Related papers: Distance Distribution in Extreme Modular Networks
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing…
We examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts--``communities'' or modules. We develop an analytical approach allowing us to obtain the statistics…
We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…
We investigate the impact of community structure on information diffusion with the linear threshold model. Our results demonstrate that modular structure may have counter-intuitive effects on information diffusion when social reinforcement…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
The rapid diffusion of information and the adoption of social behaviors are of critical importance in situations as diverse as collective actions, pandemic prevention, or advertising and marketing. Although the dynamics of large cascades…
We study the extreme events taking place on complex networks. The transport on networks is modelled using random walks and we compute the probability for the occurance and recurrence of extreme events on the network. We show that the nodes…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes…
Networks that are organized as a hierarchy of modules have been the subject of much research, mainly focusing on algorithms that can extract this community structure from data. The question of why modular hierarchical organizations are so…
We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to…
Generally, networks are classified into two sides of inequality and equality with respect to the number of links at nodes by the types of degree distributions. One side includes many social, technological, and biological networks which…
The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular…
Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting…
Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…