world applicability example generalized network

The gap

Supporting evidence — 7 representative gaps

• A study on rough graphs (2026) · doi

  We have established a unified framework for rough graph theory by extending the foundational definitions from partition-based to covering-based models. Recognizing that real-world systems—such as social networks and biological pathways—rarely adhere to disjoint classifications, we relaxed the strict requirement of equivalence relations. This shift allows for a more realistic mathematical modeling of overlapping communities and structural ambiguity. Our main theoretical and practical contributions are summarized as follows: • We generalized vertex-based rough graphs to settings where the vertex universe is granulated by a covering. Recognizing that Zakowski’s induced covering approach on Cartesian products 32 H. M. HAFEZ, K. A. DIB, R. EL-SHANAWANY, AND A. A. EL ATIK {P1, P4} P1 P4 P3 P5 {P2} P2 Core (Lower Approx) {P3, P5} Figure 7. PPI Network Example. The pathway H consists of {P1, P2, P3} (red). The covering (colored blobs) groups proteins by functional domain. P2 is the only node whose functional group is exclusive to the pathway. is only structurally sufficient for complete graphs, we introduced generalized approximation operators for arbitrary graphs and digraphs. We proved that this new framework inherently preserves topological consistency by eliminating invalid edges, while encompassing standard partition-based models (e.g., Sarwar’s approach) as special cases. • We introduced three distinct types of edge-based rough graphs, each tailored to handle structural approximations differently. The Type I model utilizes linked vertex and edge coverings to inherently guarantee the validity of the approximated subgraphs by preventing the formation of hanging edges. The Type II model applies an element-based granular approach to the entire graph universe. Finally, the Type III model refines this by providing a strictly edge-centric framework, which prevents overly coarse upper approximations by requiring explicit edge overlap. • We proposed three hybrid rough graph models that synthesize the vertex-priority and edge- priority approaches. By combining an independent vertex covering and an edge covering with their respective induced dependent coverings, we established a comprehensive multi-granulation environment for both the vertex and edge universes. We demonstrated that the intersection of these single-source approximations elegantly realizes a pessimistic multi-granulation rough set (MGRS) approximation, providing a robust, dual-perspective framework for graph granulation. • We demonstrated the practical utility of our proposed models through applications in social network analysis and protein-protein interaction (PPI) networks. These applications highlight how the upper approximation effectively captures “boundary” nodes—entities that act as vital bridges between a core community and external clusters. The theoretical foundation established in this paper opens several promising directions for future research. First, we plan to extend this framework by considering generalized binary relations, which will further relax the structural constraints and broaden the theoretical applicability of rough graphs. Second, while this study focused on one specific type of covering-based rough graph, the broader literature on covering-based rough sets offers a wide variety of approximation models. For instance, adapting the A STUDY ON ROUGH GRAPHS 33 diverse neighborhood operators and subsystem-based definitions explored by Yao [33] into the context of graph theory represents a rich and natural avenue for our future work.

  Keywords: rough based covering edge graph vertex graphs framework models approximation type established structural theoretical generalized
• Data Leakage Detection and Prevention System (2026) · doi

  Future enhancements to this project may include deploying the honeypot in a live network environment to capture real- world attack data, integrating automated alert notifications through email or messaging services, and implementing automated response mechanisms to block attackers dynamically. Additional analysis features such as long-term trend analysis, user behavior analytics, and integration with other security tools can further improve the system. These enhancements would make the project more scalable and closer to a real-world enterprise SOC implementation. © Author(s). This work is peer-reviewed, openly published, and permanently archived This article is openly accessible and reusable with proper attribution. https://ijsmt.org/ , Email: [email protected] 7 International Journal of Science, Strategic Management and Technology Volume 02 Issue 03 March-2026 | ISSN: 3108-1762 (Online) | Impact Factor: 3.8 An International, Peer-Reviewed, Open Access Scholarly Journal Indexed in recognized academic databases REFERENCE 1. Lance Spitzner, Honeypots: Tracking Hackers, Addison-Wesley Professional — Classic book explaining honeypots, including web-based honeypots and attacker analysis. 2. Chris Sanders, Practical Web Penetration Testing, Wiley — Covers web application attacks, logging, and monitoring techniques useful for web honeypots. 3. Mukesh Choudhary, Mastering Honeypots: Art of Deception for Cybersecurity Defense, BPB Publications — Practical guide on deploying and managing web-based honeypots integrated with SOCs. 4. Chee Keong Ng, Lei Pan & Yang Xiang, Honeypot Frameworks and Their Applications: A New Framework, Springer — Includes framework design for web honeypots and analysis workflows. 5. Alfred Basta & Nadine Basta, Open Source Security Operations Center (SOC): A Complete Guide — Explains SOC monitoring, log analysis, and response mechanisms relevant for web-based honeypots. REFERENCE WEBSITES 1. OWASP Web Application Security Testing Guide — Guidelines for testing web apps, attacks, and monitoring which is useful for web honeypots. https://owasp.org/www-project-web-security-testing-guide/ 2. The Honeynet Project – Web Honeypot Resources — Tools, research, and case studies specifically for web-based honeypots. https://www.honeynet.org/projects/ 3. Splunk – Monitoring Web-based Honeypots — Blog explaining how to log, analyze, and visualize web attack data in SOC dashboards. https://www.splunk.com/en_us/blog/learn/cybersecurity-honeypots.html 4. GitHub – HoneyWeb Project — Open-source web honeypot examples and scripts for research and SOC integration. https://github.com/search?q=web+honeypot

  Keywords: honeypots project honeypot https based security testing monitoring guide open enhancements deploying real world attack
• Integrating integrated circuit wastewater into the metal catalyst supply chain (2026) · doi

  The study demonstrates catalyst performance on PET conversion, but application to diverse real-world plastics beyond PET requires further investigation to establish broad applicability.

  Keywords: demonstrates catalyst performance conversion application diverse real world plastics beyond requires further investigation establish broad
• PENGARUH VARIASI SUHU PEMADATAN CAMPURAN TERHADAP KINERJA COLD PAVING HOT MIX ASBUTON (CPHMA) DENGAN PENAMBAHAN SEMEN PORTLAND (2026) · doi

  The paper does not address long-term durability or field performance testing of the optimized CPHMA mixture, limiting understanding of real-world applicability.

  Keywords: address long term durability field performance testing optimized cphma mixture limiting understanding real world applicability
• A path-integral approach to coupled discrete-continuous problems (2026) · doi

  Applicability to typical atmospheric situations is explored but not thoroughly validated against real-world atmospheric data or complex scenarios.

  Keywords: atmospheric applicability typical situations explored thoroughly validated against real world complex scenarios
• Ladder operators for Laguerre-type and Jacobi-type orthogonal polynomials (2026) · doi

  These conclusions can also be generalized to α > −1, based on the analysis in Example 13.

  Keywords: conclusions generalized based example
• Efficient machine learning approach for classification of malware with portable executable (PE) headers (2026) · doi

  Implementation of the system in real-world cybersecurity systems is needed to validate practical applicability.

  Keywords: implementation system real world cybersecurity systems needed validate practical applicability