network there will necessarily be Network Central Node.Structural map G is only comprising two node
Complete graph, then scheme the presence of two Network Central Nodes in G, that is, the Centroid for scheming G is not unique.
2 are proved on the premise of breadth First rule is followed, using network topology Centroid as starting point, whole network is traveled through
Traversal depth it is minimum, traversal depth refers to the ultimate range of traversal tree interior joint and Network Central Node.
Prove：According to breadth first traversal principle, using Network Central Node v ∈ V as the traverse path of starting point, corresponding to figure
Spanning tree T in G by root node of v.Proved below using induction：For arbitrary node u ∈ V, if the P in figure GL(u,v)
=k, then node u and add spanning tree T during only in the kth time traversal using v as starting point (root node), and kth time traversal is obtained
Generate subtreeInterior joint and node v ultimate range are k.
As k=1, all nodes adjacent with v are added spanning tree T, even P by the 1st traversal by starting point of vL
(u, v)=1 item node u and add spanning tree T during only in the 1st time by starting point of v traversal, and the 1st traversal is generated
SubtreeInterior joint and node v ultimate range are 1.Set up.
Assuming that setting up during k≤l, it will be proven below setting up during k=l+1：
If L=v, v1,v2,…,u1, u is any one shortest path between node v, u；It is apparent from L1=v, v1,v2,…,
u1For node v, u1Between shortest path, and PL(u1, v)=l.According to assumed condition, node u1And only using v as starting point
Spanning tree T is added during the l times traversal, and the l times traversal obtains generation subtreeThe ultimate range of interior joint and node v is
l.Discuss in two kinds of situation below：
(1) if node u has added spanning tree T when traveling through for first l times：Because preceding l traversal obtains generation subtreeIn
The ultimate range of node and node v is not more than l, so the beeline between node v, u is not more than l, with PL(u, v)=l+1
It is invalid that contradiction, i.e. node u have added spanning tree T when traveling through for first l times.
(2) if node u does not add spanning tree T when traveling through for first l times：
If set U={ u1|u1It is adjacent with u, and u1On shortest path between v and u }, and l traversal is given birth to before setting
It is into subtree(it is apparent from).Because side collection { (u1,u)|u1∈ U } it is both contained in figure G and node u is not included in T ',
So node u and add spanning tree T during only in the l+1 times using v as starting point (root node) traversal, and the l+1 times traversal is obtained
The ultimate range that subtree interior joint and node v must be generated is l+1.
Therefore, if figure G in PL(u, v)=k, then node u and only in the kth time traversal using v as starting point (root node)
When add spanning tree T, and kth time traversal obtains generation subtreeInterior joint and node v ultimate range are k.
According to above-mentioned proof, if the ultimate range for being apparent from scheming G interior joints and node v is k, using v as starting point (root node)
Traversal depth be k.If Network Central Nodes of the node v for figure G, the i.e. node traverses degree of node v is minimum, therefore, using v for
Point, the traversal depth for traveling through whole network is minimum.
Prove half of the 3 network traverser degree not less than maximum node traverses degree.
Prove：If L=v1,v2,…,vnTo scheme G diameter, i.e. L is node v1,vnBetween shortest path, and L for figure G
In most long shortest path；Then network traverser degree is not less than the half of maximum node traversal degree.
It is apparent from, maximum node traversal degree is n.If v is the arbitrary node in figure G, if Nd(v) the node traverses degree for being v, and
If L1=v, u1,u2,…,v1And L2=v, u '1,u′2,…,vnRespectively node v to v1And vnShortest path.It is apparent from L1And L2
Length no more than Nd(v).Because L is node v1,vnBetween shortest path, so path L1∪L2=v1,…,u1,v,
v,u′1,…,vnLength be not less than n.Therefore, 2Nd(v) it is not less than L1∪L2Length, and L1∪L2Length be not less than n,
That is Nd(v)≥n/2。
Therefore, the node traverses degree of arbitrary node is not less than the half of maximum node traversal degree in figure G.Network center saves
Point is the node in figure G, and network traverser degree is that the node traverses degree of Network Central Node, i.e. network traverser degree are not less than maximum
The half of node traverses degree.
All there is Network Central Node in Netcentricity, any one network.Node traverses degree is equal to network traverser degree
Node is referred to as Network Central Node.On the premise of breadth First rule is followed, whole network is traveled through by Network Central Node
Travel through depth minimum.
