Community detection is a significant and challenging task in network research. Nowadays, plenty of attention has been focused on local methods of community detection. Among them, community detection with a greedy algorithm typically starts from the identification of local essential nodes called central nodes of the network; communities expand later from these central nodes by optimizing a modularity function. In this paper, we propose a new central node indicator and a new modularity function. Our central node indicator, which we call local centrality indicator (LCI), is as efficient as the well-known global maximal degree indicator and local maximal degree indicator; on certain special network structure, LCI performs even better. On the other hand, our modularity function F2 overcomes certain disadvantages,such as the resolution limit problem,of the modularity functions raised in previous literature. Combined with a greedy algorithm, LCI and F2 enable us to identify the right community structures for both the real world networks and the simulated benchmark network. Evaluation based on the normalized mutual information (NMI) suggests that our community detection method with a greedy algorithm based on LCI and F2 performs superior to many other methods. Therefore, the method we proposed in this paper is potentially noteworthy.
Community-aware centrality is an emerging research area in network science concerned with the importance of nodes in relation to community structure. Measures are a function of a network's structure and a given partition. Previous approaches extend classical centrality measures to account for community structure with little connection to community detection theory. In contrast, we propose cluster-quality vitality measures, i.e., modularity vitality, a community-aware measure which is well-grounded in both centrality and community detection theory. Modularity vitality quantifies positive and ne…
In this paper I'll speak about non-spectral clustering techniques and see how a node ordering based on centrality measures can improve the quality of communities detected. I'll also discuss an improvement to existing techniques, which further improves modularity.
It is of paramount importance to uncover influential nodes to control diffusion phenomena in a network. In recent works, there is a growing trend to investigate the role of the community structure to solve this issue. Up to now, the vast majority of the so-called community-aware centrality measures rely on non-overlapping community structure. However, in many real-world networks, such as social networks, the communities overlap. In other words, a node can belong to multiple communities. To overcome this drawback, we propose and investigate the "Overlapping Modularity Vitality" centrality measu…
Targeting influential nodes in complex networks allows fastening or hindering rumors, epidemics, and electric blackouts. Since communities are prevalent in real-world networks, community-aware centrality measures exploit this information to target influential nodes. Researches show that they compare favorably with classical measures that are agnostic about the community structure. Although the diffusion process is of prime importance, previous studies consider mainly the famous Susceptible-Infected-Recovered (SIR) epidemic propagation model. This work investigates the consistency of previous a…
Unlike classical centrality measures, recently developed community-aware centrality measures use a network's community structure to identify influential nodes in complex networks. This paper investigates their relationship on a set of fifty real-world networks originating from various domains. Results show that classical and community-aware centrality measures generally exhibit low to medium correlation values. These results are consistent across networks. Transitivity and efficiency are the most influential macroscopic network features driving the correlation variation between classical and c…
In our recent works, we developed a probabilistic framework for structural analysis in undirected networks and directed networks. The key idea of that framework is to sample a network by a symmetric and asymmetric bivariate distribution and then use that bivariate distribution to formerly defining various notions, including centrality, relative centrality, community, and modularity. The main objective of this paper is to extend the probabilistic definition to attributed networks, where sampling bivariate distributions by exponentially twisted sampling. Our main finding is that we find a way to…
We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity Laplacian. Instead of using traditional spectral relaxation, we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective. With the explicit nonnegative constraint, our solutions are very close to the ideal community indicator …
In this paper we present a novel strategy to discover the community structure of (possibly, large) networks. This approach is based on the well-know concept of network modularity optimization. To do so, our algorithm exploits a novel measure of edge centrality, based on the k-paths. This technique allows to efficiently compute a edge ranking in large networks in near linear time. Once the centrality ranking is calculated, the algorithm computes the pairwise proximity between nodes of the network. Finally, it discovers the community structure adopting a strategy inspired by the well-known state…
Information flow, opinion, and epidemics spread over structured networks. When using individual node centrality indicators to predict which nodes will be among the top influencers or spreaders in a large network, no single centrality has consistently good ranking power. We show that statistical classifiers using two or more centralities as input are instead consistently predictive over many diverse, static real-world topologies. Certain pairs of centralities cooperate particularly well in statistically drawing the boundary between the top spreaders and the rest: local centralities measuring th…
A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [Bonacich, 2001], measures the number of attenuated paths that exist between nodes. We introduce a normalized version of this metric and use it to study network structure, specifically, to rank nodes and find community structure of the network. Specifically, we extend the modularity-maximization method [Newman and Girvan, 2004] for community detection to use this metric as the measure of node connectivity. Normalized alpha-centrality is a powerful tool for network an…
