CN109120452B - Complex network overall efficiency optimization method based on network pruning - Google Patents
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Abstract
The invention discloses a complex network overall efficiency optimization method based on network pruning. The method comprises the following steps: solving the maximum connected branch of the network and calculating the overall efficiency of the network; respectively calculating the overall efficiency corresponding to each deleted node according to the obtained maximum connected branch, and comparing the overall efficiency with the original overall efficiency one by one; acquiring a node set to be pruned; judging whether to optimize according to the number of elements in the node set; selecting to execute or finish optimization according to the judgment result; and under the condition of executing optimization, deleting the nodes and the adjacent edges thereof in the node set to be pruned to form a new network, and executing the steps again. The invention is suitable for simplifying the structure of a large number of actual complex systems, and provides a reference scheme for improving the network communication performance, the overall intercommunication efficiency, saving hardware facilities, optimizing energy consumption and the like.
Description
Technical Field
The invention relates to a method for optimizing the overall efficiency of a network, in particular to a method for optimizing the overall efficiency of a complex network based on network pruning.
Background
Human life and production activities depend on a large number of complex systems, both natural and man-made, and for a given system, the connections and interaction patterns between the components can be represented by networks, the components of the system can be abstracted into nodes in the network, and the connections between the components can be abstracted into edges.
The efficiency of the network is a measure of the transmission and exchange capabilities of carriers such as information, and therefore, the network has attracted much attention in the application fields of network science, Internet of things and the like. The inverse of the path length between nodes is usually calculated efficiently, so it is easier to measure unconnected nodes than the average path length.
Network efficiency can be applied to the whole and local parts of the network, wherein the whole efficiency quantifies the capacity of the carrier to exchange at each part of the network at the same time, and the local efficiency quantifies the resistance of the network to small-scale faults. Currently, some of the research on network efficiency focuses on efficiency and cost to achieve efficiency under different network topologies. In addition, much research is focused on the influence of network scale change and network attack on efficiency. In view of the existing research combination, whether the network is attacked randomly in a small scale or intentionally at important nodes with certain centralized indexes, the overall efficiency of the network is usually reduced, and only under different network structures, the reduction proportion is different. Current techniques lack active optimization of overall efficiency and instead passively suffer from a drop in efficiency after a random or deliberate attack.
Disclosure of Invention
In order to solve the optimization problem of the overall efficiency of the network, the invention compares the influence on the overall efficiency before and after each node is deleted on the basis of pruning the original network into the maximum connected branch, and then implements further pruning. And continuously repeating the pruning process on the pruned network to implement the dynamic optimization of the overall efficiency of the network.
In order to achieve the technical purpose, the technical scheme of the invention is that a complex network overall efficiency optimization method based on network pruning comprises the following steps,
the method comprises the following steps: and solving the maximum connected branch of the network and calculating the overall efficiency of the network. The maximum connected branch of the network is solved, and the overall efficiency is calculated.
Step two: respectively calculating the overall efficiency of each deleted node according to the maximum connected branch obtained in the step one, and obtaining an array of the overall efficiency values of the deleted nodes;
step three: subtracting the integral efficiency value obtained in the first step from the integral efficiency value obtained in the second step to obtain an efficiency deviation array; then screening the non-positive numerical values in the deviation array, and taking the corresponding nodes as elements of a node set to be trimmed; judging whether to execute optimization according to the number of elements in the set and the size of the pruning scale;
step four: deleting the nodes and the adjacent edges thereof in the set in the maximum connected branch obtained in the step one according to the optimization execution situation in the judgment result obtained in the step three, thereby generating a new network; and returning to the step one again, and circulating the steps to implement dynamic optimization.
The initial network is defined as G (N, G), where N is the set of nodes of the network and G is the set of edges of the network.
In the method, the step of calculating the maximum connected branch of the network in the step one is as follows:
step 1, solving all connected branches:
wherein, N 'is the set of nodes in the network connected branch, and g' is the set of edges in the network connected branch.
Π G (N ', G') represents the set of all connected branches, i, j ∈ N 'and ij ∈ G represents that in the process of searching all nodes, each connected branch G (N', G ') is established, and the conditions that the node i and the node j belong to N' and a path exists between the node i and the node j in G (N, G) to be connected must be met simultaneously.
