Graph Centrality Calculation via Subgraph Sampling
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Solution Overview
Problem
The calculation of graph centrality in large networks is resource-intensive and time-consuming, leading to excessive overheads and timeliness issues due to the increasing size of networks with millions of nodes and billions of edges.
Innovation Solution
A method involving sampling sequentially connected nodes and edges in an original graph to obtain sampled sub-graphs, calculating node influence, mapping results back to the original graph, clustering, and sorting to identify top-ranked nodes, thereby reducing the size of the graph and improving calculation efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If graph centrality is calculated on the original large graph, then calculation accuracy is maintained, but calculation resource overheads and time overheads increase significantly
Solution Approach 1:
The original large graph is segmented into multiple sampled sub-graphs through random sampling of nodes and edges. This allows the centrality calculation to be performed on smaller, manageable sub-graphs rather than the entire large graph, significantly reducing computation time while maintaining acceptable accuracy through aggregation of results from multiple samples.
Solution Approach 2:
Instead of calculating centrality for all nodes in the original graph, the method performs partial calculations on sampled sub-graphs. Multiple samples are taken and their results aggregated, providing an approximate solution that is sufficiently accurate for practical purposes while requiring far less computational resources than a complete calculation.
2Reliability
If graph centrality is calculated on the original large graph, then complete node influence assessment is achieved, but calculation resource overheads become excessive
Solution Approach 1:
The graph is divided into multiple sampled sub-graphs, allowing centrality calculations to be distributed across these smaller segments. This segmentation reduces the computational burden on any single processing unit while collectively providing a comprehensive assessment of node influence through aggregation of multiple samples.
Solution Approach 2:
Multiple copies of the sampling process are performed independently on the original graph. Each sample creates a sub-graph copy that is processed separately, and the results are then combined. This approach allows parallel processing and reduces the resource overhead compared to processing the single large graph comprehensively.
3Productivity
If sampling is performed to reduce graph size, then calculation time is reduced, but calculation complexity increases due to multiple sampling iterations
Solution Approach 1:
The sampling process is performed periodically multiple times with different random seeds to generate multiple independent sub-graph samples. This periodic sampling approach systematically explores the graph structure from different perspectives, and the results are aggregated to produce a robust centrality estimate that balances speed and accuracy.
Solution Approach 2:
The method incorporates feedback mechanisms where the results from each sampling iteration are aggregated and used to refine the overall centrality estimation. The aggregation process provides feedback that helps determine when sufficient sampling has been performed, allowing the system to balance computational effort with result quality.
Data Source
AI summary
A graph centrality determining method includes sampling, at least twice, nodes that are sequentially-connected and connection edges between the nodes, in an original graph representing a network structure, to obtain sampled sub-graphs, determining an influence of each of nodes in the sampled sub-graphs, forming a graph centrality determining result of each of the sampled sub-graphs, based on the influence of each of the nodes in the sampled sub-graphs, determining result of each of the sampled sub-graphs, to the original graph, to obtain an influence of each of the nodes in the original graph, clustering the influence of each of the nodes in the original graph, sorting the influence of each of the nodes in the original graph in descending order of a result of the clustering, and obtaining a predetermined quantity of nodes having influences that are top-ranked, in the original graph.