Random Graph Generators for Hyperbolic Community Structures

As an open issue, the measure of community influential is no uniform standard, how to measure the influence of community has attracted extensive attention. This paper proposed a quantitative measure to identify the influence of community. Based on the state of critical functionality (SCF), a new function, which names as the weighted state of critical functionality (WSCF), is defined. For the WSCF, not only the connections among communities but also the topology within community is considered. When the community structure of the complex network is divided, each community is renormalized as a node by the renormalization method. Then, the influence of community is measured by the values of WSCF, the greater the value of WSCF, the less the influence of the corresponding community. The influence of community of three classic constructed networks (i.e., a Erodös-Rényi (ER) random network, a BA scale free network and a small-word (SW) network) is measured by the proposed method. To further verify the feasibility of the method, two community detection algorithms are used to divide community structure in the real networks. The influence of the community of the 9/11 terrorist network, a US Air network and a PolBooks network is measured by the proposed method. The influence of each community could be measured and the most influential community in each network is identified by the proposed method. The results reveal that the proposed method is a feasible measure to identify the influence of community, its recognition effect is better than SCF, and accuracy is higher. The SCF is a special case of WSCF, when the weights and cluster coefficients are equal to 1. For the proposed method, once the community structure of the network is divided, the corresponding community influence is identified by the proposed method, which is not affected by the community division algorithms.

Networks have become a widely used tool for modeling complex systems in many different fields. This approach is extremely useful for representing interactions among genes, social relationships, Internet communications or correlations of prices within a stock market, to name just a few examples. By analyzing the structure of these networks and understanding how their different elements interact, we could improve our knowledge of the whole system. Usually, nodes that compose these networks tend to create tightly knit groups. This property, of high interest in many scientific fields, is called community structure and improving its detection and characterization is what this thesis is all about. The first objective of this work is the generation of efficient methods able to characterize the communities of a network and to understand its structure. Second, we will try to create a set of tests where such methods can be studied. Finally, we will suggest a statistical measure in order to be able to properly assess the quality of the community structure of a network. To accomplish these objectives, first, we generate a set of algorithms that can transform a network into a hierarchical tree and, from there, to determine their most relevant communities. Furthermore, we have developed a new type of benchmarks for effectively testing these and other community detection algorithms. Finally, and as the most important contribution of this work, it is shown that the community structure of a network can be accurately evaluated using a hypergeometric distribution-based index. Thus, the maximization of this measure, called Surprise, appears as the best proposed strategy for detecting the optimal partition into communities of a network. Surprise exhibits an excellent behavior in all networks analyzed, qualitatively outperforming any previous method. Thus, it appears as the best measure proposed to this end and the data suggests that it could be an optimal strategy to determine the quality of the community structure of complex networks.

Community detection is one of the primary tools to discover useful information that is hidden in complex networks. Some community detection algorithms for bipartite networks have been proposed from various viewpoints. However, the performance of these algorithms deteriorates when the community structure becomes unclear. Enhancing community structure remains a nontrivial task. In this paper, we propose a community detection algorithm, called ECD, that enhances community structure in bipartite networks. In the proposed ECD, the topology of a network is modified by reducing unnecessary edges that are connected to neighboring low-weight communities. Therefore, an ambiguous community structure is converted into a structure that is much clearer than the original structure. The experimental results on both artificial and real-world networks verify the accuracy and reliability of our algorithm. Compared with existing community detection algorithms using state-of-the-art methods, our algorithm has better performance.

Community structure in networks indicates some meaningful groups or organizations in the real world. Various algorithms to detect community in complex networks were proposed. However, problems about how to judge the goodness and performance of algorithms are still open. This paper reviewed and analyzed the related work and algorithms for community detection, hoping to benefit researchers in related field.