Indicating that N ' is a non-empty set and that N ' and g ' belong to N and g. It is easy to understand that when N ' is determined in each connected branch, the edges connecting the nodes included in N ' in G (N, G) constitute G '.
Step 2 finding the maximum connected branch
Obtaining the maximum connected branch from the connected branch set obtained in the step 1 of the step one:
C(NC,gc)＝G(max(Π(N')),g'max)
where C (NC, gc) represents the maximum connected branch, max (Π (N ')) represents the maximum subset of the set of all N ', g 'maxIndicating that this maximum subset of nodes corresponds to the set of edges in g.
Step 3, calculating the length of the shortest path between any two nodes in the maximum connected branch;
dij＝min{P1 i→j,P2 i→j,...,Pn i→j}
wherein d isijRepresenting the shortest path length from node i to node j (i < j), n is the number statistic of the shortest paths from node i to node j, Pk i→jThe length value of the k path from the node i to the node j is represented, namely the number of edges passed by the k path; { P1 i→j,P2 i→j,...,Pn i→jIs the set of all path length values from node i to node j.
Step 4 calculating the overall efficiency of the maximum connected branch
Wherein E represents the overall efficiency of the maximum connected branch, NC is the set of nodes in the maximum connected branch, and gc is the set of edges in the maximum connected branch;
in the second step, the step of calculating the overall efficiency after deleting each node is as follows:
step 1 calculating the overall efficiency after deleting each node
Wherein E (G)i) Overall efficiency of the network obtained after deletion for node i and adjacent edges
Step 2, obtaining the whole efficiency array after the node deletion
AE＝(E(Gi))
Wherein A isEArray of overall efficiency values (E (G) for the network obtained after deletion for each node ii))
In the method, the step of calculating the overall efficiency deviation in the step three is as follows:
step 1 calculating the overall efficiency deviation
A＝AE-E
Wherein A isAnd subtracting the overall efficiency value of the network obtained after deleting each node i from the overall efficiency E of the maximum connected branch to obtain an array.
Step 2, solving a node set to be deleted
Nr＝{i|A(i)≤0}
Wherein N isrFor node sets to be deleted, i.e. AThe set of nodes corresponding to the numerical values of 0 or less.
Step 3, judging whether to optimize;
judging whether to optimize according to the node pair set obtained in the step 2 in the third step and the number of elements in the set and the size of the trimming scale, wherein the step is as follows:
wherein
Is represented by the pair "NrThe number of elements in the tree is more than or equal to 1, and the ratio of the trimmed connected branch node scale NC to the original network scale N is more than a threshold value
"this proposition is judged true and false; t represents that the proposition judgment result is true, namely entering the next optimization stage; f represents that the proposition judgment result is false, namely the optimization is terminated. Threshold value
The user can set the trimming scale, and a certain degree of freedom is given to the user.
In the method, the step four of performing optimization includes:
optimizing according to the situation that the optimization needs to be executed in step 3 in the third step, wherein the steps are as follows:
Gnew(NW,gw)＝C(NC,gc)-G(Nr,gr)
this step prunes the largest connected branch, where Gnew(NW, gw) is a new network obtained after pruning the network, NW is a set of nodes in the new network, and gw is a set of edges in the network; gr is N in the maximum connected branchrOf the set of adjacent edges.
The invention implements the optimization of the whole efficiency from two network branches and node deletion efficiency levels. The first level is to prune the smaller branches of the network, leaving the largest branch. For real-world network structures, a branch occupying most of the network exists in a large number of social networks and information networks, and the communication and efficiency of the network are mainly reflected in the branch. For branches other than the maximum branch, especially for branches composed of isolated single nodes, pruning the branches will reduce the number of nodes. According to the calculation formula of the overall efficiency, the overall efficiency is improved under the condition that the path length is kept unchanged and the number of nodes is reduced. And the other layer is to prune the nodes with non-positive efficiency and the adjacent edges thereof in the maximum connected branch by comparing the overall efficiency of the network after the single node is deleted with the original overall efficiency. If the pruned network is not completely connected, the steady state of the network structure and the overall efficiency can be achieved by repeating the pruning. The network finally obtained after optimization only comprises one connected branch, the optimization can improve the efficiency and the economy of the structure, the user trimming scale freedom degree is given, and the scale of the connected branch after trimming is limited through a trimming threshold value.
