The World-Wide Web (WWW) is characterized by a strong community structure in which groups of webpages (e.g. those devoted to a common topic or belonging to the same organization) are densely interconnected by hyperlinks. We study how such network architecture affects the average Google rank of individual communities. Using a mean-field approximation, we quantify how the average Google rank of community webpages depends on the degree to which it is isolated from the rest of the world in both incoming and outgoing directions, and $α$ -- the only intrinsic parameter of Google's PageRank algorithm. Based on this expression we introduce a concept of a web-community being decoupled or conversely coupled to the rest of the network. We proceed with empirical study of several internal web-communities within two US universities. The predictions of our mean-field treatment were qualitatively verified in those real-life networks. Furthermore, the value $α=0.15$ used by Google seems to be optimized for the degree of isolation of communities as they exist in the actual WWW.
Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative model based on an interplay between community and hierarchical structures. It assumes that each node has a preference in the interaction mechanism and nodes with the same preference are more likely to interact, while heterogeneous interactions are still allowed. The sparsity of the network is exploited for implementing a more efficient algorithm. We demonstra…
Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it ignores a potentially important feature of the dynamics: where flow moves to may depend on where it comes from. Here we analyse pathways from different systems, and while we only observe marginal consequences for disease spreading, we show that ignoring the effects of second-order Markov dynamics has important consequences for community detection, ranking, and i…
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…
We explore the statistical structure of scientific community based on multivariate analysis of publication (or other identifiable metrics) distribution in the author space. Here, we define community based on keywords, i.e. projecting semantic content of the documents on predefined meanings; however, more complex approaches based on semantic clustering of publications are possible. Remarkably, this simple statistical analysis of publication metadata allows understanding of internal interactions with community in general agreement with experience acquired over decades of social interaction withi…
Community structure is an important factor in the behavior of real-world networks because it strongly affects the stability and thus the phase transition order of the spreading dynamics. We here propose a reversible social contagion model of community networks that includes the factor of social reinforcement. In our model an individual adopts a social contagion when the number of received units of information exceeds its adoption threshold. We use mean-field approximation to describe our proposed model, and the results agree with numerical simulations. The numerical simulations and theoretical…
Mining the silent members of an online community, also called lurkers, has been recognized as an important problem that accompanies the extensive use of online social networks (OSNs). Existing solutions to the ranking of lurkers can aid understanding the lurking behaviors in an OSN. However, they are limited to use only structural properties of the static network graph, thus ignoring any relevant information concerning the time dimension. Our goal in this work is to push forward research in lurker mining in a twofold manner: (i) to provide an in-depth analysis of temporal aspects that aims to …
In this paper we present an original approach for community detection in complex networks. The approach belongs to the family of seed-centric algorithms. However, instead of expanding communities around selected seeds as most of existing approaches do, we explore here applying an ensemble clustering approach to different network partitions derived from ego-centered communities computed for each selected seed. Ego-centered communities are themselves computed applying a recently proposed ensemble ranking based approach that allow to efficiently combine various local modularities used to guide a …
How difficult is it for an early career academic to climb the ranks of their discipline? We tackle this question with a comprehensive bibliometric analysis of 57 disciplines, examining the publications of more than 5 million authors whose careers started between 1986 and 2008. We calibrate a simple random walk model over historical data of ranking mobility, which we use to (1) identify which strata of academic impact rankings are the most/least mobile and (2) study the temporal evolution of mobility. By focusing our analysis on cohorts of authors starting their careers in the same year, we fin…
The problem and implications of community detection in networks have raised a huge attention, for its important applications in both natural and social sciences. A number of algorithms has been developed to solve this problem, addressing either speed optimization or the quality of the partitions calculated. In this paper we propose a multi-step procedure bridging the fastest, but less accurate algorithms (coarse clustering), with the slowest, most effective ones (refinement). By adopting heuristic ranking of the nodes, and classifying a fraction of them as `critical', a refinement step can be …
Given a real-world graph, how can we measure relevance scores for ranking and link prediction? Random walk with restart (RWR) provides an excellent measure for this and has been applied to various applications such as friend recommendation, community detection, anomaly detection, etc. However, RWR suffers from two problems: 1) using the same restart probability for all the nodes limits the expressiveness of random walk, and 2) the restart probability needs to be manually chosen for each application without theoretical justification. We have two main contributions in this paper. First, we propo…
Distributed, controllable energy storage devices offer several benefits to electric power system operation. Three such benefits include reducing peak load, providing standby power, and enhancing power quality. These benefits, however, are only realized during peak load or during an outage, events that are infrequent. This paper presents a means of realizing additional benefits by taking advantage of the fluctuating costs of energy in competitive energy markets. An algorithm for optimal charge/discharge scheduling of community energy storage (CES) devices as well as an analysis of several of th…
Community detection is a commonly used technique for identifying groups in a network based on similarities in connectivity patterns. To facilitate community detection in large networks, we recast the network to be partitioned into a smaller network of 'super nodes', each super node comprising one or more nodes in the original network. To define the seeds of our super nodes, we apply the 'CoreHD' ranking from dismantling and decycling. We test our approach through the analysis of two common methods for community detection: modularity maximization with the Louvain algorithm and maximum likelihoo…
Ranking node importance is crucial in understanding network structure and function on complex networks. Degree, h-index and coreness are widely used, but which one is more proper to a network associated with a dynamical process, e.g. SIR spreading process, is still unclear. To fill this gap, a, which is extracted from the fitting function (f(x)=1-1/(e^(2a(x-b))+1)) of the average number of nodes in each radius of the neighborhood of a node, is proposed. Experiment results which are carried out on twenty real-world networks show that a can classify which of the three measures (degree, h-index a…
Community detection is one of the pivotal tools for discovering the structure of complex networks. Majority of community detection methods rely on optimization of certain quality functions characterizing the proposed community structure. Perhaps, the most commonly used of those quality functions is modularity. Many heuristics are claimed to be efficient in modularity maximization, which is usually justified in relative terms through comparison of their outcomes with those provided by other known algorithms. However as all the approaches are heuristics, while the complete brute-force is not fea…
To obtain the optimal number of communities is an important problem in detecting community structure. In this paper, we extend the measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic $Ω(c)$ is proposed to detect the optimal number of communities. In general, when $Ω(c)$ reaches its local maximum, especially the first one, the corresponding number of communities \emph{c} is likely to be optimal in community detection. Moreover, the statist…
The characterization of network community structure has profound implications in several scientific areas. Therefore, testing the algorithms developed to establish the optimal division of a network into communities is a fundamental problem in the field. We performed here a highly detailed evaluation of community detection algorithms, which has two main novelties: 1) using complex closed benchmarks, which provide precise ways to assess whether the solutions generated by the algorithms are optimal; and, 2) A novel type of analysis, based on hierarchically clustering the solutions suggested by mu…
We develop a method to infer community structure in directed networks where the groups are ordered in a latent one-dimensional hierarchy that determines the preferred edge direction. Our nonparametric Bayesian approach is based on a modification of the stochastic block model (SBM), which can take advantage of rank alignment and coherence to produce parsimonious descriptions of networks that combine ordered hierarchies with arbitrary mixing patterns between groups. Since our model also includes directed degree correction, we can use it to distinguish non-local hierarchical structure from local …
