Fergal Reid

An Analysis of Anonymity in the Bitcoin System

Anonymity in Bit coin, a peer-to-peer electronic currency system, is a complicated issue. Within the system, users are identified by public-keys only. An attacker wishing to de-anonymize its users will attempt to construct the one to-many mapping between users and public-keys and associate information external to the system with the users. Bitcoinfrustrates this attack by storing the mapping of a user to his or her public-keys on that users node only and by allowing each user to generate as many public-keys as required. In this paper we consider the topological structure of two networks derived from Bitcoins public transaction history. We show that the two networks have a non-trivial topological structure, provide complementary views of the Bit coin system and have implications for anonymity. We combine these structures with external information and techniques such as context discovery and flow analysis to investigate an alleged theft of Bit coins, which, at the time of the theft, had a market value of approximately half a million U.S. dollars.

Partitioning Breaks Communities

Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping communities. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across separate partitions, as produced by such algorithms. We examine the largest connected component of the sub graph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number of cliques split. We conclude that, due to the connectedness of many networks, any community finding algorithm that produces partitions must fail to find at least some significant structures. Moreover, contrary to traditional intuition, in some empirical networks, strong ties and cliques frequently do cross community boundaries.

Percolation Computation in Complex Networks

K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using clique graphs, certain aspects of k-clique percolation are computationally challenging in practice. In this paper we investigate aspects of empirical social networks, such as the large numbers of overlapping maximal cliques contained within them, that make clique percolation, and clique graph representations, computationally expensive. We motivate a simple algorithm to conduct clique percolation, and investigate its performance compared to current best-in-class algorithms. We present improvements to this algorithm, which allow us to perform k-clique percolation on much larger empirical datasets. Our approaches perform much better than existing algorithms on networks exhibiting pervasively overlapping community structure, especially for higher values of k. However, clique percolation remains a hard computational problem, current algorithms still scale worse than some other overlapping community finding algorithms.

Seeding for pervasively overlapping communities.

In some social and biological networks, the majority of nodes belong to multiple communities. It has recently been shown that a number of the algorithms specifically designed to detect overlapping communities do not perform well in such highly overlapping settings. Here, we consider one class of these algorithms, those which optimize a local fitness measure, typically by using a greedy heuristic to expand a seed into a community. We perform synthetic benchmarks which indicate that an appropriate seeding strategy becomes more important as the extent of community overlap increases. We find that distinct cliques provide the best seeds. We find further support for this seeding strategy with benchmarks on a Facebook network and the yeast interactome.

Efficient and reliable network tomography in heterogeneous networks using BitTorrent broadcasts and clustering algorithms

In the area of network performance and discovery, network tomography focuses on reconstructing network properties using only end-to-end measurements at the application layer. One challenging problem in network tomography is reconstructing available bandwidth along all links during multiple source / multiple destination transmissions. The traditional measurement procedures used for bandwidth tomography are extremely time consuming. We propose a novel solution to this problem. Our method counts the fragments exchanged during a BitTorrent broadcast. While this measurement has a high level of randomness, it can be obtained very efficiently, and aggregated into a reliable metric. This data is then analyzed with state-of-the-art algorithms, which correctly reconstruct logical clusters of nodes interconnected by high bandwidth, as well as bottlenecks between these logical clusters. Our experiments demonstrate that the proposed two-phase approach efficiently solves the presented problem for a number of settings on a complex grid infrastructure.

Diffusion in Networks with Overlapping Community Structure

In this work we study diffusion in networks with community structure. We first replicate and extend work on networks with non-overlapping community structure. We then study diffusion on network models that have overlapping community structure. We study contagions in the standard SIR model, and complex contagions thought to be better models of some social diffusion processes. Finally, we investigate diffusion on empirical networks with known overlapping community structure, by analysing the structure of such networks, and by simulating contagion on them. We find that simple and complex contagions can spread fast in networks with overlapping community structure. We also find that short paths exist through overlapping community structure on empirical networks.

Analysing structure in complex networks using quality functions evolved by genetic programming

When studying complex networks, we are often interested in identifying structures within the networks. Previous work has successfully used algorithmically identified network structures to predict functional groups; for example, where structures extracted from protein-protein interaction networks have been predictive of functional protein complexes. One way structures in complex networks have previously been described is as collections of nodes that maximise a local quality function. For a particular set of structures, we search the space of quality functions using Genetic Programming, to find a function that locally describes that set of structures. This technique allows us to investigate the common network properties of defined sets of structures. We also use this technique to classify and differentiate between different types of structure. We apply this method on several synthetic benchmarks, and on a protein-protein interaction network. Our results indicate this is a useful technique of investigating properties that sets of network structures have in common.