Anonymity in the Wild: Mixes on Unstructured Networks

Echo state network (ESN) has recently attracted increasing interests because of its superior capability in modeling nonlinear dynamic systems. In the conventional echo state network model, its dynamic reservoir (DR) has a random and sparse topology, which is far from the real biological neural networks from both structural and functional perspectives. We hereby propose three novel types of echo state networks with new dynamic reservoir topologies based on complex network theory, i.e., with a small-world topology, a scale-free topology, and a mixture of small-world and scale-free topologies, respectively. We then analyze the relationship between the dynamic reservoir structure and its prediction capability. We utilize two commonly used time series to evaluate the prediction performance of the three proposed echo state networks and compare them to the conventional model. We also use independent and identically distributed time series to analyze the short-term memory and prediction precision of these echo state networks. Furthermore, we study the ratio of scale-free topology and the small-world topology in the mixed-topology network, and examine its influence on the performance of the echo state networks. Our simulation results show that the proposed echo state network models have better prediction capabilities, a wider spectral radius, but retain almost the same short-term memory capacity as compared to the conventional echo state network model. We also find that the smaller the ratio of the scale-free topology over the small-world topology, the better the memory capacities.

It is now known that the complexity of network topology has a great impact on the stabilization of complex dynamical networks. In this work, we study the control of random networks and scale-free networks. Conditions are investigated for globally or locally stabilizing such networks. Our strategy is to apply local feedback control to a small fraction of network nodes. We propose the concept of virtual control for microscopic dynamics throughout the process with different pinning schemes for both random networks and scale-free networks. We explain the main reason why significantly less local controllers are required by specifically pinning the most highly connected nodes in a scale-free network than those required by the randomly pinning scheme, and why there is no significant difference between specifically and randomly pinning schemes for controlling random dynamical networks. We also study the synchronization phenomenon of controlled dynamical networks in the stabilization process, both analytically and numerically.

Uncorrelated random scale-free (URSF) networks are useful null models for checking the effects of scale-free topology on network-based dynamical processes. Here, we present a comparative study of the jamming level of gradient networks based on URSF networks and Erdős–Rényi (ER) random networks. We find that the URSF networks are less congested than ER random networks for the average degree ⟨k⟩>kc (kc ≈ 2 denotes a critical connectivity). In addition, by investigating the topological properties of the two kinds of gradient networks, we discuss the relations between the topological structure and the transport efficiency of the gradient networks. These findings show that the uncorrelated scale-free structure might allow more efficient transport than the random structure.

Page rank is a ranking algorithm based on a random surfer model which is used in Google search engine and many other domains. Because of its initial success in Google search engine, page rank has become the de-facto choice when it comes to ranking nodes in a network structure. Despite the ubiquitous utility of the algorithm, little is known about the effect of topology on the performance of the page rank algorithm. Hence this paper discusses the performance of page rank algorithm under different topological conditions. We use scale-free networks and random networks along with a custom search engine we implemented in order to experimentally prove that the performance of page rank algorithm is deteriorated when the random network is perturbed. In contrast, scale-free topology is proven to be resilient against degree preserving perturbations which aids the page rank algorithm to deliver consistent results across multiple networks that are perturbed to varying proportions. Not only does the top ranking results emerge as stable nodes, but the overall performance of the algorithm is proven to be remarkably resilient which deepens our understanding about the risks in applying page rank algorithm without an initial analysis on the underlying network structure. The results conclusively suggests that while page rank algorithm can be applied to scale-free networks with relatively low risk, applying page rank algorithm to other topologies can be risky as well as misleading. Therefore, the success of the page rank algorithm in real world in search engines such as Google is at least partly due to the fact that the world wide web is a scale-free network. Since the world wide web is constantly evolving, we postulate that if the topological structure of the world wide web changes significantly so that it loses its scale-free nature to some extent, the page rank algorithm will not be as effective.

We consider the effect of segregation on opinion formation in social networks with and without influential leaders in scale-free random networks, which is found in many social and natural phenomena. We have used agent-based modeling and simulation, focusing on the social impact model of opinion formation. Two simulation scenarios of this opinion formation model have been considered: (1) the original scenario which randomly assigns persuasion strengths to the agents, and (2) a centrality-based scenario, which assigns persuasion strengths proportional to the agents’ centralities. In the latter scenario, hubs are considered more influential leaders who are more connected to others and have higher persuasion strengths than others. The simulation results show a correlation between segregation and change of population opinion in the original model, but no correlation between both variables in the centrality-based scenario. The results lead us to conclude that with strong influential leaders in society, the effect of segregation in opinion formation is neglectable.

A cuckoo search algorithm with scale-free population topology

We study a system consisting of diffusively coupled noisy bistable elements on a scale-free random network. This system exhibits an order-disorder phase transition as the noise intensity is varied. The phase ordering process takes place consecutively and in order of the degrees, reflecting strong degree heterogeneity of the scale-free network. A nonlinear Fokker-Planck equation describing the network dynamics is derived under mean-field approximation of the network, and is used to explain the phase ordering dynamics of the system.

The development of digital media, the increasing use of social networks, the easier access to modern technological devices, is perturbing thousands of people in their public and private lives. People love posting their personal news without consider the risks involved. Privacy has never been more important. Privacy enhancing technologies research have attracted considerable international attention after the recent news against users personal data protection in social media websites like Facebook. It has been demonstrated that even when using an anonymous communication system, it is possible to reveal user’s identities through intersection attacks or traffic analysis attacks. Combining a traffic analysis attack with Analysis Social Networks (SNA) techniques, an adversary can be able to obtain important data from the whole network, topological network structure, subset of social data, revealing communities and its interactions. The aim of this work is to demonstrate how intersection attacks can disclose structural properties and significant details from an anonymous social network composed of a university community.

