Steepest Ascent Graph Network Analysis with Weighted Slope Measures
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Solution Overview
Problem
Conventional methods for analyzing networks, such as those based on Eigenvector centrality (EVC) and steepest ascent graphs (SAG), do not fully reveal inherent nodal structures in all types of networks, leading to suboptimal analysis, monitoring, and control of information flow.
Innovation Solution
A system and method that compute node values and slope measures using link weight measures to generate a steepest ascent graph (SAG), which considers the strength of links to assign nodes to regions, providing a more detailed visualization of network structure and enabling better control of information flow.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Eigenvector centrality (EVC) and steepest ascent graph (SAG) methods are used to analyze networks, then the analysis method is simple and computationally efficient, but the inherent nodal structures in all types of networks are not fully revealed
Solution Approach 1:
The patent modifies the slope calculation by introducing a function of link weight measures to scale the differences in node values. This parameter change allows the analysis to capture weighted network structures more accurately while maintaining the overall EVC-SAG framework, thereby improving measurement precision without excessive complexity increase
Solution Approach 2:
The patent segments the network analysis into distinct components: node value calculation, slope measure determination with weight scaling, and SAG construction. This segmentation allows each component to be optimized independently, improving overall analysis accuracy while managing complexity through modular processing
2Loss of information
If link weight measures are incorporated into slope calculations to improve network structure visualization, then the analysis reveals more detailed network configurations, but the computational complexity increases
Solution Approach 1:
The patent performs preliminary calculation and storage of link weight measures before the slope calculation phase. This preliminary action ensures that weight information is readily available when computing slopes, reducing redundant calculations and minimizing computation time while still achieving complete network information representation
Solution Approach 2:
By changing the slope calculation parameter to include a function of link weights, the patent efficiently incorporates additional information about network structure. The functional form allows for scalable computation that balances information completeness with computational efficiency
Data Source
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AI summary
A system for analyzing a network including a plurality of nodes associated and/or connected together by links includes a processor coupled to a data memory. The processor is configured to access a first representation of the network and associated link weight measures w in the memory. Moreover, the system is configured to provide node values for the nodes and determine from the node values corresponding slope measures for links existing between the nodes, the slope measures being computed from a function of differences in node values and from the weight measures w for the links, the weight measures w being used for scaling the function of differences in nodes values; to select for at least some of the nodes one or more steepest ascent links having one or more greatest positive slope measures; and to generate a second representation corresponding to a steepest ascent graph of the network derived from information included in the steepest ascent links. The second representation is beneficially used for one or more of: (a) acting upon and/or modifying the selected nodes and/or links so as to improve network performance; and (b) presenting in a display the selected nodes and/or links for informing and supporting human intervention in the network's operation.