The proliferation in the use of Online Social Networks has revolutionized information sharing and consumption, leading to the development of advanced techniques such as link prediction, recommendation systems, community detection, node classification, and network representation learning. However, the availability and quality of real-world datasets for testing these algorithms pose challenges. Synthetic signed datasets generated through signed network reconstruction models offer alternatives for algorithm testing and experimentation. This survey presents an overview of state-of-the-art signed network reconstruction modeling techniques, evaluates their performance through rigorous experimental analysis, explores real-world applications, discusses challenges and open research problems, and guides future research efforts in the field. By consolidating knowledge and providing insights into existing models, this survey contributes to advancing the understanding and improvement of signed network reconstruction modeling. Various research papers discussed in this survey along with publicly available links to their codes are available at: https://github.com/Aikta-Arya/Signed-Network-Reconstruction-Modeling .

The proliferation in the use of social media and networking platforms has enhanced frequent interactions among individuals. The signed networks can be utilized to best perceive such complex relations. However, these real-world signed network datasets are scarce as the real-world signed datasets often involve dealing with sensitive information about individuals and their relationships. The ethical and privacy concerns of various social media platforms can further limit the availability of datasets for research and academic purposes. Furthermore, the availability of signed bipartite network datasets is even scarcer than signed network datasets. Existing signed network datasets also lack node/edge level attributes, yet recent trends in graph analytics have shown the significance of these features, for example, with GNNs, to advance benchmarking. To address such issues, we present three datasets in this paper: Reddit Posts (bipartite network with primary node level attributes and secondary level edge attributes), Bitcoin-OTC, and Bitcoin-Alpha datasets (signed networks with primary node and edge level attributes). Additionally, we explore potential research applications the dataset opens up across various domains. Various datasets discussed in this paper, along with already existing signed network datasets, are made publicly available using Signed Network Dataset Repository (SigNET Repo) at: https://aikta-arya.github.io/SigNET-/

Designing and analyzing network science algorithms, such as node classification, link prediction, and pattern identification (communities, triangles, dense sub-graphs, cliques), require diverse real-world datasets for performance evaluation. However, these datasets are often limited and small due to privacy concerns and platform access policies. This scarcity is even more pronounced for signed networks, as negative relationship data is rarely shared publicly. This PhD thesis aims to address this problem by generating realistic synthetic signed networks using the SNSRM and SISSRM models. Preserving the mesoscopic spectral and structural characteristics of the input signed network is crucial in this process. Additionally, this thesis tackles the challenge of efficiently analyzing elementary network property of triad enumeration by developing an triangle counting algorithm capable of enumerating balanced and unbalanced triads.

Privacy is one of the major concerns in the availability of large-scale real-world network datasets for various applications. Therefore, we require network models that can generate realistic synthetic networks of a very large scale that are capable of preserving patterns of given structural property in its evolution period. In this article, we proffer a novel network reconstruction model for signed networks, i.e., sequentially induced signed subnetwork reconstruction model (SISSRM), that is able to preserve the distribution of degrees, obsolescence, unbalanced, and balanced triangles, correlation among diverse triad types, spectral radius, degree correlation, and network balancedness during its growth process. SISSRM reproduces different structural properties of a given real-world signed network more accurately as compared to the considered state-of-the-art network models. The extensive experimentation on nine real-world empirical networks validates the significance of our proposed model in the generation of realistic synthetic signed networks.

Network modeling has been explored extensively by means of theoretical analysis as well as numerical simulations for Network Reconstruction (NR). The network reconstruction problem requires the estimation of the power-law exponent (γ) of a given input network. Thus, the effectiveness of the NR solution depends on the accuracy of the calculation of γ. In this article, we re-examine the degree distribution-based estimation of γ, which is not very accurate due to approximations. We propose X -distribution, which is more accurate than degree distribution. Various state-of-the-art network models, including CPM, NRM, RefOrCite2, BA, CDPAM, and DMS, are considered for simulation purposes, and simulated results support the proposed claim. Further, we apply X -distribution over several real-world networks to calculate their power-law exponents, which differ from those calculated using respective degree distributions. It is observed that X -distributions exhibit more linearity (straight line) on the log-log scale than degree distributions. Thus, X -distribution is more suitable for the evaluation of power-law exponent using linear fitting (on the log-log scale). The MATLAB implementation of power-law exponent (γ) calculation using X -distribution for different network models and the real-world datasets used in our experiments are available at https://github.com/Aikta-Arya/X-distribution-Retraceable-Power-Law-Exponent-of-Complex-Networks.git .

Modeling real-world signed networks is a challenging task due to the highly dynamic microlevel growth processes involved in it. The network reconstruction is a problem in which we define a model that not only captures the patterns followed by different structural and spectral properties of real-world networks but also minimizes numerical error. In this article, we define a simple yet an effective network generation mechanism that can learn model parameters efficiently and produces simulated networks having structural properties close to a given input real-world signed social network. In the proposed model, corresponding to each node, a characteristic function is defined that controls its dynamics and its link formation process. A family of exponential functions is suited well to include aging and local growth, including triangle formation of different types of balanced and unbalanced triangles, and produce a wide range of degree distributions. In the proposed model, two layers are modeled independently, and further superimposition of layers is applied to get the final simulated signed network. Apart from that, the experimental results manifest that our proposed model, signed network structural reconstruction model (SNSRM), is able to replicate the characteristic properties of the various real-world signed networks more closely compared to the state-of-the-art models.

Triangle count is a frequently used network statistic, possessing high computational cost. Moreover, this task gets even more complex in the case of signed networks which consist of unbalanced and balanced triangles. In this work, we propose a fastIncrementalTriangleCounting (ITC) algorithm for counting all types of triangles, including balanced and unbalanced. The proposed algorithm updates the count of different types of triangles for newly added nodes and edges only instead of recalculating the same triangle multiple times for the entire network repeatedly. Thus, the proposed ITC algorithm also works for dynamic networks. The experimental results show that the proposed method is practically efficient having run time complexity of$O(m k_{{\max}})$, where$m$represents the number of edges and$k_{{\max}}$represents the maximum degree of the given signed network.