Little is known about geographic properties of large-scale social networks. In this paper, we examine the geospatial attributes of a planetary-scale social network of 240 million people and 1.3 billion edges. We study the interplay among topological, geographical, and algorithmically generated paths connecting pairs of nodes in a social network. Starting in the realm of cyberspace, we find that topologically shortest paths of average length of 6.6 exist between pairs of nodes in the network and that the average degree of separation among nodes is robust to removal of hub nodes. Moving to the realm of locations and distances in geographic space, we find that topologically shortest paths in the social graph grow with increasing geographic distance between path's endpoint nodes. We discover that shortest topological paths are geographically inefficient, but that geography provides an important cue for local algorithmic policies for navigating between source and target nodes. Local algorithmic strategies for navigating the larger network structure in the absence of global navigation procedures have varying success. At the early stages of the navigation, navigating to a hub node helps, while in the middle stage, geography provides the most important clue. While local algorithms for navigating have trouble reaching the target node, they are successful in reaching nodes that are geographically close to the target. Taken together, our results demonstrate a complex interplay between topological and geographical properties of social networks and explain the success of local strategies for navigating such networks.

Scale-free networks, as one major class of complex networks, are characterized by a specific structural feature of power-law degree distributions. Examples of scale-free real-world networks include World Wide Web (WWW), email networks, citation and co-author scientific networks, social networks (Facebook, Twitter), networks of Internet routers, and protein-protein interaction networks. In this paper we model and evaluate the reliability of scale-free complex networks using a binary decision diagram (BDD)-based method. Two-terminal reliability is considered, which is defined as the probability that a specified pair of nodes can communication through at least one fault-tree path in the network. This reliability metric can measure, for example, how reliable the information can be shared between two parties or in general how reliable the information can be disseminated within a social network. The Barabasi-Albert model is used for generating the sample scale-free networks studied in this paper. The reliability performance of scale-free networks is compared to that of random networks under the Erdos-Renyi model. Degree distributions and clustering coefficients (average fraction of pairs of neighbors of a node which are also neighbors of each other) of sample scale-free and random networks are illustrated and compared. Their effects on the performance of the BDD-based method for the reliability analysis of both scale-free and random networks are also discussed.

In a network cliques are fully connected subgraphs that reveal which are the tight communities present in it. Cliques of size c > 3 are present in random Erdös and Renyi graphs only in the limit of diverging average connectivity.Starting from the finding that real scale-free graphs have large cliques, we study the clique number in uncorrelated scale-free networks finding both upper and lower bounds. Interestingly, we find that in scale-free networks large cliques appear also when the average degree is finite, i.e. even for networks with power law degree distribution exponents γ∊(2,3). Moreover, as long as γ < 3, scale-free networks have a maximal clique which diverges with the system size.

The coherent exciton transport on a class of deterministic and random scale-free networks (DSFNs and RSFNs) generated by simple rules is studied in this paper. The coherent exciton dynamics is modeled by continuous-time quantum walks, and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For DSFNs, the probabilities of finding the excitation at the initial central nodes are nearly periodic, in contrast to the flat behavior found for RSFNs. In the long time limit, the transition probabilities on DSFNs show characteristic patterns with identical values. For RSFNs, we find that the excitation is most likely to be found at the initial nodes with high connectivity. All these features of quantum transport are significantly different from those of the classical transport modeled by continuous-time random walks.

Alliance networks are the underlying structures of social systems in business, management, and society. The sustainability and dynamics of a social system rely on the structural evolutions of the topologies. Understanding the evolution sheds light on the dynamics and sustainability of a social system. Minority game models have been successfully applied across social science, economy, management, and engineering. They provide simple yet applicable modeling to articulate the evolutionary cooperation dynamics of competitive players in binary decision situations. By extending the minority games played in alliance networks, the cooperation in structured systems of different network topologies is analyzed. In this model, local and global score strategies are considered with and without cooperation rewiring options. The cooperation level, the score, and the topological properties are investigated. The research uses a numerical simulation approach on random networks, scale-free networks, and small-world networks. The results suggest that the network rewiring strategy leads to higher systemic performance with a higher score and a higher level of stability in decision-making. Competitive decision-making can lead to a higher level of cooperation from a poor initial start. However, stubbornness in decision-making can lead to a poor situation when cooperation is discouraged. Players with local or global information adopt local and global score strategies. The results show that local strategies might lead to imbalance, while a global strategy might achieve a relatively stable outcome. This work contributes to bridge minority games in structured networks to study the cooperation between formation and evolution, and calls for future minority game modeling on social networks.

Shuffling is an effective method to build a publicly verifiable mix network to implement verifiable anonymous channels that can be used for important cryptographic applications like electronic voting and electronic cash. One shuffling scheme by Groth is claimed to be secure and efficient. However, its soundness has not been formally proven. An attack against the soundness of this shuffling scheme is presented in this paper. Such an attack compromises the soundness of the mix network based on it. Two new shuffling protocols are designed on the basis of Groth`s shuffling and batch verification techniques. The first new protocol is not completely sound, but is formally analyzed in regards to soundness, so it can be applied to build a mix network with formally proven soundness. The second new protocol is completely sound, so is more convenient to apply. Formal analysis in this paper guarantees that both new shuffling protocols can be employed to build mix networks with formally provable soundness. Both protocols prevent the attack against soundness in Groth`s scheme. Both new shuffling protocols are very efficient as batch-verification-based efficiency-improving mechanisms have been adopted. The second protocol is even simpler and more elegant than the first one as it is based on a novel batch cryptographic technique.

Dynamical properties of spiking neural networks with small world topologies