Connectivity strategies to enhance the capacity of weight-bearing networks

The connectivity properties of a weight-bearing network are exploited to enhance it's capacity. We study a 2-d network of sites where the weight-bearing capacity of a given site depends on the capacities of the sites connected to it in the layers above. The network consists of clusters viz. a set of sites connected with each other with the largest such collection of sites being denoted as the maximal cluster. New connections are made between sites in successive layers using two distinct strategies. The key element of our strategies consists of adding as many disjoint clusters as possible to the sites on the trunk $T$ of the maximal cluster. The new networks can bear much higher weights than the original networks and have much lower failure rates. The first strategy leads to a greater enhancement of stability whereas the second leads to a greater enhancement of capacity compared to the original networks. The original network used here is a typical example of the branching hierarchical class. However the application of strategies similar to ours can yield useful results in other types of networks as well.Comment: 17 pages, 3 EPS files, 5 PS files, Phys. Rev. E (to appear

A model for cascading failures in complex networks

Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show that the breakdown of a single node is sufficient to collapse the efficiency of the entire system if the node is among the ones with largest load. This is particularly important for real-world networks with an highly hetereogeneous distribution of loads as the Internet and electrical power grids.Comment: 4 pages, 4 figure

Hierarchical Organization in Complex Networks

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale-free topology. In hierarchical networks the degree of clustering characterizing the different groups follows a strict scaling law, which can be used to identify the presence of a hierarchical organization in real networks. We find that several real networks, such as the World Wide Web, actor network, the Internet at the domain level and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems

Smallest small-world network

Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show that among all networks with the small-world structure, the most efficient ones have a single ``center'', from which all shortcuts are connected to uniformly distributed nodes over the network. The networks with several centers and a connected subnetwork of shortcuts are shown to be ``almost'' as efficient. Genetic-algorithm simulations further support our results.Comment: 5 pages, 6 figures, REVTeX

Growing Scale-Free Networks with Small World Behavior

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases logartihmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive expressions for the clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure

Evolving networks with disadvantaged long-range connections

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 distance $d$ is proportional to $d^{-\alpha}$, where $\alpha$ is a tunable parameter of the model. We show that the properties of the networks grown with $\alpha <1$ are close to those of the genuine scale-free construction, while for $\alpha >1$ the structure of the network is vastly different. Thus, in this regime, the node degree distribution is no more a power law, and it is well-represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of $\alpha$.Comment: REVTeX, 6 pages, 5 figure

Mean-field theory for clustering coefficients in Barabasi-Albert networks

We applied a mean field approach to study clustering coefficients in Barabasi-Albert networks. We found that the local clustering in BA networks depends on the node degree. Analytic results have been compared to extensive numerical simulations finding a very good agreement for nodes with low degrees. Clustering coefficient of a whole network calculated from our approach perfectly fits numerical data.Comment: 8 pages, 3 figure

Properties of highly clustered networks

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study SIR-type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.Comment: 7 pages, 2 figures, 1 tabl

Growing dynamics of Internet providers

In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks

Topology of the conceptual network of language

We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of languages, but also for cognitive science. We study this issue quantitatively, by mapping out the conceptual network of the English language, with the connections being defined by the entries in a Thesaurus dictionary. We find that this network presents a small-world structure, with an amazingly small average shortest path, and appears to exhibit an asymptotic scale-free feature with algebraic connectivity distribution.Comment: 4 pages, 2 figures, Revte