Fast centrality approximation in modular networks

Community detection in complex networks using edge-deleting with restrictions

PageRank is a popular measure of centrality that is often applied to rank nodes in real-world networks. However, in many cases, the notion of teleportation is counterintuitive because it implies that whatever is moving around the network will jump or ‘teleport’ directly from one node to any other, without considering how far apart the nodes are. To overcome this issue, we propose here a general measure of PageRank centrality whereby the teleportation probabilities depend, in some way, on the distance separating the nodes. We accomplish this by drawing upon recent advances in non-local random walks, which allow the proposed measure to be tailored for various real-world networks and applications. To illustrate the flexibility of the proposed measure and to demonstrate how it differs from PageRank centrality, we present and discuss experimental results for a selection of real-world spatial and social networks, including an air transportation network, a collaboration network and an urban street network.

Many systems, ranging from biological and engineering systems to social systems, can be modeled as directed networks, with links representing directed interaction between two nodes. To assess the importance of a node in a directed network, various centrality measures based on different criteria have been proposed. However, calculating the centrality of a node is often difficult because of the overwhelming size of the network or because the information held about the network is incomplete. Thus, developing an approximation method for estimating centrality measures is needed. In this study, we focus on modular networks; many real-world networks are composed of modules, where connection is dense within a module and sparse across different modules. We show that ranking-type centrality measures, including the PageRank, can be efficiently estimated once the modular structure of a network is extracted. We develop an analytical method to evaluate the centrality of nodes by combining the local property (i.e. indegree and outdegree of nodes) and the global property (i.e. centrality of modules). The proposed method is corroborated by real data. Our results provide a linkage between the ranking-type centrality values of modules and those of individual nodes. They also reveal the hierarchical structure of networks in the sense of subordination (not nestedness) laid out by connectivity among modules of different relative importance. The present study raises a novel motive for identifying modules in networks.

Identifying influential spreaders in networks is an essential issue in order to prevent epidemic spreading, or to accelerate information diffusion. Several centrality measures take advantage of various network topological properties to quantify the notion of influence. However, the vast majority of works ignore its community structure while it is one of the main features of many real-world networks. In a recent study, we show that the centrality of a node in a network with non-overlapping communities depends on two features: Its local influence on the nodes belonging to its community, and its global influence on the nodes belonging to the other communities. Using global and local connectivity of the nodes, we introduced a framework allowing to redefine all the classical centrality measures (designed for networks without community structure) to non-overlapping modular networks. In this paper, we extend the so-called “Modular Centrality” to networks with overlapping communities. Indeed, it is a frequent scenario in real-world networks, especially for social networks where nodes usually belong to several communities. The “Overlapping Modular Centrality” is a two-dimensional measure that quantifies the local and global influence of overlapping and non-overlapping nodes. Extensive experiments have been performed on synthetic and real-world data using the Susceptible-Infected-Recovered (SIR) epidemic model. Results show that the Overlapping Modular Centrality outperforms its alternatives designed for non-modular networks. These investigations provide better knowledge on the influence of the various parameters governing the overlapping community structure on the nodes’ centrality. Additionally, two combinations of the components of the Overlapping Modular Centrality are evaluated. Comparative analysis with competing methods shows that they produce more efficient centrality scores.

Community detection in social networks based on fire propagation

Identifying influential nodes in a network is a fundamental issue due to its wide applications, such as accelerating information diffusion or halting virus spreading. Many measures based on the network topology have emerged over the years to identify influential nodes such as Betweenness, Closeness, and Eigenvalue centrality. However, although most real-world networks are made of groups of tightly connected nodes which are sparsely connected with the rest of the network in a so-called modular structure, few measures exploit this property. Recent works have shown that it has a significant effect on the dynamics of networks. In a modular network, a node has two types of influence: a local influence (on the nodes of its community) through its intra-community links and a global influence (on the nodes in other communities) through its inter-community links. Depending on the strength of the community structure, these two components are more or less influential. Based on this idea, we propose to extend all the standard centrality measures defined for networks with no community structure to modular networks. The so-called “Modular centrality” is a two-dimensional vector. Its first component quantifies the local influence of a node in its community while the second component quantifies its global influence on the other communities of the network. In order to illustrate the effectiveness of the Modular centrality extensions, comparison with their scalar counterparts is performed in an epidemic process setting. Simulation results using the Susceptible-Infected-Recovered (SIR) model on synthetic networks with controlled community structure allows getting a clear idea about the relation between the strength of the community structure and the major type of influence (global/local). Furthermore, experiments on real-world networks demonstrate the merit of this approach.

Community detection in networks plays a key role in understanding their structures, and the application of clustering algorithms in community detection tasks in complex networks has attracted intensive attention in recent years. In this paper, based on the definition of uncertainty of node community belongings, the node density is proposed first. After that, the DD (the combination of node density and node degree centrality) is proposed for initial node selection in community detection. Finally, based on the DD and k-means clustering algorithm, we proposed a community detection approach, the density-degree centrality-jaccard-k-means method (DDJKM). The DDJKM algorithm can avoid the problem of random selection of initial cluster centers in conventional k-means clustering algorithms, so that isolated nodes will not be selected as initial cluster centers. Additionally, DDJKM can reduce the iteration times in the clustering process and the over-short distances between the initial cluster centers can be avoided by calculating the node similarity. The proposed method is compared with state-of-the-art algorithms on synthetic networks and real-world networks. The experimental results show the effectiveness of the proposed method in accurately describing the community. The results also show that the DDJKM is practical a approach for the detection of communities with large network datasets.

