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Abstract As networks grow in size and complexity, backbones become an essential network representation. Indeed, they provide a simplified yet informative overview of the underlying organization by retaining the most significant and structurally influential connections within a network. Network heterogeneity often results in complex and intricate structures, making it challenging to identify the backbone. In response, we introduce the Multilevel Backbone Extraction Framework, a novel approach that diverges from conventional backbone methodologies. This generic approach prioritizes the mesoscopic organization of networks. First, it splits the network into homogeneous-density components. Second, it extracts independent backbones for each component using any classical Backbone technique. Finally, the various backbones are combined. This strategy effectively addresses the heterogeneity observed in network groupings. Empirical investigations on real-world networks underscore the efficacy of the Multilevel Backbone approach in preserving essential network structures and properties. Experiments demonstrate its superiority over classical methods in handling network heterogeneity and enhancing network integrity. The framework is adaptable to various types of networks and backbone extraction techniques, making it a versatile tool for network analysis and backbone extraction across diverse network applications.

Spatial synergy is strengthened integration and connection between cities in a mega-city region, transcending administrative boundaries. The central flow theory suggests that the mega-city regions are formed by the interconnected flows of people across cities, making the spatial synergy can be measured by assessing the aggregation and intensity of flows and interactions between cities and regions. Human mobility data, such as mobile phone data and social media check-ins, enable the tracking of human movements, thus facilitating the transition of central flow theory from theoretical constructs to empirical research. To this end, this study presents an alternative data-driven framework to reveal the multi-scale spatial synergy of mega-city regions from a human mobility perspective. It uncovers homogeneously spatial communities with high inter-city integration using community detection. Strong internal spatial connections of 2.13 billion mobility are filtered using network backbone extraction. An experiment in the Pearl River Delta (PRD), China, demonstrates a multi-scale and multi-core hierarchical spatial synergy in the PRD region. The detailed findings are as follows: (1) Three cities attract the majority of human mobility. Mobility distance is short in urban centers and long in suburban areas. (2) The spatial integration pattern shows the detected communities reveal the hierarchical integration pattern with three main integrated regions: Guangzhou-Foshan-Zhaoqing, Shenzhen-Dongguan-Huizhou, and Zhuhai-Zhongshan-Jiangmen. (3) The spatial connection pattern illustrates the close ties of 9 cities and three core cities, including Guangzhou, Shenzhen, and Foshan. These results provide a human-centric understanding of urban synergy and deeper insights into central flow theory, which supports cooperative development in mega-city regions.

Accurately analyzing the flow and transport behavior in a large discrete fracture network is computationally expensive. Fortunately, recent research shows that most of the flow and transport occurs within a small backbone in the network, and identifying the backbone to replace the original network can greatly reduce computational consumption. However, the existing machine learning based methods mainly focus on the features of the fracture itself to evaluate the importance of the fracture, the local structural information of the fracture network is not fully utilized. More importantly, these machine learning methods can neither control the identified backbone's size nor ensure the backbone's connectivity. To solve these problems, a deep learning model named multi-aggregator graph neural network (MA-GNN) is proposed for identifying the backbone of discrete fracture networks. Briefly, MA-GNN uses multiple aggregators to aggregate neighbors' structural features and thus generates an inductive embedding to evaluate the criticality score of each node in the entire fracture network. Then, a greedy algorithm, which can control the backbone's size and connectivity, is proposed to identify the backbone based on the criticality score. Experimental results demonstrate that the backbone identified by MA-GNN can recover the transport characteristics of the original network, outperforming state-of-the-art baselines. In addition, MA-GNN can identify influential fractures with higher Kendall's τ correlation coefficient and Jaccard similarity coefficient. With the ability of size control, our proposed MA-GNN can provide an effective balance between accuracy and computational efficiency by choosing a suitable backbone size. [ABSTRACT FROM AUTHOR]

With the availability and utilization of Inter-Country Input-Output (ICIO) tables, it is possible to construct quantitative indices to assess its impact on the Global Value Chain (GVC). For the sake of visualization, ICIO networks with tremendous low- weight edges are too dense to show the substantial structure. These redundant edges, inevitably make the network data full of noise and eventually exert negative effects on Social Network Analysis (SNA). In this case, we need a method to filter such edges and obtain a sparser network with only the meaningful connections.

With the availability and utilization of Inter-Country Input-Output (ICIO) tables, it is possible to construct quantitative indices to assess its impact on the Global Value Chain (GVC). For the sake of visualization, ICIO networks with tremendous low- weight edges are too dense to show the substantial structure. These redundant edges, inevitably make the network data full of noise and eventually exert negative effects on Social Network Analysis (SNA). In this case, we need a method to filter such edges and obtain a sparser network with only the meaningful connections. In this paper, we propose two parameterless pruning algorithms from the global and local perspectives respectively, then the performance of them is examined using the ICIO table from different databases. The Searching Paths (SP) method extracts the strongest association paths from the global perspective, while Filtering Edges (FE) method captures the key links according to the local weight ratio. The results show that the FE method can basically include the SP method and become the best solution for the ICIO networks. There are still two limitations in this research. One is that the computational complexity may increase rapidly while processing the large-scale networks, so the proposed method should be further improved. The other is that much more empirical networks should be introduced to testify the scientificity and practicability of our methodology. The network pruning methods we proposed will promote the analysis of the ICIO network, in terms of community detection, link prediction, and spatial econometrics, etc. Also, they can be applied to many other complex networks with similar characteristics. This paper improves the existing research from two aspects, namely, considering the heterogeneity of weights and avoiding the interference of parameters. Therefore, it provides a new idea for the research of network backbone extraction. [ABSTRACT FROM AUTHOR]