The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general considered as an ill-posed problem, and its solution may depend on a person's view on this problem. In this book chapter, we adopt the framework of sampled graphs that treat a person's view as a sampling method for a network. The modularity for a sampled graph, called the generalized modularity in the book chapter, is a similarity matrix that has a specific probabi…
The roles of different nodes within a network are often understood through centrality analysis, which aims to quantify the capacity of a node to influence, or be influenced by, other nodes via its connection topology. Many different centrality measures have been proposed, but the degree to which they offer unique information, and such whether it is advantageous to use multiple centrality measures to define node roles, is unclear. Here we calculate correlations between 17 different centrality measures across 212 diverse real-world networks, examine how these correlations relate to variations in…
The problem of clustering large complex networks plays a key role in several scientific fields ranging from Biology to Sociology and Computer Science. Many approaches to clustering complex networks are based on the idea of maximizing a network modularity function. Some of these approaches can be classified as global because they exploit knowledge about the whole network topology to find clusters. Other approaches, instead, can be interpreted as local because they require only a partial knowledge of the network topology, e.g., the neighbors of a vertex. Global approaches are able to achieve hig…
Corporations across the world are highly interconnected in a large global network of corporate control. This paper investigates the global board interlock network, covering 400,000 firms linked through 1,700,000 edges representing shared directors between these firms. The main focus is on the concept of centrality, which is used to investigate the embeddedness of firms from a particular country within the global network. The study results in three contributions. First, to the best of our knowledge for the first time we can investigate the topology as well as the concept of centrality in corpor…
In this work we look at the structure of the influences between Western art painters as revealed by their biographies on Wikipedia. We use a modified version of modularity maximisation with metadata to detect a partition of artists into communities based on their artistic genre and school in which they belong. We then use this community structure to discuss how influential artists reached beyond their own communities and had a lasting impact on others, by proposing modifications on standard centrality measures.
Influential nodes play a critical role in boosting or curbing spreading phenomena in complex networks. Numerous centrality measures have been proposed for identifying and ranking the nodes according to their importance. Classical centrality measures rely on various local or global properties of the nodes. They do not take into account the network community structure. Recently, a growing number of researches have shifted to community-aware centrality measures. Indeed, it is a ubiquitous feature in a vast majority of real-world networks. In the literature, the focus is on designing community-awa…
In this work, we analyse and predict the stability of communities in complex networks. We use a variant of closeness centrality, known as profile closeness, to measure the loyalty of a member towards its community. We show that the profile closeness is an adequate indicator of how communities evolve in a network. We investigate this in static as well as dynamic (temporal) networks and establish the relevance of profile closeness in predicting the evolution of a complex network. Keywords: Small world networks , Centrality , Community , Closeness , Clustering
Detecting communities or the modular structure of real-life networks (e.g. a social network or a product purchase network) is an important task because the way a network functions is often determined by its communities. Traditional approaches to community detection involve modularity-based algorithms, which generally speaking, construct partitions based on heuristics that seek to maximize the ratio of the edges within the partitions to those between them. On the other hand, node embedding approaches represent each node in a graph as a real-valued vector and is thereby able to transform the pro…
Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the Fiedler vector of centered graph adjacency matrix (graph Laplacian), we propose spectral decomposition approaches to graph PCA and graph dictionary learning that integrate multiple features, including graph walk statistics, centrality measures and graph distances to reference nodes. In this paper we propose a new PCA method …
The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in time, the influence of each node changes in time as well, and the corresponding hierarchies are modified accordingly. However, there is still a lack of systematic study into the ways in which the centrality of a node evolves when a graph changes. In this paper we introduce a taxonomy of metrics of equality and hierarchical mobility in networks that evolve in t…
Temporal networks, i.e., networks in which the interactions among a set of elementary units change over time, can be modelled in terms of time-varying graphs, which are time-ordered sequences of graphs over a set of nodes. In such graphs, the concepts of node adjacency and reachability crucially depend on the exact temporal ordering of the links. Consequently, all the concepts and metrics proposed and used for the characterisation of static complex networks have to be redefined or appropriately extended to time-varying graphs, in order to take into account the effects of time ordering on causa…
Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social, financial, engineering and biological networks as well. Extending our ability to analyze complex networks to multiplex network structures increases greatly the level of information that is possible to extract from Big Data. For these reasons characterizing the centrality of nodes in multiplex networks and finding new ways to solve challenging inference proble…
