Distribution of node characteristics in complex networks (original) (raw)
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Classes of complex networks defined by role-to-role connectivity profiles
Nature Physics, 2007
Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most current research on complex networks is on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most real-world networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation, and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes based on their link type frequency. Importantly, we demonstrate that the above structural features cannot be captured by means of often studied global properties.
Analysis of the structure of complex networks at different resolution levels
Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality relationship. The standard approach is based on the optimization of a quality function, modularity, which is a relative quality measure for a partition of a network into modules. Recently some authors have pointed out that the optimization of modularity has a fundamental drawback: the existence of a resolution limit beyond which no modular structure can be detected even though these modules might have own entity. The reason is that several topological descriptions of the network coexist at different scales, which is, in general, a fingerprint of complex systems. Here we propose a method that allows for multiple resolution screening of the modular structure. The method has been validated using synthetic networks, discovering the predefined structures at all scales. Its application to two real social networks allows to find the exact splits reported in the literature, as well as the substructure beyond the actual split.
Some insights into the relevance of nodes' characteristics in complex network structures
Designing Networks for Innovation and Improvisation, Proceedings of the 6th International COINs Conference
Network structures describe a variety of systems and it is crucial to recognise essential functionalities that affect the dynamic of interactions. Nodes are often identified by certain characteristics, such as age or gender, and the tendency to link nodes with similar features is referred to as homophily. To verify which characteristic is able to address such behaviour has a computational complexity that becomes hard for large networks. In this paper we present a methodology that can be used as a pre-processing tool in order to avoid the study of non-effective nodes' characteristics.
Statistical mechanics of complex networks
Computing Research Repository, 2001
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Lecture Notes in Physics, 2004
In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on the classical random graph model and then survey a large variety of recently studied network models. Next, we analyze the structural properties of the graphs in these ensembles in terms of both local and global characteristics, such as degrees, degree-degree correlations, component sizes, and spectral properties. We conclude with topological phase transitions and show examples for both continuous and discontinuous transitions.
A Realistic Model for Complex Networks
2003
It appeared recently that the classical random network model used to represent complex networks does not capture their main properties (clustering, degree distribution). Since then, various attempts have been made to provide network models having these properties. We propose here the first model which achieves the following challenges: it produces networks which have the three main wanted properties, it is based on some real-world observations, and it is sufficiently simple to make it possible to prove its main properties. We first give an overview of the field by presenting the main models introduced until now, then we discuss some remarks on some complex networks which lead us to the definition of our model. We then show that the model has the expected properties and that it can actually be seen as a general model for complex networks.
Hierarchical Characterization of Complex Networks
Journal of Statistical Physics, 2006
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.
EPL (Europhysics Letters), 2008
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animation.