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

Radial Structure of the Internet

The structure of the Internet at the Autonomous System (AS) level has been studied by both the Physics and Computer Science communities. We extend this work to include features of the core and the periphery, taking a radial perspective on AS network structure. New methods for plotting AS data are described, and they are used to analyze data sets that have been extended to contain edges missing from earlier collections. In particular, the average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure. Common vertex-specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices. Two data sets are analyzed using these measures as well as two common generative models (Barabasi-Albert and Inet). We find a clear distinction between the highly connected core and a sparse periphery. We also find that the periphery has a more complex structure than that predicted by degree distribution or the two generative models

The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy

The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the rest of the elements in the distribution. Because classical entropy-based Maxent collapses cases confounding all distinct degrees of randomness and pseudo-randomness, here we take into consideration the generative mechanism of the systems considered in the ensemble to separate objects that may comply with the principle under some restriction and whose entropy is maximal but may be generated recursively from those that are actually algorithmically random offering a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code. Using the distinction between computable and algorithmic randomness we quantify the cost in information loss associated with reprogramming. To illustrate this we apply the algorithmic refinement to Maxent on graphs and introduce a Maximal Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. We discuss practical implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation.Comment: 30 page

Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis

An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models