The hyperbolic network models exhibit very fundamental and essential features, like small-worldness, scale-freeness, high-clustering coefficient, and community structure. In this paper, we comprehensively explore the presence of an important feature, the core-periphery structure, in the hyperbolic network models, which is often exhibited by real-world networks. We focused on well-known hyperbolic models such as popularity-similarity optimization model (PSO) and S1/H2 models and studied core-periphery structures using a well-established method that is based on standard random walk Markov chain model. The observed core-periphery centralization values indicate that the core-periphery structure can be very pronounced under certain conditions. We also validate our findings by statistically testing for the significance of the observed core-periphery structure in the network geometry. This study extends network science and reveals core-periphery insights applicable to various domains, enhancing network performance and resiliency in transportation and information systems.

The topological importance of nodes in complex networks has been analyzed in the literature from the perspectives of core-periphery structure and centrality metrics. While the core-periphery structure analysis of a network is more of a qualitative approach (and sometimes quantitative) at a mesoscopic level, centrality metrics are designed to quantify the topological importance of individual nodes in a network. The core-periphery analysis of a network is aimed at categorizing a node as either a core node or a peripheral node. The current status quo in the literature on the definitions of core nodes and peripheral nodes is that the core nodes need to be of larger degree and form a highly dense backbone to which the low degree peripheral nodes are connected to; the peripheral nodes are expected to be not connected to other peripheral nodes as well. Some of the works (e.g., [1-3]) in the literature have suggested that high degree nodes need not always be core nodes; but they still analyze the core-periphery structure and quantify the extent of coreness of a node within the realms of the above model.

Drawing on differing notions of core-periphery structure From a broad perspective, innovation is understood as a form of from [21] and [2], we distinguish decentralized core-periphery, collective problem-solving. For this and other reasons, the process centralized core-periphery, and affinity network structure. We generate of innovation is understood as a social process, as social collectives networks of these three classes from stochastic block models are capable of, and in some cases optimized for, both retaining (SBMs), and use them to run an agent-based model (ABM) of collective the knowledge of previous generations while building upon this cultural innovation, in which agents can only directly interact knowledge for subsequent innovations, a phenemonon we refer to with their network neighbors. In order to discover the highestscoring as "cumulative" culture [18, 19]. Human social networks tend to innovation, agents must discover and combine the highest exhibit core-periphery structures, whereby a'core' population is innovations from two completely parallel technology trees. We find heavily inter-connected, and connected in turn to more'peripheral' that decentralized core-periphery networks outperform both centralized individuals and subcommunities [2]. Prior work on the structure core-periphery networks and affinity networks, in terms of of human networks has suggested that innovation emerges at the mean crossover time for this final innovation. We hypothesize that boundary between the core and periphery of creative networks [4, decentralized core-periphery network structure provides a more 6]. Individual innovators are often in an intermediate position with fruitful environment for collective problem-solving, by allowing many core and peripheral connections, and successfully innovative for the relative shielding of periphery nodes from the optimal innovations teams tend to include both core and peripheral individuals [4].

Exploring meaningful structural regularities embedded in networks is a key to understanding and analyzing the structure and function of a network. The node-attribute information can help improve such understanding and analysis. However, most of the existing methods focus on detecting traditional communities, i.e., groupings of nodes with dense internal connections and sparse external ones. In this paper, based on the connectivity behavior of nodes and homogeneity of attributes, we propose a principle model (named GNAN), which can generate both topology information and attribute information. The new model can detect not only community structure, but also a range of other types of structure in networks, such as bipartite structure, core-periphery structure, and their mixture structure, which are collectively referred to as generalized structure. The proposed model that combines topological information and node-attribute information can detect communities more accurately than the model that only uses topology information. The dependency between attributes and communities can be automatically learned by our model and thus we can ignore the attributes that do not contain useful information. The model parameters are inferred by using the expectation-maximization algorithm. And a case study is provided to show the ability of our model in the semantic interpretability of communities. Experiments on both synthetic and real-world networks show that the new model is competitive with other state-of-the-art models.

In network analysis, the core structure of modeling interest is usually hidden in a larger network in which most structures are not informative. The noise and bias introduced by the non-informative component in networks can obscure the salient structure and limit many network modeling procedures' effectiveness. This paper introduces a novel core-periphery model for the non-informative periphery structure of networks without imposing a specific form for the informative core structure. We propose spectral algorithms for core identification as a data preprocessing step for general downstream network analysis tasks based on the model. The algorithm enjoys a strong theoretical guarantee of accuracy and is scalable for large networks. We evaluate the proposed method by extensive simulation studies demonstrating various advantages over many traditional core-periphery methods. The method is applied to extract the informative core structure from a citation network and give more informative results in the downstream hierarchical community detection.

Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering - clustering the vertices of a graph based on their spectral embedding - is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian or Adjacency spectral embedding (LSE or ASE). Recent theoretical results provide new understanding of the problem and solutions, and lead us to a 'Two Truths' LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome data set: the different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core-periphery structure.

A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the core. Interactions between pairs of nodes in the fringe, however, are not recorded by this process, and hence not present in the resulting graph data. For example, a phone service provider may only have records of calls in which at least one of the participants is a customer; this can include calls between a customer and a non-customer, but not between pairs of non-customers. Knowledge of which nodes belong to the core is an important piece of metadata that is crucial for interpreting the network dataset. But in many cases, this metadata is not available, either because it has been lost due to difficulties in data provenance, or because the network consists of found data obtained in settings such as counter-surveillance. This leads to a natural algorithmic problem, namely the recovery of the core set. Since the core set forms a vertex cover of the graph, we essentially have a planted vertex cover problem, but with an arbitrary underlying graph. We develop a theoretical framework for analyzing this planted vertex cover problem, based on results in the theory of fixed-parameter tractability, together with algorithms for recovering the core. Our algorithms are fast, simple to implement, and out-perform several methods based on network core-periphery structure on various real-world datasets.