2,857 research outputs found
Mining (maximal) span-cores from temporal networks
When analyzing temporal networks, a fundamental task is the identification of
dense structures (i.e., groups of vertices that exhibit a large number of
links), together with their temporal span (i.e., the period of time for which
the high density holds). We tackle this task by introducing a notion of
temporal core decomposition where each core is associated with its span: we
call such cores span-cores.
As the total number of time intervals is quadratic in the size of the
temporal domain under analysis, the total number of span-cores is quadratic
in as well. Our first contribution is an algorithm that, by exploiting
containment properties among span-cores, computes all the span-cores
efficiently. Then, we focus on the problem of finding only the maximal
span-cores, i.e., span-cores that are not dominated by any other span-core by
both the coreness property and the span. We devise a very efficient algorithm
that exploits theoretical findings on the maximality condition to directly
compute the maximal ones without computing all span-cores.
Experimentation on several real-world temporal networks confirms the
efficiency and scalability of our methods. Applications on temporal networks,
gathered by a proximity-sensing infrastructure recording face-to-face
interactions in schools, highlight the relevance of the notion of (maximal)
span-core in analyzing social dynamics and detecting/correcting anomalies in
the data
Span-core Decomposition for Temporal Networks: Algorithms and Applications
When analyzing temporal networks, a fundamental task is the identification of
dense structures (i.e., groups of vertices that exhibit a large number of
links), together with their temporal span (i.e., the period of time for which
the high density holds). In this paper we tackle this task by introducing a
notion of temporal core decomposition where each core is associated with two
quantities, its coreness, which quantifies how densely it is connected, and its
span, which is a temporal interval: we call such cores \emph{span-cores}.
For a temporal network defined on a discrete temporal domain , the total
number of time intervals included in is quadratic in , so that the
total number of span-cores is potentially quadratic in as well. Our first
main contribution is an algorithm that, by exploiting containment properties
among span-cores, computes all the span-cores efficiently. Then, we focus on
the problem of finding only the \emph{maximal span-cores}, i.e., span-cores
that are not dominated by any other span-core by both their coreness property
and their span. We devise a very efficient algorithm that exploits theoretical
findings on the maximality condition to directly extract the maximal ones
without computing all span-cores.
Finally, as a third contribution, we introduce the problem of \emph{temporal
community search}, where a set of query vertices is given as input, and the
goal is to find a set of densely-connected subgraphs containing the query
vertices and covering the whole underlying temporal domain . We derive a
connection between this problem and the problem of finding (maximal)
span-cores. Based on this connection, we show how temporal community search can
be solved in polynomial-time via dynamic programming, and how the maximal
span-cores can be profitably exploited to significantly speed-up the basic
algorithm.Comment: ACM Transactions on Knowledge Discovery from Data (TKDD), 2020. arXiv
admin note: substantial text overlap with arXiv:1808.0937
Cores and Other Dense Structures in Complex Networks
Complex networks are a powerful paradigm to model complex systems. Specific
network models, e.g., multilayer networks, temporal networks, and signed
networks, enrich the standard network representation with additional
information to better capture real-world phenomena. Despite the keen interest
in a variety of problems, algorithms, and analysis methods for these types of
network, the problem of extracting cores and dense structures still has
unexplored facets. In this work, we present advancements to the state of the
art by the introduction of novel definitions and algorithms for the extraction
of dense structures from complex networks, mainly cores. At first, we define
core decomposition in multilayer networks together with a series of
applications built on top of it, i.e., the extraction of maximal multilayer
cores only, densest subgraph in multilayer networks, the speed-up of the
extraction of frequent cross-graph quasi-cliques, and the generalization of
community search to the multilayer setting. Then, we introduce the concept of
core decomposition in temporal networks; also in this case, we are interested
in the extraction of maximal temporal cores only. Finally, in the context of
discovering polarization in large-scale online data, we study the problem of
identifying polarized communities in signed networks. The proposed
methodologies are evaluated on a large variety of real-world networks against
na\"{\i}ve approaches, non-trivial baselines, and competing methods. In all
cases, they show effectiveness, efficiency, and scalability. Moreover, we
showcase the usefulness of our definitions in concrete applications and case
studies, i.e., the temporal analysis of contact networks, and the
identification of polarization in debate networks.Comment: arXiv admin note: text overlap with arXiv:1812.0871
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
Fundamental structures of dynamic social networks
Social systems are in a constant state of flux with dynamics spanning from
minute-by-minute changes to patterns present on the timescale of years.
Accurate models of social dynamics are important for understanding spreading of
influence or diseases, formation of friendships, and the productivity of teams.
While there has been much progress on understanding complex networks over the
past decade, little is known about the regularities governing the
micro-dynamics of social networks. Here we explore the dynamic social network
of a densely-connected population of approximately 1000 individuals and their
interactions in the network of real-world person-to-person proximity measured
via Bluetooth, as well as their telecommunication networks, online social media
contacts, geo-location, and demographic data. These high-resolution data allow
us to observe social groups directly, rendering community detection
unnecessary. Starting from 5-minute time slices we uncover dynamic social
structures expressed on multiple timescales. On the hourly timescale, we find
that gatherings are fluid, with members coming and going, but organized via a
stable core of individuals. Each core represents a social context. Cores
exhibit a pattern of recurring meetings across weeks and months, each with
varying degrees of regularity. Taken together, these findings provide a
powerful simplification of the social network, where cores represent
fundamental structures expressed with strong temporal and spatial regularity.
Using this framework, we explore the complex interplay between social and
geospatial behavior, documenting how the formation of cores are preceded by
coordination behavior in the communication networks, and demonstrating that
social behavior can be predicted with high precision.Comment: Main Manuscript: 16 pages, 4 figures. Supplementary Information: 39
pages, 34 figure
Discovering Patterns of Interest in IP Traffic Using Cliques in Bipartite Link Streams
Studying IP traffic is crucial for many applications. We focus here on the
detection of (structurally and temporally) dense sequences of interactions,
that may indicate botnets or coordinated network scans. More precisely, we
model a MAWI capture of IP traffic as a link streams, i.e. a sequence of
interactions meaning that devices and exchanged
packets from time to time . This traffic is captured on a single
router and so has a bipartite structure: links occur only between nodes in two
disjoint sets. We design a method for finding interesting bipartite cliques in
such link streams, i.e. two sets of nodes and a time interval such that all
nodes in the first set are linked to all nodes in the second set throughout the
time interval. We then explore the bipartite cliques present in the considered
trace. Comparison with the MAWILab classification of anomalous IP addresses
shows that the found cliques succeed in detecting anomalous network activity
Distance-generalized Core Decomposition
The -core of a graph is defined as the maximal subgraph in which every
vertex is connected to at least other vertices within that subgraph. In
this work we introduce a distance-based generalization of the notion of
-core, which we refer to as the -core, i.e., the maximal subgraph in
which every vertex has at least other vertices at distance within
that subgraph. We study the properties of the -core showing that it
preserves many of the nice features of the classic core decomposition (e.g.,
its connection with the notion of distance-generalized chromatic number) and it
preserves its usefulness to speed-up or approximate distance-generalized
notions of dense structures, such as -club.
Computing the distance-generalized core decomposition over large networks is
intrinsically complex. However, by exploiting clever upper and lower bounds we
can partition the computation in a set of totally independent subcomputations,
opening the door to top-down exploration and to multithreading, and thus
achieving an efficient algorithm
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