Nonlocal evolution of weighted scale-free networks

We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the network is determined nonlocally, this approach can explain the generic nonlinear scaling between the strength and the degree of a node. We demonstrate by a simple model that the strength-driven evolution scheme recently introduced can be generalized to a nonlinear preferential attachment rule, generating the power-law behaviors in degree and in strength simultaneously.Comment: 4 pages, 4 figures, final version published in PR

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

The networked seceder model: Group formation in social and economic systems

The seceder model illustrates how the desire to be different than the average can lead to formation of groups in a population. We turn the original, agent based, seceder model into a model of network evolution. We find that the structural characteristics our model closely matches empirical social networks. Statistics for the dynamics of group formation are also given. Extensions of the model to networks of companies are also discussed

Comparing Recent Organizing Templates for Test Content between ACS Exams in General Chemistry and AP Chemistry

Two different versions of “big ideas” rooted content maps have recently been published for general chemistry. As embodied in the content outline from the College Board, one of these maps is designed to guide curriculum development and testing for advanced placement (AP) chemistry. The Anchoring Concepts Content Map for general chemistry from the ACS Exams Institute is a component of a larger content map for the four-year undergraduate curriculum. This article compares the structure and content in these two maps to provide perspective on the current nature of the general chemistry curriculum. This contribution is part of a special issue on teaching introductory chemistry in the context of the AP chemistry course redesign

Cascade-based attacks on complex networks

We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized by the loads on nodes, is important. We show that for such networks where loads can redistribute among the nodes, intentional attacks can lead to a cascade of overload failures, which can in turn cause the entire or a substantial part of the network to collapse. This is relevant for real-world networks that possess a highly heterogeneous distribution of loads, such as the Internet and power grids. We demonstrate that the heterogeneity of these networks makes them particularly vulnerable to attacks in that a large-scale cascade may be triggered by disabling a single key node. This brings obvious concerns on the security of such systems.Comment: 4 pages, 4 figures, Revte

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.

Dynamic scaling regimes of collective decision making

We investigate a social system of agents faced with a binary choice. We assume there is a correct, or beneficial, outcome of this choice. Furthermore, we assume agents are influenced by others in making their decision, and that the agents can obtain information that may guide them towards making a correct decision. The dynamic model we propose is of nonequilibrium type, converging to a final decision. We run it on random graphs and scale-free networks. On random graphs, we find two distinct regions in terms of the "finalizing time" -- the time until all agents have finalized their decisions. On scale-free networks on the other hand, there does not seem to be any such distinct scaling regions

Multiscale Analysis of Spreading in a Large Communication Network

In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how some dynamic process mediated by the network unfolds. We have explored the limiting case of the speed of spreading in the SI model, set up such that an event between an infectious and susceptible individual always transmits the infection. The speed of this process sets an upper bound for the speed of any dynamic process that is mediated through the interaction events of the network. With the help of temporal networks derived from large scale time-stamped data on mobile phone calls, we extend earlier results that point out the slowing-down effects of burstiness and temporal inhomogeneities. In such networks, links are not permanently active, but dynamic processes are mediated by recurrent events taking place on the links at specific points in time. We perform a multi-scale analysis and pinpoint the importance of the timings of event sequences on individual links, their correlations with neighboring sequences, and the temporal pathways taken by the network-scale spreading process. This is achieved by studying empirically and analytically different characteristic relay times of links, relevant to the respective scales, and a set of temporal reference models that allow for removing selected time-domain correlations one by one

Attack Resilience of the Evolving Scientific Collaboration Network

Stationary complex networks have been extensively studied in the last ten years. However, many natural systems are known to be continuously evolving at the local (“microscopic”) level. Understanding the response to targeted attacks of an evolving network may shed light on both how to design robust systems and finding effective attack strategies. In this paper we study empirically the response to targeted attacks of the scientific collaboration networks. First we show that scientific collaboration network is a complex system which evolves intensively at the local level – fewer than 20% of scientific collaborations last more than one year. Then, we investigate the impact of the sudden death of eminent scientists on the evolution of the collaboration networks of their former collaborators. We observe in particular that the sudden death, which is equivalent to the removal of the center of the egocentric network of the eminent scientist, does not affect the topological evolution of the residual network. Nonetheless, removal of the eminent hub node is exactly the strategy one would adopt for an effective targeted attack on a stationary network. Hence, we use this evolving collaboration network as an experimental model for attack on an evolving complex network. We find that such attacks are ineffectual, and infer that the scientific collaboration network is the trace of knowledge propagation on a larger underlying social network. The redundancy of the underlying structure in fact acts as a protection mechanism against such network attacks

Structural transitions in scale-free networks

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabasi-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean field rate equation for the problem. This is solved for a specific case with the result C(k) ~ 1/k for the clustering of a node of degree k. Numerical results agree with such a mean-field exponent which also reproduces the clustering of many real networks.Comment: 4 pages, 3 figures, RevTex forma