The solution thought and the propagation of internet worm of network topology Centroid, the diffusion of network public-opinion and ntp server
Layering time service principle it is consistent, therefore Netcentricity both can for complex network defence the oretical Foundation Stone be provided, or
The precision time service of complex network information system provides solution.
Network topology Centroid searching algorithm
Input：Simple Connected undigraph G=(V, E), wherein | | V | |=n.
Output：Network Central Node collection Vc。
Step1. dijkstra's algorithm is used, V={ v are calculated1,v2,…,vnIn shortest path between arbitrary node pair
Length, and set up shortest path length matrix D=(dij)n×n, wherein dijRepresent node viWith vjBetween shortest path length,
dii=0 (i=1,2 ..., n).Turn Step2.
Step2. vector is calculatedWhereinAnd calculating network traversal degreeTurn Step3.
Step3. calculating network centromere point set：Algorithm terminates.
The application of network topology Centroid searching algorithm, the network topology of a Complex Information System as shown in Figure 2
Structure.In fig. 2, node G1, G2, G3, G4, G5, G6, G7, G8, G9, G10, G11, G12, G13, G14 and G15 node time
Degree of going through is respectively 6,5,4,5,5,5,6,5,6,7,5,5,5,6 and 7.
Understand accordingly, network traverser degree is that 4, G3 is network topology Centroid.
, can on-premise network time master server at heart node G3 in a network for the unified time service of Complex Information System
(NTP), by 4 layers of layering time service, the most precision time service to whole system can be reached, error only adds up by 4 times, and network
Time master server is deployed in other nodes, and error is cumulative to be not less than 4 times.
For the cyber-defence of Complex Information System, key protection targetedly can be carried out to Network Central Node G3,
To take precautions against the network attack of enemy.
Claims (4)
1. a kind of searching algorithm of complex network topologies Centroid, it is characterized in that：Its step is as follows：
1), network topology structure is obtained, and scans objective network, finds mobile host computers, obtains network topology structure；
2), node non-directed graph is obtained, and each node and connectedness of the objective network topological structure that step 1 is obtained use simple undirected
Connected network structure G=(V, E) expressions, wherein V and E are respectively the set on node and side；
3), node traverses degree is solved, solution node v ∈ V in the simple undirected connected network structure G=(V, E) obtained to step 2
To the shortest path of other nodes, the maximum for choosing shortest path is node traverses degree；If node v1,v2∈ V are scheming G most
Short path length is PL(v1,v2), then node v is in network structure G node traverses degree：Nd(v)=maxu∈V(PL(u,v))；
4), network traverser degree is solved, according to step 3, solves each node v in simple undirected connected network structure G=(V, E)
Node traverses degree, the minimum value for choosing node traverses degree is network traverser degree；Network structure G network traverser degree is：Nd=
minv∈V(Nd(v))；
5), network topology Centroid is solved, according to step 4, if node v ∈ V node traverses degree is equal to network traverser degree, i.e.,
Nd(v)=Nd, then predicate node v is network topology Centroid.
2. a kind of searching algorithm of complex network topologies Centroid, it is characterized in that：There is Centroid, root in the network topology
According to defining 1,2 and 3, network there will necessarily be Network Central Node, and construction only includes the network structure G of two nodes, then network knot
There are two Network Central Nodes in structure G, i.e. the Centroid of network structure G is not unique；Define 1 node traverses degree：In network,
Node is to the shortest path of each other node, the maximum of fewest number of hops；Define 2 network traverser degree：All nodes in network
The minimum value of traversal degree；Define 3 network topology Centroids：Node traverses degree is referred to as network equal to the node of network traverser degree and opened up
Flutter Centroid.
