# US 12,764,152 B2 · Evaluation of stability of edge-based communication networks > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,764,152 B2 - Document ID: US12764152B2 - Status: Granted - Kind: B2 - Application number: 19/008,739 - Filed: 2025-01-03 - Published: 2026-07-09 - Granted: 2026-10-13 - Earliest claimed: 2025-01-03 - Assignees: International Business Machines Corporation - Applicants: International Business Machines Corporation - Inventors: Rajesh Kumar Saxena; Harish Bharti; Sandeep Sukhija - Web page: https://patentgrep.com/patent/US12764152B2 ## CPC - H04L 63/1433: {Vulnerability analysis} - H04L 63/1416: {Event detection, e.g. attack signature detection} - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) ## Abstract Evaluation of stability in edge-based communication networks includes obtaining a first attribute of a candidate entity within a plurality of entities in the network. A partition model is generated based on the first attribute and a semantic graph representing relationships among entities. Time-series data reflecting various states of the network over time is generated, followed by the generation of stability data using advanced scalar functions that is the Lyapunov function. By analyzing the stability data and transitions between network states, causal entities contributing to instability are identified. The root cause data is generated and targeted repair commands are output to resolve the instability. ## Claims ### Claim 1 A computer-implemented method, comprising: obtaining, by a computer, at least one first attribute of a plurality of attributes, wherein each attribute of the plurality of attributes is associated with an entity of a plurality of entities within an edge-based network of communication devices, and wherein the at least one first attribute is associated with a candidate entity of the plurality of entities; generating, by the computer, at least one partition model of the edge-based network based on the at least one first attribute of the candidate entity and a semantic graph of the edge-based network, wherein the semantic graph includes a plurality of nodes that correspond to the plurality of attributes, and wherein the at least one partition model is parameterized as a time-evolving function that defines a plurality of first states of the edge-based network as a function of time; generating, by the computer, time-series data corresponding to a plurality of second states of the plurality of first states of the edge-based network between a first time epoch and a second time epoch of the edge-based network, based on the at least one partition model, wherein each state of the plurality of second states corresponds to a respective time instance of a plurality of time instances between the first time epoch and the second time epoch; generating, by the computer, stability data for the edge-based network, based on the time-series data and a scalar function, wherein the stability data indicates at least one scalar measurement of stability antipattern for the edge-based network, and wherein the at least one scalar measurement corresponds to at least one solution of an optimization problem for at least one time instance of the plurality of time instances between the first time epoch and the second time epoch; determining, by the computer, a curvature of a state transition for the edge-based network between the plurality of time instances, based on the stability data, wherein the at least one solution of the optimization problem defines the state transition for the edge-based network; determining, by the computer, at least one second attribute of the plurality of attributes based on the stability data and the curvature of the state transition, wherein the at least one second attribute is associated with a causal entity of the plurality of entities that contributes to instability in the edge-based network; and generating, by the computer, root cause data corresponding to the instability in the edge-based network, based on the at least one second attribute of the causal entity. ### Claim 2 (depends on 1) The computer-implemented method of claim 1, further comprising: querying the semantic graph based on the at least one first attribute of the candidate entity; and extracting at least one node of the plurality of nodes, based on the querying of the semantic graph, wherein the at least one node corresponds to the at least one first attribute of the candidate entity. ### Claim 3 (depends on 1) The computer-implemented method of claim 1, wherein the plurality of attributes comprises a region identifier associated with each entity of the plurality of entities, a device identifier associated with each entity of the plurality of entities, a time epoch for emitting data for each entity of the plurality of entities, and a satellite identifier associated with each entity of the plurality of entities. ### Claim 4 (depends on 1) The computer-implemented method of claim 1, further comprising: receiving, by the computer, incident data corresponding to a distributed denial of service in the edge-based network; and extracting, by the computer, the at least one first attribute of the candidate entity, based on the incident data. ### Claim 5 (depends on 1) The computer-implemented method of claim 1, further comprising generating the at least one partition model of the edge-based network, based on at least one template that defines at least one structural relationship between the plurality of entities. ### Claim 6 (depends on 1) The computer-implemented method of claim 1, wherein the scalar function is a Lyapunov function, and the curvature of the state transition corresponds to Lyapunov drift. ### Claim 7 (depends on 1) The computer-implemented method of claim 1, wherein the root cause data includes the at least one second attribute of the causal entity and causal relationship information defining a causal relationship between the causal entity and the instability in the edge-based network. ### Claim 8 (depends on 1) The computer-implemented method of claim 1, further comprising generating, targeted repair commands for fixing the instability in the edge-based network, based on the root cause data. ### Claim 9 A computer system, comprising: a processor set; one or more computer-readable storage media; and program instructions stored on the one or more computer-readable storage media, the program instructions executable by the processor set to cause the processor set to: obtain at least one first attribute of a plurality of attributes, wherein each attribute of the plurality of attributes is associated with an entity of a plurality of entities within an edge-based network of communication devices, and wherein the at least one first attribute is associated with a candidate entity of the plurality of entities; generate at least one partition model of the edge-based network based on the at least one first attribute of the candidate entity and a semantic graph of the edge-based network, wherein the semantic graph comprises a plurality of nodes that correspond to the plurality of attributes, and wherein the at least one partition model is parameterized as a time-evolving function that defines a plurality of first states of the edge-based network as a function of time; generate time-series data, corresponding to a plurality of second states of the plurality of first states of the edge-based network between a first time epoch and a second time epoch of the edge-based network, based on the at least one partition model, wherein