Aug 2026· Iconic research and engineering journals· Vol 10, pp. 1437-1445· 0 citations· 12 references
TL;DR
This paper conducts a case study on Zachary's Karate Club network and a synthetically generated scale-free network, computing centrality measures, detecting communities using the Louvain algorithm, and analysing degree-distribution behavior.
Abstract
- Social networks generate vast amounts of relational data whose value lies not in individual data points but in the structure of connections among them. Graph analytics offers a mathematically grounded toolkit for uncovering this structure, ranging from simple degree counts to sophisticated community-detection and influence-propagation models. This paper presents a self-contained treatment of graph analytics as applied to social networks. We review the foundational graph-theoretic concepts underlying social network analysis, survey the principal families of graph analytics methods, and examine community detection and influence analysis in depth. To ground the discussion empirically, we conduct a case study on Zachary's Karate Club network and a synthetically generated scale-free network, computing centrality measures, detecting communities using the Louvain algorithm, and analysing degree-distribution behavior. The Louvain method partitions the Karate Club network into four communities with a modularity of 0.4266, closely matching the network's known factional split, while the synthetic network exhibits an approximate power-law degree distribution with exponent 1.76, consistent with preferential-attachment growth. We conclude with a discussion of open challenges and directions for future research, including dynamic graph analytics, scalability to billion-edge networks, and privacy-preserving analysis.
Graph theory has evolved from a branch of discrete mathematics concerned with abstract vertex-edge structures into the principal mathematical language for representing and analyzing complex networks, systems whose components interact through relationships that themselves carry structural, and often computationally exploitable, information. This paper reviews the foundational and applied graph-theoretic literature underlying complex network analysis and intelligent system design, tracing the field's development from classical random graph theory through the small-world and scale-free network models that reshaped network science at the turn of the century, and into the more recent graph representation learning and graph neural network (GNN) literature that has integrated graph-theoretic structure directly into machine learning architectures. The review synthesizes foundational random-graph and preferential-attachment models, structural analysis techniques including centrality measures and community detection, and the graph embedding and graph neural network methods that now underlie intelligent system design across recommendation, molecular modelling, and physical simulation domains. Distinct comparative tables map generative network model families onto their structural signature and generating mechanism, cross-reference classical structural analysis measures against their intelligent-system design application, and set graph neural network architecture families against the computational mechanism and task type each is best suited to address. The paper concludes that intelligent system design increasingly depends on selecting a graph-theoretic representation and analysis method whose structural assumptions match the target network's actual generative structure, rather than applying a single default graph model universally, and identifies the theoretical understanding of graph neural network expressiveness limits as the central future research prospect.
Unknown authors· International journal of com...· 0 citations
A novel heuristic community detection algorithm, termed CoDeSEG, which identifies communities by minimizing the network's two-dimensional structural entropy within a potential game framework, and introduces a structural entropy-based node overlapping heuristic for detecting overlapping communities, with a near-linear time complexity.
Centrality measures are defined for simple graphs -- directed, undirected, weighted or unweighted. Attributed graphs have to be reduced to simple graphs for computing centrality measures. However, when applications with multiple types of relationships are modeled using multilayer networks (MLNs), simple graph algorithms cannot be directly used. Existing approaches typically analyze MLNs by aggregating layers of an MLN into a single graph, which results in the loss of structural and semantic information. The semantic information loss can be more pronounced particularly, in weighted networks. This work focuses on computing degree centrality in weighted homogeneous multilayer networks (HoMLNs) using a decoupling-based framework. The framework performs independent layer-wise analysis on MLNs without reducing them to simple graphs. The decoupling approach allows use of exiting algorithms for each layer and uses minimal information from individual layers for computing degree centrality of HoMLNs. We propose heuristic-based algorithms that strike a balance between accuracy and efficiency. The proposed methods are evaluated against ground truth (GT) results obtained using Boolean OR aggregation and naive baselines. Experimental results on both synthetic and real-world HoMLN datasets demonstrate that the heuristics achieve accuracy comparable to the ground truth while significantly improving computational efficiency, thereby establishing the scalability and effectiveness of the HoMLN algorithms developed using the decoupling approach.
A. Ayowole-Obi, Abhishek Santra, Sharma Chakravarthy· 0 citations
A diffusion-enhanced inductive link prediction framework that combines Graph Diffusion Convolution (GDC), structural node descriptors, and neighborhood aggregation from GraphSAGE is proposed that achieves higher accuracy than the other models on the benchmark datasets.
This study introduces a new ranking framework that integrates a quasi-Laplacian structural measure with a gravity-inspired aggregation process and demonstrates that the proposed framework consistently outperforms existing techniques in terms of accuracy, resolution, and computational simplicity.
Statistical analysis of collections of networks, where each network is treated as the primary unit of observation, is of growing importance across a wide range of application domains, including gene regulatory, social, and financial networks. As networks consist of vertices and edges that do not naturally reside in Euclidean space, the direct application of conventional statistical methodologies, such as the computation of means and covariances, principal component analysis, and hypothesis testing, to samples of networks is not straightforward. A central challenge lies in defining meaningful measures of similarity or distance between networks of potentially varying sizes and structural types (e.g., directed, undirected, weighted or unweighted), particularly when no predefined node correspondence exists. To address these challenges, we introduce a framework termed functional topological data analysis (funTDA), which integrates tools from functional data analysis and topological data analysis to facilitate exploratory data analysis and inference on samples of networks. The proposed framework enables the computation of summary statistics, including means and variances, and supports the application of principal component analysis and hypothesis testing to topological features extracted from network data. Through simulation studies involving networks with varying connectivity structures, we demonstrate the ability of funTDA to distinguish between distinct network configurations. The methodology is illustrated through two real-data applications: networks constructed from pairwise word co-occurrences in novels by Jane Austen and Charles Dickens, and gene regulatory networks derived from gene expression measurements for seventeen individuals exposed to H3N2 influenza. In both applications, differences in network topology are assessed using principal component analysis and hypothesis testing.