Structural Properties Of Complex Networks Research Articles

Joint Detection of Community and Structural Hole Spanner of Networks in Hyperbolic Space.

Community detection and structural hole spanner (the node bridging different communities) identification, revealing the mesoscopic and microscopic structural properties of complex networks, have drawn much attention in recent years. As the determinant of mesoscopic structure, communities and structural hole spanners discover the clustering and hierarchy of networks, which has a key impact on transmission phenomena such as epidemic transmission, information diffusion, etc. However, most existing studies address the two tasks independently, which ignores the structural correlation between mesoscale and microscale and suffers from high computational costs. In this article, we propose an algorithm for simultaneously detecting communities and structural hole spanners via hyperbolic embedding (SDHE). Specifically, we first embed networks into a hyperbolic plane, in which, the angular distribution of the nodes reveals community structures of the embedded network. Then, we analyze the critical gap to detect communities and the angular region where structural hole spanners may exist. Finally, we identify structural hole spanners via two-step connectivity. Experimental results on synthetic networks and real networks demonstrate the effectiveness of our proposed algorithm compared with several state-of-the-art methods.

Percolation in random graphs with higher-order clustering.

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally treelike and does not contain short-range loops between neighbors. In this paper we use the generating function formulation to examine clustered networks that contain simple cycles and cliques of any order. We use the natural generalization to the Molloy-Reed criterion for these networks to describe their critical properties and derive an approximate analytical description of the size of the giant component, providing solutions for Poisson and power-law networks. We find that networks comprising larger simple cycles behave increasingly more treelike. Conversely, clustering composed of larger cliques increasingly deviate from the treelike solution, although the behavior is strongly dependent on the degree-assortativity.

A new structural entropy measurement of networks based on the nonextensive statistical mechanics and hub repulsion.

The structure properties of complex networks are an open issue. As the most important parameter to describe the structural properties of the complex network, the structure entropy has attracted much attention. Recently, the researchers note that hub repulsion plays an role in structural entropy. In this paper, the repulsion between nodes in complex networks is simulated when calculating the structure entropy of the complex network. Coulomb's law is used to quantitatively express the repulsive force between two nodes of the complex network, and a new structural entropy based on the Tsallis nonextensive statistical mechanics is proposed. The new structure entropy synthesizes the influence of repulsive force and betweenness. We study several construction networks and some real complex networks, the results show that the proposed structure entropy can describe the structural properties of complex networks more reasonably. In particular, the new structural entropy has better discrimination in describing the complexity of the irregular network. Because in the irregular network, the difference of the new structure entropy is larger than that of degree structure entropy, betweenness structure entropy and Zhang's structure entropy. It shows that the new method has better discrimination for irregular networks, and experiments on Graph, Centrality literature, US Aire lines and Yeast networks confirm this conclusion.

Community Detection by Motif-Aware Label Propagation

Community detection (or graph clustering) is crucial for unraveling the structural properties of complex networks. As an important technique in community detection, label propagation has shown the advantage of finding a good community structure with nearly linear time complexity. However, despite the progress that has been made, there are still several important issues that have not been properly addressed. First, the label propagation typically proceeds over the lower order structure of the network and only the direct one-hop connections between nodes are taken into consideration. Unfortunately, the higher order structure that may encode design principle of the network and be crucial for community detection is neglected under this regime. Second, the stability of the identified community structure may also be seriously affected by the inherent randomness in the label propagation process. To tackle the above issues, this article proposes a Motif-Aware Weighted Label Propagation method for community detection. We focus on triangles within the network, but our technique extends to other kinds of motifs as well. Specifically, the motif-based higher order structure mining is conducted to capture structural characteristics of the network. First, the motif of interest (locally meaningful pattern) is identified, and then, the motif-based hypergraph can be constructed to encode the higher order connections. To further utilize the structural information of the network, a re-weighted network is designed, which unifies both the higher order structure and the original lower order structure. Accordingly, a novel voting strategy termed NaS (considering both <underline>N</underline>umber <underline>a</underline>nd <underline>S</underline>trength of connections) is proposed to update node labels during the label propagation process. In this way, the random label selection can be effectively eliminated, yielding more stable community structures. Experimental results on multiple real-world datasets have shown the superiority of the proposed method.