Communities are virtually ubiquitous in real-world networks, and the statistic of modularity index Q is the classical measurement for community detection algorithms. However, the relationship between the modularity property and network multilever micro-scale structures is still not clear. In this paper, we study community detection results both in artificial and real-life complex networks by constructing different order null networks, and the results uncover that how micro-structures (such as degree distribution, assortativity and clustering coefficient) affect community properties. Meanwhile, we also propose two novel null networks (increasing or decreasing community structures) to verify the robustness of different community detection algorithms. Our results indicate that the modularity index Q is not a suitable statistic to measure the weak community property which is widely available in empirical networks. Our findings can not only be used to test the robustness of different community detection methods, but also be helpful to uncover the correlation of network structures between microcosmic and mesoscopic scales.

This paper tests the robustness of four centrality measures – degree, betweenness, closeness, and eignvector centrality – using graphs simulating real world networks by Stochastic Kronecker Graphs approach. Existing studies have used Erdos-Renyi (1959) random graphs which are poor match for real world networks. Stochastic Kronecker Graphs have been found to display real world network properties. Results suggest revision of some conclusions arrived at using random graphs. Mistakes in recording nodes affect accuracy of centrality measures more than mistakes in recording connections (edges). This supports conventional wisdom, and seeks revision of Borgatti et al. (2006). Supporting some existing studies, betweenness was found to be most robust of these four centrality measures, and closeness the least robust. This paper also demonstrates how confidence intervals around centrality measures can be created using simulation to help arrive at robust analysis.

Graph clustering, often addressed as community detection, is a prominent task in the domain of graph data mining with dozens of algorithms proposed in recent years. In this paper, we focus on several popular community detection algorithms with low computational complexity and with decent performance on the artificial benchmarks, and we study their behaviour on real-world networks. Motivated by the observation that there is a class of networks for which the community detection methods fail to deliver good community structure, we examine the assortativity coefficient of ground-truth communities and show that assortativity of a community structure can be very different from the assortativity of the original network. We then examine the possibility of exploiting the latter by weighting edges of a network with the aim to improve the community detection outputs for networks with assortative community structure. The evaluation shows that the proposed weighting can significantly improve the results of community detection methods on networks with assortative community structure.

Evolutionary Algorithm for overlapping community detection using a merged maximal cliques representation scheme

In network analysis, the betweenness centrality of a node informally captures\nthe fraction of shortest paths visiting that node. The computation of the\nbetweenness centrality measure is a fundamental task in the analysis of modern\nnetworks, enabling the identification of the most central nodes in such\nnetworks. Additionally to being massive, modern networks also contain\ninformation about the time at which their events occur. Such networks are often\ncalled temporal networks. The temporal information makes the study of the\nbetweenness centrality in temporal networks (i.e., temporal betweenness\ncentrality) much more challenging than in static networks (i.e., networks\nwithout temporal information). Moreover, the exact computation of the temporal\nbetweenness centrality is often impractical on even moderately-sized networks,\ngiven its extremely high computational cost. A natural approach to reduce such\ncomputational cost is to obtain high-quality estimates of the exact values of\nthe temporal betweenness centrality. In this work we present ONBRA, the first\nsampling-based approximation algorithm for estimating the temporal betweenness\ncentrality values of the nodes in a temporal network, providing rigorous\nprobabilistic guarantees on the quality of its output. ONBRA is able to compute\nthe estimates of the temporal betweenness centrality values under two different\noptimality criteria for the shortest paths of the temporal network. In\naddition, ONBRA outputs high-quality estimates with sharp theoretical\nguarantees leveraging on the \\emph{empirical Bernstein bound}, an advanced\nconcentration inequality. Finally, our experimental evaluation shows that ONBRA\nsignificantly reduces the computational resources required by the exact\ncomputation of the temporal betweenness centrality on several real world\nnetworks, while reporting high-quality estimates with rigorous guarantees.\n

Tunable path centrality: Quantifying the importance of paths in networks

Recent years have seen the rapid development of online social networks. Many algorithms have been proposed to assign each node to more than a single community. The traditional approaches have focused on the node community, while some recent studies have shown the great advantage of edge community detection methods. This paper presents a novel algorithm used to discover local communities in networks. A local edge community can be detected by maximizing a local edge fitness function from a seed edge which was previously ranked. Meanwhile, the method can effectively control the scale and scope of the local community based on the boundary node identification, so as to obtain complete structural information of the local community. The algorithm has been tested on both synthetic and real-world networks, and has been compared to other community detection algorithms. The experimental results show significant improvement in the detection of community structures.

Burnout is typically viewed as an individual condition, and no link has been identified between burnout and loneliness. To investigate the association of burnout with loneliness and social network degree and centrality. A survey containing the Maslach Burnout Inventory (MBI), a 3-question loneliness scale, and a social connectivity component was sent to residents in a large urban academic medical center internal medicine residency program. The response rate was 77% (95 of 124 residents). We defined significant burnout as MBI subscores of ≥ 27 for emotional exhaustion (EE), ≥ 10 for depersonalization (DP), or both. This was met by 43 (45%), 47 (49%), and 31 (33%) out of 95 respondents, respectively. Those with significant burnout had higher loneliness scores: 5.6 versus 4.5 for EE (P = .002; OR = 1.50; 95% CI 1.15-1.95); 5.4 versus 4.6 for DP (P = .024; OR = 1.33; 95% CI 1.03-1.71); and 5.8 versus 4.6 for both EE and DP (P = .001; OR = 1.54; 95% CI 1.17-2.02). Rating a larger number of coresidents as closer connections on a 5-point Likert scale was not associated with lower burnout scores. No measures of centrality were associated with burnout scores for EE and/or DP. High personal accomplishment subscores on the MBI did correlate significantly with several measures of centrality. Burnout was associated with loneliness in a dose-dependent fashion. Greater sense of personal accomplishment was associated with greater network centrality.