K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases

We consider the $k$-core decomposition of network models and Internet graphs at the autonomous system (AS) level. The $k$-core analysis allows to characterize networks beyond the degree distribution and uncover structural properties and hierarchies due to the specific architecture of the system. We compare the $k$-core structure obtained for AS graphs with those of several network models and discuss the differences and similarities with the real Internet architecture. The presence of biases and the incompleteness of the real maps are discussed and their effect on the $k$-core analysis is assessed with numerical experiments simulating biased exploration on a wide range of network models. We find that the $k$-core analysis provides an interesting characterization of the fluctuations and incompleteness of maps as well as information helping to discriminate the original underlying structure

Understanding edge-connectivity in the Internet through core-decomposition

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization

NEMESYS: Enhanced Network Security for Seamless Service Provisioning in the Smart Mobile Ecosystem

As a consequence of the growing popularity of smart mobile devices, mobile malware is clearly on the rise, with attackers targeting valuable user information and exploiting vulnerabilities of the mobile ecosystems. With the emergence of large-scale mobile botnets, smartphones can also be used to launch attacks on mobile networks. The NEMESYS project will develop novel security technologies for seamless service provisioning in the smart mobile ecosystem, and improve mobile network security through better understanding of the threat landscape. NEMESYS will gather and analyze information about the nature of cyber-attacks targeting mobile users and the mobile network so that appropriate counter-measures can be taken. We will develop a data collection infrastructure that incorporates virtualized mobile honeypots and a honeyclient, to gather, detect and provide early warning of mobile attacks and better understand the modus operandi of cyber-criminals that target mobile devices. By correlating the extracted information with the known patterns of attacks from wireline networks, we will reveal and identify trends in the way that cyber-criminals launch attacks against mobile devices.Comment: Accepted for publication in Proceedings of the 28th International Symposium on Computer and Information Sciences (ISCIS'13); 9 pages; 1 figur

Truss Decomposition in Massive Networks

The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core which is also efficient to compute, k-truss represents the "core" of a k-core that keeps the key information of, while filtering out less important information from, the k-core. However, existing algorithms for computing k-truss are inefficient for handling today's massive networks. We first improve the existing in-memory algorithm for computing k-truss in networks of moderate size. Then, we propose two I/O-efficient algorithms to handle massive networks that cannot fit in main memory. Our experiments on real datasets verify the efficiency of our algorithms and the value of k-truss.Comment: VLDB201

Decoupling of brain function from structure reveals regional behavioral specialization in humans

The brain is an assembly of neuronal populations interconnected by structural pathways. Brain activity is expressed on and constrained by this substrate. Therefore, statistical dependencies between functional signals in directly connected areas can be expected higher. However, the degree to which brain function is bound by the underlying wiring diagram remains a complex question that has been only partially answered. Here, we introduce the structural-decoupling index to quantify the coupling strength between structure and function, and we reveal a macroscale gradient from brain regions more strongly coupled, to regions more strongly decoupled, than expected by realistic surrogate data. This gradient spans behavioral domains from lower-level sensory function to high-level cognitive ones and shows for the first time that the strength of structure-function coupling is spatially varying in line with evidence derived from other modalities, such as functional connectivity, gene expression, microstructural properties and temporal hierarchy

Shared-memory Graph Truss Decomposition

We present PKT, a new shared-memory parallel algorithm and OpenMP implementation for the truss decomposition of large sparse graphs. A k-truss is a dense subgraph definition that can be considered a relaxation of a clique. Truss decomposition refers to a partitioning of all the edges in the graph based on their k-truss membership. The truss decomposition of a graph has many applications. We show that our new approach PKT consistently outperforms other truss decomposition approaches for a collection of large sparse graphs and on a 24-core shared-memory server. PKT is based on a recently proposed algorithm for k-core decomposition.Comment: 10 pages, conference submissio

Embedding Graphs under Centrality Constraints for Network Visualization

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates two graph embedding approaches with centrality considerations to comply with node hierarchy. The problem is formulated first as one of constrained multi-dimensional scaling (MDS), and it is solved via block coordinate descent iterations with successive approximations and guaranteed convergence to a KKT point. In addition, a regularization term enforcing graph smoothness is incorporated with the goal of reducing edge crossings. A second approach leverages the locally-linear embedding (LLE) algorithm which assumes that the graph encodes data sampled from a low-dimensional manifold. Closed-form solutions to the resulting centrality-constrained optimization problems are determined yielding meaningful embeddings. Experimental results demonstrate the efficacy of both approaches, especially for visualizing large networks on the order of thousands of nodes.Comment: Submitted to IEEE Transactions on Visualization and Computer Graphic