Dense networks are very pervasive in social analytics, biometrics, communication, architecture, etc. Analyzing and visualizing such large-scale networks are significant challenges, which are generally met by reducing the redundancy on the level of nodes or edges. Motifs, patterns of the higher order organization compared with nodes and edges, are recently found to be the novel fundamental unit structures of complex networks. In this work, we proposed a novel motif h-backbone (Motif-h) method to extract functional cores of directed networks based on both motif strength and h-bridge. Compared with the state-of-the-art method Motif-DF and Entropy, our method solves two main issues which are often found in existing methods: the Motif-h reconsiders weak ties into our candidate set, and those weak ties often have critical functions of bridges in networks; moreover, our method provides a trade-off between the motif size and the edge strength, which quantifies the core edges accordingly. In the simulations, we compare our method with Motif-DF in four real-world networks and found that Motif-h can streamline the extraction of crucial structures compared with the others with limited edges. [ABSTRACT FROM AUTHOR]

Network backbone extraction techniques reduce the size of networks while trying to preserve their key topological and spatial features. Various backbone extraction algorithms have been proposed in different scientific fields. Although of clear interest to transport geographers, backbone extraction techniques have been adopted unevenly and in an ad hoc fashion in transport geography research. In this paper we therefore present a conceptual and experimental comparison of backbone extraction techniques in a transport-geographical context, and explore the new insights each technique can offer to enhance our understanding of the Southeast Asian intercity air transport network (SAAN). We review six frequently-used methods, i.e. global weight thresholding method (GWTM), k-core decomposition method (KCDM), minimum spanning tree method (MSTM), primary linkage analysis method (PLAM), multiple linkage analysis method (MLAM), and the disparity filter algorithm method (DFAM), and elaborate their analytical essence by applying them to extract the backbone of the SAAN. The abstracted networks are compared in terms of their geographical and topological structures using the initial network as a benchmark. This comparison is then used to point out the different techniques' potential in light of different transport geography research applications. [ABSTRACT FROM AUTHOR]

Dendritic spines are tiny membranous protrusions from neuron's dendrites. They play a very important role in the nervous system. A number of mental diseases such as Alzheimer's disease and mental retardation are revealed to have close relations with spine morphologies or spine number changes. Spines have various shapes, and spine images are often not of good quality; hence it is very challenging to detect spines in neuron images. This paper presents a novel pipeline to detect dendritic spines in 2D maximum intensity projection (MIP) images and a new dendrite backbone extraction method is developed in the pipeline. The strategy for the backbone extraction approach is that it iteratively refines the extraction result based on directional morphological filtering and improved Hessian filtering until a satisfactory extraction result is obtained. A shortest path method is applied along a backbone to extract the boundary of the dendrites. Spines are then segmented from the dendrites outside the extracted boundary. Touching spines will be split using a marker-controlled watershed algorithm. We present the results of our algorithm on real images and compare our algorithm with two other spine detection methods. The results show that the proposed approach can detect dendrites and spines more accurately. Measurements and classification of spines are also made in this paper. [ABSTRACT FROM AUTHOR]

Backbone curves are usually obtained by analyzing nonlinear oscillators (e.g., the Duffing equation) whereas the backbones of linear oscillators are incidental by-products of such studies. Nevertheless, we focus on the harmonic oscillator, a linear, homogeneous constant-coefficient second-order ordinary differential equation. The backbone of the sinusoidally forced harmonic oscillator is well known, but the backbone of the unforced harmonic oscillator seems to have received essentially no attention. Since the 1980s, various computerized methods of backbone extraction have been under development, one of which is based on analytic-signal theory, a subfield of digital signal processing that involves Hilbert transform computations. By focusing on linear-theory backbones, a prerequisite to nonlinear analysis, we aim to pinpoint some of the theoretical and computational issues that arise when dealing with analytic-signal backbones. This paper examines the Mirror Periodic Method (MPM) as a practical way to reduce end effects in Hilbert transform computations and approximate analytic-signal backbones of unforced harmonic oscillators with light damping (less than 10 percent of critical). Using numerical examples, we demonstrate that MPM works well with both displacement and acceleration data, even for short signals, meaning just one or two damped cycles of oscillation. We then apply MPM techniques to accelerometer data that were recorded as part of earthquake-engineering teaching demonstrations involving a small-scale laboratory model of a linear single-degree-of-freedom system. [ABSTRACT FROM AUTHOR]