Related papers: Navigability is a Robust Property
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics…
A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…
Airbnb is a two-sided marketplace, bringing together hosts who own listings for rent, with prospective guests from around the globe. Applying neural network-based learning to rank techniques has led to significant improvements in matching…
The presence of hierarchy in many real-world networks is not yet fully explained. Complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for…
A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites which link to earlier sites with a probability A_k which depends on the number of…
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…
In this paper we show that the small world and weak ties phenomena can spontaneously emerge in a social network of interacting agents. This dynamics is simulated in the framework of a simplified model of opinion diffusion in an evolving…
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
The Penna bit-string model successfully encompasses many phenomena of population evolution, including inheritance, mutation, evolution and ageing. If we consider social interactions among individuals in the Penna model, the population will…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
In the classical preferential attachment model, links form instantly to newly arriving nodes and do not change over time. We propose a hierarchical random graph model in a spatial setting, where such a time-variability arises from an…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
We prove logarithmic upper bounds for the diameters of the random-surfer Webgraph model and the PageRank-based selection Webgraph model, confirming the small world phenomenon holds for them. In the special case when the generated graph is a…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
Natural systems are modeled by networks with nodes and links. Often the nodes are segregated into communities with different connectivity patterns. Node heterogeneity such as political affiliation in social networks or biological function…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…