42,650 research outputs found
Temporal Networks
A great variety of systems in nature, society and technology -- from the web
of sexual contacts to the Internet, from the nervous system to power grids --
can be modeled as graphs of vertices coupled by edges. The network structure,
describing how the graph is wired, helps us understand, predict and optimize
the behavior of dynamical systems. In many cases, however, the edges are not
continuously active. As an example, in networks of communication via email,
text messages, or phone calls, edges represent sequences of instantaneous or
practically instantaneous contacts. In some cases, edges are active for
non-negligible periods of time: e.g., the proximity patterns of inpatients at
hospitals can be represented by a graph where an edge between two individuals
is on throughout the time they are at the same ward. Like network topology, the
temporal structure of edge activations can affect dynamics of systems
interacting through the network, from disease contagion on the network of
patients to information diffusion over an e-mail network. In this review, we
present the emergent field of temporal networks, and discuss methods for
analyzing topological and temporal structure and models for elucidating their
relation to the behavior of dynamical systems. In the light of traditional
network theory, one can see this framework as moving the information of when
things happen from the dynamical system on the network, to the network itself.
Since fundamental properties, such as the transitivity of edges, do not
necessarily hold in temporal networks, many of these methods need to be quite
different from those for static networks
Multiscale Analysis of Spreading in a Large Communication Network
In temporal networks, both the topology of the underlying network and the
timings of interaction events can be crucial in determining how some dynamic
process mediated by the network unfolds. We have explored the limiting case of
the speed of spreading in the SI model, set up such that an event between an
infectious and susceptible individual always transmits the infection. The speed
of this process sets an upper bound for the speed of any dynamic process that
is mediated through the interaction events of the network. With the help of
temporal networks derived from large scale time-stamped data on mobile phone
calls, we extend earlier results that point out the slowing-down effects of
burstiness and temporal inhomogeneities. In such networks, links are not
permanently active, but dynamic processes are mediated by recurrent events
taking place on the links at specific points in time. We perform a multi-scale
analysis and pinpoint the importance of the timings of event sequences on
individual links, their correlations with neighboring sequences, and the
temporal pathways taken by the network-scale spreading process. This is
achieved by studying empirically and analytically different characteristic
relay times of links, relevant to the respective scales, and a set of temporal
reference models that allow for removing selected time-domain correlations one
by one
Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses
Recent decades have seen the discovery of numerous complex materials. At the
root of the complexity underlying many of these materials lies a large number
of possible contending atomic- and larger-scale configurations and the
intricate correlations between their constituents. For a detailed
understanding, there is a need for tools that enable the detection of pertinent
structures on all spatial and temporal scales. Towards this end, we suggest a
new method by invoking ideas from network analysis and information theory. Our
method efficiently identifies basic unit cells and topological defects in
systems with low disorder and may analyze general amorphous structures to
identify candidate natural structures where a clear definition of order is
lacking. This general unbiased detection of physical structure does not require
a guess as to which of the system properties should be deemed as important and
may constitute a natural point of departure for further analysis. The method
applies to both static and dynamic systems.Comment: (23 pages, 9 figures
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
LiveRank: How to Refresh Old Datasets
This paper considers the problem of refreshing a dataset. More precisely ,
given a collection of nodes gathered at some time (Web pages, users from an
online social network) along with some structure (hyperlinks, social
relationships), we want to identify a significant fraction of the nodes that
still exist at present time. The liveness of an old node can be tested through
an online query at present time. We call LiveRank a ranking of the old pages so
that active nodes are more likely to appear first. The quality of a LiveRank is
measured by the number of queries necessary to identify a given fraction of the
active nodes when using the LiveRank order. We study different scenarios from a
static setting where the Liv-eRank is computed before any query is made, to
dynamic settings where the LiveRank can be updated as queries are processed.
Our results show that building on the PageRank can lead to efficient LiveRanks,
for Web graphs as well as for online social networks
Intrinsically Dynamic Network Communities
Community finding algorithms for networks have recently been extended to
dynamic data. Most of these recent methods aim at exhibiting community
partitions from successive graph snapshots and thereafter connecting or
smoothing these partitions using clever time-dependent features and sampling
techniques. These approaches are nonetheless achieving longitudinal rather than
dynamic community detection. We assume that communities are fundamentally
defined by the repetition of interactions among a set of nodes over time.
According to this definition, analyzing the data by considering successive
snapshots induces a significant loss of information: we suggest that it blurs
essentially dynamic phenomena - such as communities based on repeated
inter-temporal interactions, nodes switching from a community to another across
time, or the possibility that a community survives while its members are being
integrally replaced over a longer time period. We propose a formalism which
aims at tackling this issue in the context of time-directed datasets (such as
citation networks), and present several illustrations on both empirical and
synthetic dynamic networks. We eventually introduce intrinsically dynamic
metrics to qualify temporal community structure and emphasize their possible
role as an estimator of the quality of the community detection - taking into
account the fact that various empirical contexts may call for distinct
`community' definitions and detection criteria.Comment: 27 pages, 11 figure
- …