2,208 research outputs found
A Selectivity based approach to Continuous Pattern Detection in Streaming Graphs
Cyber security is one of the most significant technical challenges in current
times. Detecting adversarial activities, prevention of theft of intellectual
properties and customer data is a high priority for corporations and government
agencies around the world. Cyber defenders need to analyze massive-scale,
high-resolution network flows to identify, categorize, and mitigate attacks
involving networks spanning institutional and national boundaries. Many of the
cyber attacks can be described as subgraph patterns, with prominent examples
being insider infiltrations (path queries), denial of service (parallel paths)
and malicious spreads (tree queries). This motivates us to explore subgraph
matching on streaming graphs in a continuous setting. The novelty of our work
lies in using the subgraph distributional statistics collected from the
streaming graph to determine the query processing strategy. We introduce a
"Lazy Search" algorithm where the search strategy is decided on a
vertex-to-vertex basis depending on the likelihood of a match in the vertex
neighborhood. We also propose a metric named "Relative Selectivity" that is
used to select between different query processing strategies. Our experiments
performed on real online news, network traffic stream and a synthetic social
network benchmark demonstrate 10-100x speedups over selectivity agnostic
approaches.Comment: in 18th International Conference on Extending Database Technology
(EDBT) (2015
The method of moments and degree distributions for network models
Probability models on graphs are becoming increasingly important in many
applications, but statistical tools for fitting such models are not yet well
developed. Here we propose a general method of moments approach that can be
used to fit a large class of probability models through empirical counts of
certain patterns in a graph. We establish some general asymptotic properties of
empirical graph moments and prove consistency of the estimates as the graph
size grows for all ranges of the average degree including .
Additional results are obtained for the important special case of degree
distributions.Comment: Published in at http://dx.doi.org/10.1214/11-AOS904 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Subgraphs in random networks
Understanding the subgraph distribution in random networks is important for
modelling complex systems. In classic Erdos networks, which exhibit a
Poissonian degree distribution, the number of appearances of a subgraph G with
n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However,
many natural networks have a non-Poissonian degree distribution. Here we
present approximate equations for the average number of subgraphs in an
ensemble of random sparse directed networks, characterized by an arbitrary
degree sequence. We find new scaling rules for the commonly occurring case of
directed scale-free networks, in which the outgoing degree distribution scales
as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree
distribution, \gamma, as a control parameter, we show that random networks
exhibit transitions between three regimes. In each regime the subgraph number
of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where
\alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and
\alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and
\gamma_c=s+1. We find that certain subgraphs appear much more frequently than
in Erdos networks. These results are in very good agreement with numerical
simulations. This has implications for detecting network motifs, subgraphs that
occur in natural networks significantly more than in their randomized
counterparts.Comment: 8 pages, 5 figure
Graph Metrics for Temporal Networks
Temporal networks, i.e., networks in which the interactions among a set of
elementary units change over time, can be modelled in terms of time-varying
graphs, which are time-ordered sequences of graphs over a set of nodes. In such
graphs, the concepts of node adjacency and reachability crucially depend on the
exact temporal ordering of the links. Consequently, all the concepts and
metrics proposed and used for the characterisation of static complex networks
have to be redefined or appropriately extended to time-varying graphs, in order
to take into account the effects of time ordering on causality. In this chapter
we discuss how to represent temporal networks and we review the definitions of
walks, paths, connectedness and connected components valid for graphs in which
the links fluctuate over time. We then focus on temporal node-node distance,
and we discuss how to characterise link persistence and the temporal
small-world behaviour in this class of networks. Finally, we discuss the
extension of classic centrality measures, including closeness, betweenness and
spectral centrality, to the case of time-varying graphs, and we review the work
on temporal motifs analysis and the definition of modularity for temporal
graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and
Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201
Distributed network topology reconstruction in presence of anonymous nodes
International audienceThis paper concerns the problem of reconstructing the network topology from data propagated through the network by means of an average consensus protocol. The proposed method is based on the distributed estimation of graph Lapla-cian spectral properties. Precisely, the identification of the network topology is implemented by estimating both eigen-values and eigenvectors of the consensus matrix, which is related to the graph Laplacian matrix. In this paper, we focus the exposition on the estimation of the eigenvectors since the eigenvalues estimation can be achieved based on recent results of the literature using the same kind of data. We show how the topology can be reconstructed in presence of anonymous nodes, i.e. nodes that do not disclose their ID
Analytical maximum-likelihood method to detect patterns in real networks
In order to detect patterns in real networks, randomized graph ensembles that
preserve only part of the topology of an observed network are systematically
used as fundamental null models. However, their generation is still
problematic. The existing approaches are either computationally demanding and
beyond analytic control, or analytically accessible but highly approximate.
Here we propose a solution to this long-standing problem by introducing an
exact and fast method that allows to obtain expectation values and standard
deviations of any topological property analytically, for any binary, weighted,
directed or undirected network. Remarkably, the time required to obtain the
expectation value of any property is as short as that required to compute the
same property on the single original network. Our method reveals that the null
behavior of various correlation properties is different from what previously
believed, and highly sensitive to the particular network considered. Moreover,
our approach shows that important structural properties (such as the modularity
used in community detection problems) are currently based on incorrect
expressions, and provides the exact quantities that should replace them.Comment: 26 pages, 10 figure
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