Compared with the prior art, the invention implements network pruning by taking optimization of overall efficiency as a target, rather than exploring the network structure simply through efficiency reduction after attacking network nodes. In fact, the attack or deletion of a single node does not necessarily bring about the reduction of the overall efficiency of the network, so the invention starts from the global efficiency characteristic of the single node and prunes the network in a targeted manner.
The invention implements network pruning from two layers, optimizes the overall efficiency and the economy of the network, and provides an optimization scheme of the overall efficiency for the design of network communication hardware facilities.
The invention will be further explained with reference to the drawings.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a complex network in accordance with the present invention;
FIG. 3 is a schematic diagram of a first optimization performed in the present invention;
FIG. 4 is a schematic diagram of performing a second optimization in accordance with the present invention.
Detailed Description
Referring to fig. 1, fig. 1 is a flow chart of the present invention. The following illustrates a specific embodiment of the present invention.
Example 1: optimization of overall efficiency of random network
1) Obtaining complex networks
In this embodiment, a random complex network with 50 nodes is denoted as G. The network is denoted G ═ N, G, where N is the set of nodes and G is the set of edges between nodes. The nodes contained in N are { v1, v2, …, v50 }. In the network, nodes v1-v9, v1-v18, v1-v20, v1-v34, v3-v6, v5-v12, v5-v16, v5-v37, v37-v 37, v37-v 37, v-v 37, v37-v 37, v-v 37, v32-v3, v32-v6, v32-v36, v32-v41, v33-v47, v34-v7, v34-v27, v27-v 27, v27-v 27, v27-v 27, v27-v 27, v27-v 27-v, An undirected and unweighted edge exists among v43-v48, v44-v39, v45-v38, v46-v28, v46-v33, v47-v14, v47-v34, v47-v45, v48-v42, v49-v44, v50-v3, v50-v30 and v50-v43, and other nodes are not connected.
Fig. 2 is a schematic diagram of a complex network obtained according to connection between nodes in embodiment 1 of the present invention.
2) Computing maximum connectivity branch and corresponding overall efficiency of a network
The set of branches is { G (N1 ', G1'), G (N2 ', G2'), G (N3 ', G3') }. N1 ' is node v15, N2 ' is nodes v19 and v25, and N3 ' is the remaining 47 nodes in the graph. Therefore, the maximum communication branch C (NC, gc) is G (N3 ', G3'). Namely, the 3 nodes of v15, v19 and v25 are not included in the maximum communication branch. The corresponding overall efficiency was 0.4218 by combining the lengths of the shortest paths between any two nodes in G (N3 ', G3').
3) Calculating the overall efficiency and the efficiency deviation after deleting each node
The overall efficiency corresponding array after deleting each node in G (N3 ', G3') is [0.4176,0.4276,0.4230,0.4245,0.4146,0.4218,0.4211,0.4213,0.4194,0.4291,0.4216,0.4079,0.4221,0.4217,0.4242,0.4270,0.4183,0.4239,0.4171,0.4149,0.4217,0.4211,0.4226,0.4177,0.4187,0.4254,0.3926,0.4183,0.4121,0.4191,0.4149,0.4194,0.4145,0.4020,0.4100,0.4217,0.4149,0.4201,0.4143,0.4144,0.4222,0.4181,0.4227,0.4095,0.4219,0.4245,0.4217 ]. Subtracting the array from 0.42175 to obtain the deviation array [ -0.0042,0.0058,0.0013,0.0027, -0.0071,0.0001, -0.0006, -0.0005, -0.0024,0.0073, -0.0002, -0.0138,0.0004, -0.0000,0.0025,0.0053, -0.0034,0.0021, -0.0046, -0.0069, -0.0001, -0.0007,0.0008, -0.0040, -0.0030,0.0036, -0.0292, -0.0034, -0.0097, -0.0027, -0.0068, -0.0023, -0.0072, -0.0198, -0118, -0.0000, -0.0069, -0.0016, -0.0075, -0.0074,0.0005, -0.0037, 0.0079, -0009, -36465, -369, -7, 9, v49}
4) Determining whether to optimize
Assume that the user sets the threshold for the crop size to be 0.6, i.e., the crop size is cut off after exceeding 40%. Here, the number of elements in the node set to be pruned is greater than 1 (15), and the existing network size is 47 (3 nodes v15, v19 and v25 are pruned when the maximum connected branch is found), and the pruning threshold is not exceeded (47/50>0.6), so that the optimization is performed, and a network (47-15) containing 32 nodes is obtained after pruning.