Complex networks have in generally communities. These communities are very important. Network’s communities represent sets of nodes, which are very connected. In this research, we developed a new method to find the community structure in networks. Our method is based on flower pollination algorithm (FPA) witch is used in the splitting process. The splitting of networks in our method maximizes a function of quality called modularity. We provide a general framework for implementing our new method to find community structure in networks. We present the effectiveness of our method by comparison with some known methods on computer-generated and real-world networks.

Association rules are widely used to extract patterns from a given database. The association rules are capable of finding correlations among items, making it possible for the user to learn which items are present in the transactions and which of them have a significant correlation. One of the major problems with association rules is that the number of extracted rules usually exceeds the number of transactions present in the database, also surpassing the user’s capability to explore the obtained knowledge. To overcome this problem, the post-processing phase was proposed with the objective of directing the user to the rules that potentially have the most interesting knowledge. One of the used approaches is to divide the association rules into groups (or clusters), so that rules behave similarly are on the same group, facilitating the rule set understanding. In the literature, there are some works that uses clustering algorithms to split the rules while some other works use community detection algorithms. As both approaches obtain groups of association rules, but using different premises, different results can be obtained. No study has been done on the differences among clustering and community detection algorithms, which makes the selection of the algorithm hard, once their behavior is not well known in the association rule post-processing phase. This paper presents an analysis on both approaches, aiming to find the differences and the similarities among them, making it easier to select an approach by knowing its behavior.

This thesis focuses on the pressing issue of illicit drug trafficking and its impact on public health and safety at a global level. With the advent of digital technologies and social media platforms, combating drug trafficking has become increasingly challenging for law enforcement and researchers alike. Among these platforms, Instagram, a popular photo and video-sharing social networking platform, has emerged as a prominent hub for drug trafficking activities. In this study, we delve into the effectiveness of community and key player detection algorithms in identifying and disrupting illicit drug supply networks on Instagram. To conduct our research, we collected real Instagram data spanning from June to August 2022. We examined several community detection algorithms, including Louvain, Newman-Girvan, Infomap, Label Propagation, and Hierarchical Clustering. Additionally, we explored key player algorithms, namely CDKPE, TopRank, K-core, and KPEI, the latter being a novel algorithm introduced in this study. Our objective was to assess the performance of these algorithms in accurately identifying and targeting drug trafficking networks. Our findings reveal that the Louvain and Newman-Girvan algorithms outperformed others in terms of community detection, demonstrating their effectiveness in identifying cohesive groups involved in drug trafficking on Instagram. In terms of key player detection, the CDKPE and KPEI algorithms emerged as the most effective, highlighting the individuals who play pivotal roles within these networks. These algorithms offer practical applications for law enforcement agencies seeking to disrupt drug trafficking operations on Instagram. By emphasizing the importance of leveraging advanced analytical tools, our study underscores the significance of combating drug trafficking on social media platforms.

The R‐MAT graph generator introduced by Chakrabarti et al (Int Conf Data Mining, 2004) offers a simple, fast method for generating very large directed graphs. These properties have made it a popular choice as a method of generating graphs for objects of study in a variety of disciplines, from social network analysis to high performance computing. We analyze the graphs generated by R‐MAT and model the generator in terms of occupancy problems to prove results about the degree distributions of these graphs. We prove that the limiting degree distributions can be expressed as a mixture of normal distributions with means and variances that can be easily calculated from the R‐MAT parameters. Additionally, this article offers an efficient computational technique for computing the exact degree distribution and concise expressions for a number of properties of R‐MAT graphs. ©2011 Wiley Periodicals, Inc.*. NETWORKS, 2011

Community structures are inherent in social networks and finding them is an interesting and well-studied problem. Finding community structures in social networks is similar to locating densely connected clusters of nodes in a graph. One of the popular methods for finding communities is to first find the inter-community edges and then removing them to reveal the communities. It is well-known that a network centrality measure named edge betweenness can be used to detect the inter-community edges. The edges with high edge betweenness are those that fall in a large number of shortest paths out of all possible pairs of shortest paths. Finding all-pair shortest paths is a computationally expensive task, especially for large-sized graphs. So we construct a t-spanner, a known graph sparsification technique, for finding edges with high betweenness and eventually find communities by removing such edges. Using the t-spanner, we then detect the inter-community edges in O(km) running time by building a distance oracle of size O(kn1+1/k), where t = 2k-1. Compared to the traditional community detection methods dependent on calculation of betweenness values, our algorithm runs much faster. Experiments show that our algorithm finds communities of quality comparable to the other state-of-the-art community detection algorithms.