In this study we propose a method based on e-mail social network analysis to compare the communication behavior of managers who voluntarily quit their job and managers who decide to stay. Collecting 18 months of e-mail, we analyzed the communication behavior of 866 managers, out of which 111 left a large global service company. We compared differences in communication patterns by computing social network metrics, such as betweenness and closeness centrality, and content analysis indicators, such as emotionality and complexity of the language used. To study the emergence of managers' disengagem…
A network has a non-overlapping community structure if the nodes of the network can be partitioned into disjoint sets such that each node in a set is densely connected to other nodes inside the set and sparsely connected to the nodes out- side it. There are many metrics to validate the efficacy of such a structure, such as clustering coefficient, betweenness, centrality, modularity and like-mindedness. Many methods have been proposed to optimize some of these metrics, but none of these works well on the recently introduced metric like-mindedness. To solve this problem, we propose a be- haviora…
In this paper we characterize the performance of venture capital-backed firms based on their ability to attract investment. The aim of the study is to identify relevant predictors of success built from the network structure of firms' and investors' relations. Focusing on deal-level data for the health sector, we first create a bipartite network among firms and investors, and then apply functional data analysis (FDA) to derive progressively more refined indicators of success captured by a binary, a scalar and a functional outcome. More specifically, we use different network centrality measures …
Understanding the structure of communities in a network has a great importance in the economic analysis. Communities are indeed characterized by specific properties, that are different from those of both the individual node and the whole network, and they can affect various processes on the network. In the International Trade Network, community detection aims to search sets of countries (or of trade sectors) which have a high intra-cluster connectivity and a low inter-cluster connectivity. In general, exchanges among countries occur according to preferential economic relationships ranging over…
In this paper, through thinking on the modularity function that measures the standard of community division, a new algorithm for dividing communities is proposed, called the Connect Intensity Iteration algorithm, or CIIA for short. In this algorithm, a new indicator is proposed.This indicator is the difference between the actual number of edges between two nodes and the number of edges when the edges are randomly placed. It can reflect more information between the nodes. The larger the value of this index, the greater the possibility that the two nodes are divided into the same community, and …
Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null random graph model. Here we introduce a systematic dynamical framework to design and analyze a wide variety of quality functions for community detection. The quality of a partition is measured by its Markov Stability, a time-parametrized function defined in terms of the statistical properties of a Markov process taking place on the graph. The Markov process pr…
Identifying highly susceptible individuals in spreading processes is of great significance in controlling outbreaks. In this paper, we explore the susceptibility of people in susceptible-infectious-recovered (SIR) and rumor spreading dynamics. We first study the impact of community structure on people's susceptibility. Despite that the community structure can reduce the infected population given same infection rates, it will not deterministically affect nodes' susceptibility. We find the susceptibility of individuals is sensitive to the choice of spreading dynamics. For SIR spreading, since th…
Can Invisible Psychological Traits Organize Visible Network Structure? A Complex Network Analysis of Myers-Briggs Type Indicator-Based Interaction Patterns in Anonymous Social Networks
Leveraging GANs for citation intent classification and its impact on citation network analysis
Institute of Mathematics and Computer Science, University of São Paulo（圣保罗大学数学与计算机科学学院）；Observatory on Social Media, Indiana University（社交媒体观察站，印第安纳大学）
Northwestern Polytechnical University（西北工业大学）；University of Rennes 1（雷恩第一大学）；IRISA（IRISA研究所）
Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical framework of belief functions is proposed. The median variant relaxes the restriction of a metric space embedding for the objects but constrains the prototypes to be in the original data set. Due to these properties, MECM could be applied to graph clustering problems. A community detection scheme for social networks based on MECM is investigated a…
Centrality metrics have been widely applied to identify the nodes in a graph whose removal is effective in decomposing the graph into smaller sub-components. The node--removal process is generally used to test network robustness against failures. Most of the available studies assume that the node removal task is always successful. Yet, we argue that this assumption is unrealistic. Indeed, the removal process should take into account also the strength of the targeted node itself, to simulate the failure scenarios in a more effective and realistic fashion. Unlike previous literature, herein a {\…
Describing the basic properties of road network systems, such as their robustness, vulnerability, and reliability, has been a very important research topic in the field of urban transportation. Current research mainly uses several statistical indicators of complex networks to analyze the road network systems. However, these methods are essentially node-based. These node-based methods are more concerned with the number of connections between nodes, and lack of consideration for interactions. So, this leads to the well-known node paradox problem, and their ability of characterizing the local and…
A stock market is considered as one of the highly complex systems, which consists of many components whose prices move up and down without having a clear pattern. The complex nature of a stock market challenges us on making a reliable prediction of its future movements. In this paper, we aim at building a new method to forecast the future movements of Standard & Poor's 500 Index (S&P 500) by constructing time-series complex networks of S&P 500 underlying companies by connecting them with links whose weights are given by the mutual information of 60-minute price movements of the pairs of the co…