Fig. 3 is a diagram illustrating the result of the first pruning optimization in embodiment 1 of the present invention.
5) New round of optimization
And calculating the maximum connected branch of the new network, namely the new network, corresponding to the overall efficiency 0.4755, and obtaining a set of nodes to be pruned in the same calculation mode as { v7, v11, v12, v14, v22, v23, v24, v28, v33, v35, v38, v39, v40, v41 and v50 }. The number of elements of the node set to be pruned is larger than 1 (15), the existing network size is 32 (3 +15 nodes are pruned cumulatively), the pruning threshold is not exceeded (32/50>0.6), the optimization condition is still met, and the optimization is continuously executed. After pruning, a network (32-15) containing 17 nodes is obtained.
Fig. 4 is a diagram illustrating the result of the second pruning optimization in embodiment 1 of the present invention.
And calculating the maximum connected branch of the new network, namely the new network, corresponding to the overall efficiency 0.5558, and obtaining a set of nodes to be pruned in the same calculation mode as { v1, v5, v8, v18, v21, v30, v31, v32, v36 and v45 }. The number of elements in the node set to be pruned is greater than 1 (10), but the existing network size is 17 (3 +15+15 nodes have been pruned cumulatively), the pruning threshold is exceeded (17/50 ≦ 0.6), and the optimization ends.
The above is an example analysis of the overall efficiency optimization of a complex network.
Claims (5)
1. A complex network overall efficiency optimization method based on network pruning is characterized by comprising the following steps,
the method comprises the following steps: solving the maximum connected branch of the network and calculating the overall efficiency of the network;
step two: calculating and recording the overall efficiency after deleting one node according to the maximum connected branch obtained in the step one, then reselecting the deleted node for calculation until each node is selected, and obtaining an array of the overall efficiency values after deleting the nodes;
step three: subtracting the overall efficiency value obtained in the first step from the overall efficiency value obtained in the second step to obtain an efficiency deviation array; then screening a non-positive numerical value in the efficiency deviation array, and taking a corresponding node as an element of a node set to be trimmed; judging whether to execute optimization according to the number of elements in the set and the size of the pruning scale;
step four: deleting the nodes and the adjacent edges thereof in the set in the maximum connected branch obtained in the step one according to the optimization execution situation in the judgment result obtained in the step three, thereby generating a new network; and returning to the step one again, and circulating the steps to implement dynamic optimization.
2. The method of claim 1, wherein said first step comprises the steps of:
step 1, solving all connected branches:
wherein G (N, G) is an initial network, N is a set of nodes of the network, G is a set of edges of the network, N 'is a set of nodes in a network communication branch, and G' is a set of edges in a network communication branch;
II, G (N ', G') represents a set of all connected branches, i, j ∈ N 'and ij ∈ G represent that in the process of searching all nodes, each connected branch G (N', G ') is established, and the conditions that the node i and the node j belong to N' and a path exists between the node i and the node j in G (N, G) to be connected must be met simultaneously;
indicating that N ' is a non-empty set and that N ' and g ' belong to N and g;
step 2, solving a maximum connected branch:
solving the maximum connected branch from the connected branch set obtained in the step 1:
C(NC,gc)＝G(max(Π(N')),g'max)
where C (NC, gc) represents the maximum connected branch, NC is the set of nodes in the maximum connected branch, gc is the set of edges in the maximum connected branch, max (Π (N ')) represents the maximum subset of the set of all N ', g 'maxRepresenting that the maximum subset of the node corresponds to the edge set in g;
step 3, calculating the length of the shortest path between any two nodes in the maximum connected branch:
dij＝min{P1 i→j,P2 i→j,...,Pn i→j}
wherein d isijRepresenting the shortest path length from node i to node j (i < j), n is the number statistic of the shortest paths from node i to node j, Pk i→jThe length value of the k path from the node i to the node j is represented, namely the number of edges passed by the k path; { P1 i→j,P2 i→j,...,Pn i→jThe set of all path length values from node i to node j;
step 4, calculating the overall efficiency of the maximum connected branch:
where E represents the overall efficiency of the maximum connected branch and NNC represents the number of nodes in the maximum connected branch.
