Multiway spectral community detection in networks

Effect of Seeding Strategy on the Efficiency of Brand Spreading in Complex Social Networks

In social networks, consumers gather to form brand communities, and the community structure significantly impacts the dissemination of brand information. Which communication strategy is more conducive to information dissemination in different structured brand communities? Considering the above factors, we propose the word-of-mouth (WOM) agent model based on the traditional rumor model and bass model, in which the brand WOM spreading is affected by the user's psychological mechanisms, the network structure, and other factors. Through simulation experiments, the results showed the following: (1) the conclusion of the traditional bass model is no longer applicable to social marketing in brand information diffusion, that is, the effect of external marketing stimulation on information dissemination is limited. (2) The communication effect and the efficiency of information in different structures of the learning-community network are very different. (3) The strategy of hub nodes is not suitable for all types of networks, and the impact of different seeding strategies on the efficiency and effect of brand information dissemination was verified. Finally, the conclusion was verified again using the social network data on Facebook.

Modularity in Biological Networks

Network modeling, from the ecological to the molecular scale has become an essential tool for studying the structure, dynamics and complex behavior of living systems. Graph representations of the relationships between biological components open up a wide variety of methods for discovering the mechanistic and functional properties of biological systems. Many biological networks are organized into a modular structure, so methods to discover such modules are essential if we are to understand the biological system as a whole. However, most of the methods used in biology to this end, have a limited applicability, as they are very specific to the system they were developed for. Conversely, from the statistical physics and network science perspective, graph modularity has been theoretically studied and several methods of a very general nature have been developed. It is our perspective that in particular for the modularity detection problem, biology and theoretical physics/network science are less connected than they should. The central goal of this review is to provide the necessary background and present the most applicable and pertinent methods for community detection in a way that motivates their further usage in biological research.

LPA-MNI: An Improved Label Propagation Algorithm Based on Modularity and Node Importance for Community Detection

Community detection is of great significance in understanding the structure of the network. Label propagation algorithm (LPA) is a classical and effective method, but it has the problems of randomness and instability. An improved label propagation algorithm named LPA-MNI is proposed in this study by combining the modularity function and node importance with the original LPA. LPA-MNI first identify the initial communities according to the value of modularity. Subsequently, the label propagation is used to cluster the remaining nodes that have not been assigned to initial communities. Meanwhile, node importance is used to improve the node order of label updating and the mechanism of label selecting when multiple labels are contained by the maximum number of nodes. Extensive experiments are performed on twelve real-world networks and eight groups of synthetic networks, and the results show that LPA-MNI has better accuracy, higher modularity, and more reasonable community numbers when compared with other six algorithms. In addition, LPA-MNI is shown to be more robust than the traditional LPA algorithm.

Network community-based model reduction for vortical flows

A network community-based reduced-order model is developed to capture key interactions among coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows, and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.

Applications of community detection techniques to brain graphs: Algorithmic considerations and implications for neural function

The human brain can be represented as a graph in which neural units such as cells or small volumes of tissue are heterogeneously connected to one another through structural or functional links. Brain graphs are parsimonious representations of neural systems that have begun to offer fundamental insights into healthy human cognition, as well as its alteration in disease. A critical open question in network neuroscience lies in how neural units cluster into densely interconnected groups that can provide the coordinated activity that is characteristic of perception, action, and adaptive behaviors. Tools that have proven particularly useful for addressing this question are community detection approaches, which can identify communities or modules: groups of neural units that are densely interconnected with other units in their own group but sparsely interconnected with units in other groups. In this paper, we describe a common community detection algorithm known as modularity maximization, and we detail its applications to brain graphs constructed from neuroimaging data. We pay particular attention to important algorithmic considerations, especially in recent extensions of these techniques to graphs that evolve in time. After recounting a few fundamental insights that these techniques have provided into brain function, we highlight potential avenues of methodological advancements for future studies seeking to better characterize the patterns of coordinated activity in the brain that accompany human behavior. This tutorial provides a naive reader with an introduction to theoretical considerations pertinent to the generation of brain graphs, an understanding of modularity maximization for community detection, a resource of statistical measures that can be used to characterize community structure, and an appreciation of the usefulness of these approaches in uncovering behaviorally-relevant network dynamics in neuroimaging data.

Hierarchical Decomposition for Betweenness Centrality Measure of Complex Networks

Betweenness centrality is an indicator of a node’s centrality in a network. It is equal to the number of shortest paths from all vertices to all others that pass through that node. Most of real-world large networks display a hierarchical community structure, and their betweenness computation possesses rather high complexity. Here we propose a new hierarchical decomposition approach to speed up the betweenness computation of complex networks. The advantage of this new method is its effective utilization of the local structural information from the hierarchical community. The presented method can significantly speed up the betweenness calculation. This improvement is much more evident in those networks with numerous homogeneous communities. Furthermore, the proposed method features a parallel structure, which is very suitable for parallel computation. Moreover, only a small amount of additional computation is required by our method, when small changes in the network structure are restricted to some local communities. The effectiveness of the proposed method is validated via the examples of two real-world power grids and one artificial network, which demonstrates that the performance of the proposed method is superior to that of the traditional method.

The 3-cycle weighted spectral distribution in evolving community-based networks

One of the main organizing principles in real-world networks is that of network communities, where sets of nodes organize into densely linked clusters. Many of these community-based networks evolve over time, that is, we need some size-independent metrics to capture the connection relationships embedded in these clusters. One of these metrics is the average clustering coefficient, which represents the triangle relationships between all nodes of networks. However, the vast majority of network communities is composed of low-degree nodes. Thus, we should further investigate other size-independent metrics to subtly measure the triangle relationships between low-degree nodes. In this paper, we study the 3-cycle weighted spectral distribution (WSD) defined as the weighted sum of the normalized Laplacian spectral distribution with a scaling factor n, where n is the network size (i.e., the node number). Using some diachronic community-based network models and real-world networks, we demonstrate that the ratio of the 3-cycle WSD to the network size is asymptotically independent of the network size and strictly represents the triangle relationships between low-degree nodes. Additionally, we find that the ratio is a good indicator of the average clustering coefficient in evolving community-based systems.