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 .

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.

We construct a network of 1.6 million nodes from banking transactions of users of Rabobank. We assign two weights on each edge, which are the aggregate transferred amount and the total number of transactions between the users from the year 2010 to 2020. We present a detailed analysis of the unweighted and both weighted networks by examining their degree, strength, and weight distributions, as well as the topological assortativity and weighted assortativity, clustering, and weighted clustering, together with correlations between these quantities. We further study the meso-scale properties of the networks and compare them to a randomized reference system. This will be the first publicly shared dataset of intra-bank transactions, and this work highlights the unique characteristics of banking transaction networks with other scale-free networks.

In this paper we introduce a methodology to identify communities in dark multilayered networks, taking into account that the main challenges of these networks are incompleteness, fuzzy boundaries, and dynamic behavior. To account for these characteristics, we create knowledge sharing communities (KSC) that determine the community detection. KSC is driven by weighing the edge attributes as desired for the application that the communities are used. We provide an interactive algorithm that allows the operator to decide on the weights and the thresholds applied to create the communities. By choosing these variables, our results quantitatively outperform community detection on the collapsed monoplex network.

Data about terrorist networks is sparse and not consistently tagged as desired for research. Moreover, such data collections are hard to come across, which makes it challenging to propose solutions for the dynamic phenomenon driving these networks. This creates the need for generative network models based on the existing data.

In this paper we introduce a methodology to create multilayered terrorist networks, taking into account that the main challenges of the data behind the networks are incompleteness, fuzzy boundaries, and dynamic behavior. To account for these dark networks' characteristics, we use knowledge sharing communities in determining the methodology to create 3-layered networks from each of our datasets. We analyze the resulting layers of three terrorist datasets and present explanations of why three layers should be used for these models. We also use the information of just one layer, to identify the Bali 2005 attack community.

Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is O(n · m + n), where n represents total number of nodes, and m represents total number of edges in the network. In the present work, we propose a heuristic method to fast estimate the closeness rank of a node in O(α · m) time complexity, where α = 3. We also propose an extended improved method using uniform sampling technique. This method better estimates the rank and it has the time complexity O(α · m), where α ≈ 10-100. This is an excellent improvement over the classical centrality ranking method. The efficiency of the proposed methods is verified on real world scale-free social networks using absolute and weighted error functions.

Most real world dynamic networks are evolving very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties of the network. In the present work, we estimate degree rank of a node without having the entire network. The proposed methods are based on the power law degree distribution characteristic or sampling techniques. We further study the efficiency and feasibility of these approaches in different contexts. The proposed methods are simulated on synthetic networks, as well as on real world social networks. Results show that the degree rank of a node can be estimated with high accuracy using only 1% samples of the network size. The accuracy of the estimation decreases from high ranked to low ranked nodes.

Ever since the introduction of the first epidemic model, scientists have tried extrapolating the damage caused by a contagious disease, given its spreading pattern in the premature stage. However, understanding epidemiology remains an elusive mystery to researchers specifically because of the unavailability of large amount of data. We utilise the study of diffusion of memes in a social networking website to solve this problem. In this paper, we analyse the impact of specific meso-scale properties of a network on a meme traversing over it. We have employed SCCP (Scale free, Communities, Core Periphery structure) networks for analysis purpose. We propose a new meme propagation model for real world social networks and observe the cause of virality of a meme. We have tested and validated our model with the real world information spreading pattern.