Many algorithms have been designed to discover community structure in networks. Most of these detect disjoint communities, while a few can find communities that overlap. We propose a new, two-phase, method of detecting overlapping communities. In the first phase, a network is transformed to a new one by splitting vertices, using the idea of split betweenness; in the second phase, the transformed network is processed by a disjoint community detection algorithm. This approach has the potential to convert any disjoint community detection algorithm into an overlapping community detection algorithm. Our experiments, using several “disjoint” algorithms, demonstrate that the method works, producing solutions, and execution times, that are often better than those produced by specialized “overlapping” algorithms.KeywordsCommunity StructureExecution TimeOriginal NetworkTotal Execution TimeRand IndexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

To investigate coupled oscillator model and community detection algorithm, an improvement method about the phase synchronization oscillator model and an optimized method (community detection via model modification) was proposed. By using the Kuramoto oscillator model as a basis, after joining the negative coupling strength, the nodes can be divided into several different synchronized clusters. In the synchronization process, the internal nodes in the same matrix are connected closely. In this method Kuramoto coupled oscillator model are expanded. The network can realize synchronization or be partitioned into several clusters depending on its structure. If all the nodes of the network are densely connected as a whole entity, synchronization will appear. If the network consists of several groups within which the connections are dense and between which the connections are sparser, the network will be partitioned into several clusters by their phases. The networks are divided into several communities because of this clustering phenomenon. The experiments show that the method is very promising. The simulation results in a variety of community structure that the proposed algorithm is an accurate, efficient and practical method for detecting community structure in networks

Community detection is a dominant research field in social media mining. Numerous algorithms have been developed to detect community structure in network. Each of them focuses on different characteristic of data and generates different communities for same dataset. So cluster validation or comparative analysis of these algorithms is required to compare the efficiency of these algorithms. There are two known ways for cluster validation: Internal Quality Measure (IQM) and External Quality Measure (EQM). IQM evaluates the cluster without reference to external information while EQM requires already known clusters i.e. ground truth for comparison. Most of the researchers have compared Community Detection algorithms on the basis of either IQM or EQM but not both. In this paper, we have tried to compare nine existing sequential community detection algorithms on the basis of both IQM and EQM and we observed that overall performance of Louvain, Fastgreedy and Walktrap algorithm is more efficient than other algorithms. From this paper, researchers working in this area can get information about major sequential community detection algorithms and their efficiency on small real world datasets. They can incorporate the findings to develop more efficient algorithms.

Detecting community structure in complex networks is an active area of research that locates dense regions of connections in networks. We suggest a novel algorithm for community detection using a new node-node association metric (based on Markov chains) and a team formation model.

For a supercritical configuration model random graph it is well known that, subject to mild conditions, there exists a unique giant component, whose size $R_n$ is $O (n)$, where $n$ is the total number of vertices in the random graph. Moreover, there exists $0 0$, such that $var (\sqrt{n} (R_n/n -\rho)) \rightarrow \sigma^2$ as $\nr$. Moreover, an explicit, easy to compute, formula is given for $\sigma^2$. This provides a key stepping stone for computing the asymptotic variance of the size of the giant component for more general random graphs.

We present a method for generating random hypergraphs in context-free hypergraph languages. It is obtained by adapting Mairson's generation algorithm for context-free string grammars to the setting of hyperedge replacement grammars. Our main results are that for non-ambiguous hyperedge replacement grammars, the method generates hypergraphs uniformly at random and in quadratic time. We illustrate our approach by a running example of a hyperedge replacement grammar generating term graphs.