each state of the plurality of second states corresponds to a respective time instance of a plurality of time instances between the first time epoch and the second time epoch; generate stability data for the edge-based network, based on the time-series data and a scalar function, wherein the stability data indicates at least one scalar measurement of stability antipattern for the edge-based network, and wherein the at least one scalar measurement corresponds to at least one solution of an optimization problem for at least one time instance of the plurality of time instances between the first time epoch and the second time epoch; determine a curvature of a state transition for the edge-based network between the plurality of time instances, based on the stability data, wherein the at least one solution of the optimization problem defines the state transition for the edge-based network; determine at least one second attribute of the plurality of attributes, based on the stability data and the curvature of the state transition, wherein the at least one second attribute is associated with a causal entity of the plurality of entities that contributes to instability in the edge-based network; and generate, root cause data corresponding to the instability in the edge-based network, based on the at least one second attribute of the causal entity. ### Claim 10 (depends on 9) The computer system of claim 9, wherein the program instructions further cause the processor set to: query the semantic graph based on the at least one first attribute of the candidate entity; and extract at least one node of the plurality of nodes, based on the query of the semantic graph, wherein the at least one node corresponds to the at least one first attribute of the candidate entity. ### Claim 11 (depends on 9) The computer system of claim 9, wherein the plurality of attributes comprises a region identifier associated with each entity of the plurality of entities, a device identifier associated with each entity of the plurality of entities, a time epoch for emitting data for each entity of the plurality of entities, and a satellite identifier associated with each entity of the plurality of entities. ### Claim 12 (depends on 9) The computer system of claim 9, further comprising an interface configured to receive incident data corresponding to a distributed denial of service in the edge-based network, and wherein the program instructions further cause the processor set to: obtain the at least one first attribute of the candidate entity, based on the incident data. ### Claim 13 (depends on 9) The computer system of claim 9, wherein the program instructions further cause the processor set to generate the at least one partition model of the edge-based network based on at least one template that defines at least one structural relationship between the plurality of entities. ### Claim 14 (depends on 9) The computer system of claim 9, wherein the scalar function is a Lyapunov function, and the curvature of the state transition corresponds to Lyapunov drift. ### Claim 15 (depends on 9) The computer system of claim 9, wherein the root cause data includes the at least one second attribute of the causal entity and causal relationship information, wherein the causal relationship information defines a causal relationship between the causal entity and the instability in the edge-based network. ### Claim 16 (depends on 9) The computer system of claim 9, wherein the program instructions further cause the processor set to generate, targeted repair commands for fixing the instability in the edge-based network, based on the root cause data. ### Claim 17 A computer-program product for generating root cause data of instability in an edge-based network of communication devices, the computer-program product comprising: one or more computer-readable storage media; and program instructions stored on the one or more computer-readable storage media to perform operations comprising: obtaining at least one first attribute of a plurality of attributes, wherein each attribute of the plurality of attributes is associated with an entity of a plurality of entities within the edge-based network, and wherein the at least one first attribute is associated with a candidate entity of the plurality of entities; generating at least one partition model of the edge-based network based on the at least one first attribute of the candidate entity and a semantic graph of the edge-based network, wherein the semantic graph comprises a plurality of nodes that correspond to the plurality of attributes, and wherein the at least one partition model is parameterized as a time-evolving function that defines a plurality of first states of the edge-based network as a function of time; generating time-series data corresponding to a plurality of second states of the plurality of first states of the edge-based network between a first time epoch and a second time epoch of the edge-based network, based on the at least one partition model, wherein each state of the plurality of second states corresponds to a respective time instance of a plurality of time instances between the first time epoch and the second time epoch; generating stability data for the edge-based network, based on the time-series data and a scalar function, wherein the stability data indicates at least one scalar measurement of stability antipattern for the edge-based network, and wherein the at least one scalar measurement corresponds to at least one solution of an optimization problem for at least one time instance of the plurality of time instances between the first time epoch and the second time epoch; determining a curvature of a state transition for the edge-based network between the plurality of time instances, based on the stability data, wherein the at least one solution of the optimization problem defines the state transition for the edge-based network; determining at least one second attribute of the plurality of attributes, based on the stability data and the curvature of the state transition, wherein the at least one second attribute is associated with a causal entity of the plurality of entities that contributes to the instability in the edge-based network; and generating, the root cause data corresponding to the instability in the edge-based network, based on the at least one second attribute of the causal entity. ### Claim 18 (depends on 17) The computer-program product of claim 17, wherein the operations further comprise: querying the semantic graph based on the at least one first attribute of the candidate entity; and extracting at least one node of the plurality of nodes, based on the query of the semantic graph, wherein the at least one node corresponds to the at least one first attribute of the candidate entity. ### Claim 19 (depends on 17) The computer-program product of claim 17, wherein the plurality of attributes comprises a region identifier associated with each entity of the plurality of entities, a device identifier associated with each entity of the plurality of entities, a time epoch for emitting data for each entity of the plurality of entities, and a satellite identifier associated with each entity of the plurality of entities. ### Claim 20 (depends on 17) The computer-program product of claim 17, wherein the operations further comprise: receiving incident data corresponding to a distributed denial of service in the edge-based network; and extracting the at least one first attribute of the candidate entity based on the incident data.