3. a kind of searching algorithm of complex network topologies Centroid, it is characterized in that：It is described using network topology Centroid as rise
Point, the traversal depth for traveling through whole network is minimum, traversal depth refer to traversal tree interior joint and Network Central Node it is maximum away from
From；According to breadth first traversal principle, using Network Central Node v ∈ V as the traverse path of starting point, corresponding in network structure G
Spanning tree T by root node of v；Proved using induction：For arbitrary node u ∈ V, if the P in network structure GL(u, v)=
K, then node u and add spanning tree T during only in the kth time traversal using v as the root node of starting point, and kth time traversal is given birth to
Into subtreeInterior joint and node v ultimate range are k；
As k=1, all nodes adjacent with v are added spanning tree T, even P by the 1st traversal by starting point of vL(u,v)
=1 node u and add spanning tree T during only in the 1st time by starting point of v traversal, and the 1st traversal obtains generation subtreeThe ultimate range of interior joint and node v is set up for 1；
Assuming that setting up during k≤l, it will be proven below setting up during k=l+1：
If L=v, v1,v2,…,u1, u is any one shortest path between node v, u；It is apparent from L1=v, v1,v2,…,u1For
Node v, u1Between shortest path, and PL(u1, v)=l；According to assumed condition, node u1And only in the l using v as starting point
Spanning tree T is added during secondary traversal, and the l times traversal obtains generation subtreeInterior joint and node v ultimate range are l；
(1) if node u has added spanning tree T when traveling through for first l times：Because preceding l traversal obtains generation subtreeInterior joint
It is not more than l with node v ultimate range, so the beeline between node v, u is not more than l, with PL(u, v)=l+1 contradictions,
That is it is invalid that node u has added spanning tree T when traveling through for first l times；
(2) if node u does not add spanning tree T when traveling through for first l times：
If set U={ u1|u1It is adjacent with u, and u1On shortest path between v and u }, and set preceding l traversal acquisition generation
Set and be(it is apparent from)；Because side collection { (u1,u)|u1∈ U } it is both contained in network structure G and node u is not included in
T ', thus node u and add spanning tree T during only in the l+1 times using v as the root node of starting point traversal, and the l+1 time travels through
The ultimate range for obtaining generation subtree interior joint and node v is l+1；
Therefore, if in network structure G PL(u, v)=k, then node u and only in the kth time traversal using v as the root node of starting point
When add spanning tree T, and kth time traversal obtains generation subtreeInterior joint and node v ultimate range are k；
If the ultimate range for being apparent from network structure G interior joints and node v is k, the traversal depth using v as the root node of starting point is
k；If node v is network structure G Network Central Node, i.e. the node traverses degree of node v is minimum, therefore, using v as starting point, time
The traversal depth for going through whole network is minimum.
4. a kind of searching algorithm of complex network topologies Centroid, it is characterized in that：The network traverser degree is not less than maximum
The half of node traverses degree；If L=v1,v2,…,vnIt is node v for network structure G diameter, i.e. L1,vnBetween shortest path
Footpath, and L is the most long shortest path in network structure G；Then network traverser degree is not less than the half of maximum node traversal degree；
It is apparent from, maximum node traversal degree is n；If v is the arbitrary node in network structure G, if Nd(v) the node traverses degree for being v,
And set L1=v, u1,u2,…,v1And L2=v, u1′,u2′,…,vnRespectively node v to v1And vnShortest path；It is apparent from L1With
L2Length no more than Nd(v)；Because L is node v1,vnBetween shortest path, so path L1∪L2=v1,…,u1,v,v,
u1′,…,vnLength be not less than n；Therefore, 2Nd(v) it is not less than L1∪L2Length, and L1∪L2Length be not less than n, i.e.,
Nd(v)≥n/2；
Therefore, the node traverses degree of arbitrary node is not less than the half of maximum node traversal degree in network structure G；Network center
Node is the node in network structure G, and network traverser degree be the node traverses degree of Network Central Node, i.e. network traverser degree not
Less than the half of maximum node traversal degree.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101112049A (en) * | 2005-01-31 | 2008-01-23 | 松下电器产业株式会社 | Communication method and wireless communication apparatus |
| CN105812168A (en) * | 2014-12-31 | 2016-07-27 | 北京神州泰岳软件股份有限公司 | Method and device for plotting network topological diagram |
| CN105830403A (en) * | 2013-10-11 | 2016-08-03 | 瑞典爱立信有限公司 | High performance LFA path algorithms |
-
2017
- 2017-06-16 CN CN201710455259.9A patent/CN107040467B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101112049A (en) * | 2005-01-31 | 2008-01-23 | 松下电器产业株式会社 | Communication method and wireless communication apparatus |
| CN105830403A (en) * | 2013-10-11 | 2016-08-03 | 瑞典爱立信有限公司 | High performance LFA path algorithms |
| CN105812168A (en) * | 2014-12-31 | 2016-07-27 | 北京神州泰岳软件股份有限公司 | Method and device for plotting network topological diagram |
Non-Patent Citations (1)
| Title |
|---|
| 邵蓥侠、崔斌、马林、阴红志: ""一种基于Sketch的Top-k紧密中心性快速搜索算法"", 《计算机学报》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106815662A (en) * | 2017-03-28 | 2017-06-09 | 鲁可儿 | A kind of express mail service collecting and distributing centre and method for solving |
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