Empirical analysis of the user reputation and clustering property for user-object bipartite networks

User reputation is of great significance for online rating systems which can be described by user-object bipartite networks, measuring the user ability of rating accurate assessments of various objects. The clustering coefficients have been widely investigated to analyze the local structural properties of complex networks, analyzing the diversity of user interest. In this paper, we empirically analyze the relation of user reputation and clustering property for the user-object bipartite networks. Grouping by user reputation, the results for the MovieLens dataset show that both the average clustering coefficient and the standard deviation of clustering coefficient decrease with the user reputation, which are different from the results that the average clustering coefficient and the standard deviation of clustering coefficient remain stable regardless of user reputation in the null model, suggesting that the user interest tends to be multiple and the diversity of the user interests is centralized for users with high reputation. Furthermore, we divide users into seven groups according to the user degree and investigate the heterogeneity of rating behavior patterns. The results show that the relation of user reputation and clustering coefficient is obvious for small degree users and weak for large degree users, reflecting an important connection between user degree and collective rating behavior patterns. This work provides a further understanding on the intrinsic association between user collective behaviors and user reputation.

Role of time scales and topology on the dynamics of complex networks.

The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization, etc. We study the emergence of such phenomena and their transitions by considering a complex network of dynamical systems in which a fraction of systems evolves on a slower time scale on the network. We report the transition to amplitude death for the whole network and the scaling near the transitions as the connectivity pattern changes. We also discuss the suppression and recovery of oscillations and the crossover behavior as the number of slow systems increases. By considering a scale free network of systems with multiple time scales, we study the role of heterogeneity in link structure on dynamical properties and the consequent critical behaviors. In this case with hubs made slow, our main results are the escape time statistics for loss of complete synchrony as the slowness spreads on the network and the self-organization of the whole network to a new frequency synchronized state. Our results have potential applications in biological, physical, and engineering networks consisting of heterogeneous oscillators.

Community detection in networks using self-avoiding random walks

Different kinds of random walks have proven to be useful in the study of structural properties of complex networks. Among them, the restricted dynamics of self-avoiding random walks (SAW), which visit only at most once each vertex in the same walk, has been successfully used in network exploration. The detection of communities of strongly connected vertices in networks remains an open problem, despite its importance, due to the high computational complexity of the associated optimization problem and the lack of a unique formal definition of communities. In this work, we propose a SAW-based method to extract the community distribution of a network and show that it achieves high modularity scores, specially for real-world networks. We combine SAW with principal component analysis to define the dissimilarity measure to be used for agglomerative hierarchical clustering. To evaluate the performance of this method we compare it with four popular methods for community detection: Girvan–Newman, Fastgreedy, Walktrap and Infomap using two types of synthetic networks and six well-known real-world cases.

Roles of clustering properties for degree-mixing pattern networks

The clustering coefficients have been extensively investigated for analyzing the local structural properties of complex networks. In this paper, the clustering coefficients for triangle and square structures, namely [Formula: see text] and [Formula: see text], are introduced to measure the local structure properties for different degree-mixing pattern networks. Firstly, a network model with tunable assortative coefficients is introduced. Secondly, the comparison results between the local clustering coefficients [Formula: see text] and [Formula: see text] are reported, one can find that the square structures would increase as the degree [Formula: see text] of nodes increasing in disassortative networks. At the same time, the Pearson coefficient [Formula: see text] between the clustering coefficients [Formula: see text] and [Formula: see text] is calculated for networks with different assortative coefficients. The Pearson coefficient [Formula: see text] changes from [Formula: see text] to 0.98 as the assortative coefficient [Formula: see text] increasing from [Formula: see text] to 0.45, which suggests that the triangle and square structures have the same growth trend in assortative networks whereas the opposite one in disassortative networks. Finally, we analyze the clustering coefficients [Formula: see text] and [Formula: see text] for networks with tunable assortative coefficients and find that the clustering coefficient [Formula: see text] increases from 0.0038 to 0.5952 while the clustering coefficient [Formula: see text] increases from 0.00039 to 0.005, indicating that the number of cliquishness of the disassortative networks is larger than that of assortative networks.

