Efficient local strategies for vaccination and network attack

We study how a fraction of a population should be vaccinated to most efficiently top epidemics. We argue that only local information (about the neighborhood of specific vertices) is usable in practice, and hence we consider only local vaccination strategies. The efficiency of the vaccination strategies is investigated with both static and dynamical measures. Among other things we find that the most efficient strategy for many real-world situations is to iteratively vaccinate the neighbor of the previous vaccinee that has most links out of the neighborhood

Cascade control and defense in complex networks

Complex networks with heterogeneous distribution of loads may undergo a global cascade of overload failures when highly loaded nodes or edges are removed due to attacks or failures. Since a small attack or failure has the potential to trigger a global cascade, a fundamental question regards the possible strategies of defense to prevent the cascade from propagating through the entire network. Here we introduce and investigate a costless strategy of defense based on a selective further removal of nodes and edges, right after the initial attack or failure. This intentional removal of network elements is shown to drastically reduce the size of the cascade.Comment: 4 pages, 2 figures, Revte

Network dynamics of ongoing social relationships

Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this paper we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of response times (times between consecutive contacts of different direction between two actors) that has a power-law shape over a large range. We also argue that the distribution of relationship duration (the time between the first and last contacts between actors) is exponentially decaying. Methods to reanalyze the data to compensate for the finite sampling time are proposed. We find that the degree distribution for networks of ongoing contacts fits better to a power-law than the degree distribution of the network of accumulated contacts do. We see that the clustering and assortative mixing coefficients are of the same order for networks of ongoing and accumulated contacts, and that the structural fluctuations of the former are rather large.Comment: to appear in Europhys. Let

A network-based threshold model for the spreading of fads in society and markets

We investigate the behavior of a threshold model for the spreading of fads and similar phenomena in society. The model is giving the fad dynamics and is intended to be confined to an underlying network structure. We investigate the whole parameter space of the fad dynamics on three types of network models. The dynamics we discover is rich and highly dependent on the underlying network structure. For some range of the parameter space, for all types of substrate networks, there are a great variety of sizes and life-lengths of the fads -- what one see in real-world social and economical systems

Tax evasion dynamics and Zaklan model on Opinion-dependent Network

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on Stauffer-Hohnisch-Pittnauer (SHP) networks. To control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhood of the critical noise $q_{c}$ to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.Comment: 14 page, 4 figure

The diplomat's dilemma: Maximal power for minimal effort in social networks

Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social networks there is a cost of maintaining social ties. This leads to a situation (that can occur in the professional social networks of executives, lobbyists, diplomats and so on) where agents have the conflicting objectives of aiming for centrality while simultaneously keeping the degree low. We investigate this situation in an adaptive network-evolution model where agents optimize their positions in the network following individual strategies, and using only local information. The strategies are also optimized, based on the success of the agent and its neighbors. We measure and describe the time evolution of the network and the agents' strategies.Comment: Submitted to Adaptive Networks: Theory, Models and Applications, to be published from Springe

Role of Activity in Human Dynamics

The human society is a very complex system; still, there are several non-trivial, general features. One type of them is the presence of power-law distributed quantities in temporal statistics. In this Letter, we focus on the origin of power-laws in rating of movies. We present a systematic empirical exploration of the time between two consecutive ratings of movies (the interevent time). At an aggregate level, we find a monotonous relation between the activity of individuals and the power-law exponent of the interevent-time distribution. At an individual level, we observe a heavy-tailed distribution for each user, as well as a negative correlation between the activity and the width of the distribution. We support these findings by a similar data set from mobile phone text-message communication. Our results demonstrate a significant role of the activity of individuals on the society-level patterns of human behavior. We believe this is a common character in the interest-driven human dynamics, corresponding to (but different from) the universality classes of task-driven dynamics.Comment: 5 pages, 6 figures. Accepted by EP

Handling oversampling in dynamic networks using link prediction

Oversampling is a common characteristic of data representing dynamic networks. It introduces noise into representations of dynamic networks, but there has been little work so far to compensate for it. Oversampling can affect the quality of many important algorithmic problems on dynamic networks, including link prediction. Link prediction seeks to predict edges that will be added to the network given previous snapshots. We show that not only does oversampling affect the quality of link prediction, but that we can use link prediction to recover from the effects of oversampling. We also introduce a novel generative model of noise in dynamic networks that represents oversampling. We demonstrate the results of our approach on both synthetic and real-world data.Comment: ECML/PKDD 201

Signatures of currency vertices

Many real-world networks have broad degree distributions. For some systems, this means that the functional significance of the vertices is also broadly distributed, in other cases the vertices are equally significant, but in different ways. One example of the latter case is metabolic networks, where the high-degree vertices -- the currency metabolites -- supply the molecular groups to the low-degree metabolites, and the latter are responsible for the higher-order biological function, of vital importance to the organism. In this paper, we propose a generalization of currency metabolites to currency vertices. We investigate the network structural characteristics of such systems, both in model networks and in some empirical systems. In addition to metabolic networks, we find that a network of music collaborations and a network of e-mail exchange could be described by a division of the vertices into currency vertices and others.Comment: to appear in Journal of the Physical Society of Japa