3. The method according to claim 2, wherein the second step comprises the steps of:
step 1), calculating the overall efficiency after deleting each node:
wherein E (G)i) NNC for the overall efficiency of the network obtained after deletion of node i and adjacent edgesiIndicates the number of nodes remaining after deleting node i in the maximum connected branch, NCiRepresenting a node set after deleting the node i in the maximum connected branch;
step 2), obtaining an overall efficiency array after node deletion:
AE＝(E(Gi))
wherein A isEArray of overall efficiency values (E (G) for the network obtained after deletion for each node ii))。
4. The method of claim 3, wherein step three comprises the steps of:
step one, calculating the integral efficiency deviation:
A＝AE-E
wherein A isSubtracting the overall efficiency value of the network obtained after deleting each node i from the overall efficiency E of the maximum connected branch to obtain an array;
solving a node set to be deleted:
Nr＝{i|A(i)≤0}
wherein N isrFor node sets to be deleted, i.e. AA set of nodes corresponding to values of 0 or less;
step three, judging whether to optimize:
judging whether to optimize according to the number of elements in the set and the size of the trimming scale of the node pair set obtained in the step II, wherein the step II comprises the following steps:
wherein (card (N)r) Not less than 1 and
) Is represented by the pair "NrThe number of elements in the tree is more than or equal to 1, and the ratio of the trimmed connected branch node scale NC to the original network scale N is more than a threshold value
"this proposition is judged true and false; t represents that the proposition judgment result is true, namely entering the next optimization stage; f represents that the proposition judgment result is false, namely the optimization is terminated.
5. The method of claim 4, wherein said step four comprises the steps of:
optimizing according to the situation that the optimization needs to be executed, and the steps are as follows:
Gnew(NW,gw)＝C(NC,gc)-G(Nr,gr)
this step prunes the largest connected branch, where Gnew(NW, gw) is a new network obtained after pruning the network, NW is a set of nodes in the new network, and gw is a set of edges in the network; gr is N in the maximum connected branchrOf the set of adjacent edges.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104992259A (en) * | 2015-05-19 | 2015-10-21 | 浪潮软件集团有限公司 | Complex network survivability and key node analysis method based on community structure |
| CN105453494A (en) * | 2014-05-21 | 2016-03-30 | 华为技术有限公司 | Virtual shortest path tree establishment and processing method, and path computation element |
| CN108011784A (en) * | 2017-12-11 | 2018-05-08 | 湖南工程学院 | A kind of dynamic optimization method of the worst connectivity of network |
| CN108462632A (en) * | 2016-12-09 | 2018-08-28 | 湖南工程学院 | A kind of trunk path extracting method of directed complex networks |
-
2018
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105453494A (en) * | 2014-05-21 | 2016-03-30 | 华为技术有限公司 | Virtual shortest path tree establishment and processing method, and path computation element |
| EP3139552A1 (en) * | 2014-05-21 | 2017-03-08 | Huawei Technologies Co., Ltd. | Virtual shortest path tree establishment and processing method, and path computation element |
| CN104992259A (en) * | 2015-05-19 | 2015-10-21 | 浪潮软件集团有限公司 | Complex network survivability and key node analysis method based on community structure |
| CN108462632A (en) * | 2016-12-09 | 2018-08-28 | 湖南工程学院 | A kind of trunk path extracting method of directed complex networks |
| CN108011784A (en) * | 2017-12-11 | 2018-05-08 | 湖南工程学院 | A kind of dynamic optimization method of the worst connectivity of network |
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