Analysis of Statistical and Structural Properties of Complex networks with Random Networks

Analysis of Statistical and Structural Properties of Complex networks with Random Networks

Universality in network dynamics.

Despite significant advances in characterizing the structural properties of complex networks, a mathematical framework that uncovers the universal properties of the interplay between the topology and the dynamics of complex systems continues to elude us. Here we develop a self-consistent theory of dynamical perturbations in complex systems, allowing us to systematically separate the contribution of the network topology and dynamics. The formalism covers a broad range of steady-state dynamical processes and offers testable predictions regarding the system's response to perturbations and the development of correlations. It predicts several distinct universality classes whose characteristics can be derived directly from the continuum equation governing the system's dynamics and which are validated on several canonical network-based dynamical systems, from biochemical dynamics to epidemic spreading. Finally, we collect experimental data pertaining to social and biological systems, demonstrating that we can accurately uncover their universality class even in the absence of an appropriate continuum theory that governs the system's dynamics.

Influence of a network structure on the network effect in the communication service market

In this study, we analyze the network effect in a model of a personal communication market, by using a multi-agent based simulation approach. We introduce into the simulation model complex network structures as the interaction patterns of agents. With complex network models, we investigate the dynamics of a market in which two providers are competing. We also examine the structure of networks that affect the complex behavior of the market. By a series of simulations, we show that the structural properties of complex networks, such as the clustering coefficient and degree correlation, have a major influence on the dynamics of the market. We find that the network effect is increased if the interaction pattern of agents is characterized by a high clustering coefficient, or a positive degree correlation. We also discuss a suitable model of the interaction pattern for reproducing market dynamics in the real world, by performing simulations using real data of a social network.

Multiple scale analysis of complex networks using the empirical mode decomposition method

Empirical mode decomposition (EMD) method can decompose any complicated data into finite ‘intrinsic mode functions’ (IMFs). In this paper, we use EMD method to analyze and discuss the structural properties of complex networks. A random-walk method is used to collect the data series of network systems. Utilizing the EMD method, we decompose the obtained data into finite IMFs under different spatial scales. The analysis results show that EMD method is an effective tool for capturing the topological properties of network systems under different spatial scales, such as the modular structures of network systems and their energy densities.

Consensus and Cooperation in Networked Multi-Agent Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations. </para>

Inhomogeneous percolation models for spreading phenomena in random graphs

Percolation theory has been used a great deal in the study of structural properties ofcomplex networks such as the robustness, with remarkable results. Nevertheless, a purelytopological description is not sufficient for a correct characterization of network behaviourin relation to physical flows and spreading phenomena taking place on them. Thefunctionality of real networks also depends on the ability of the nodes and the edges tobear and handle loads of flows, energy, information and other physical quantities. Wepropose to study these properties, introducing a process of inhomogeneous percolation, inwhich both the nodes and the edges spread the flows out with a given probability.The generating functions approach is exploited in order to get a generalization of theMolloy–Reed criterion for inhomogeneous joint site–bond percolation in correlated randomgraphs. A series of simple assumptions allows the analysis of more realistic situations, forwhich a number of new results are presented. In particular, for the site percolationwith inhomogeneous edge transmission, we obtain the explicit expressions for thepercolation threshold for many interesting cases, which are analysed by means of simpleexamples and numerical simulations. Some possible applications are debated.