31 research outputs found
Ranking and clustering of nodes in networks with smart teleportation
Random teleportation is a necessary evil for ranking and clustering directed
networks based on random walks. Teleportation enables ergodic solutions, but
the solutions must necessarily depend on the exact implementation and
parametrization of the teleportation. For example, in the commonly used
PageRank algorithm, the teleportation rate must trade off a heavily biased
solution with a uniform solution. Here we show that teleportation to links
rather than nodes enables a much smoother trade-off and effectively more robust
results. We also show that, by not recording the teleportation steps of the
random walker, we can further reduce the effect of teleportation with dramatic
effects on clustering.Comment: 10 pages, 7 figure
Flow Motifs Reveal Limitations of the Static Framework to Represent Human interactions
Networks are commonly used to define underlying interaction structures where
infections, information, or other quantities may spread. Although the standard
approach has been to aggregate all links into a static structure, some studies
suggest that the time order in which the links are established may alter the
dynamics of spreading. In this paper, we study the impact of the time ordering
in the limits of flow on various empirical temporal networks. By using a random
walk dynamics, we estimate the flow on links and convert the original
undirected network (temporal and static) into a directed flow network. We then
introduce the concept of flow motifs and quantify the divergence in the
representativity of motifs when using the temporal and static frameworks. We
find that the regularity of contacts and persistence of vertices (common in
email communication and face-to-face interactions) result on little differences
in the limits of flow for both frameworks. On the other hand, in the case of
communication within a dating site (and of a sexual network), the flow between
vertices changes significantly in the temporal framework such that the static
approximation poorly represents the structure of contacts. We have also
observed that cliques with 3 and 4 vertices con- taining only low-flow links
are more represented than the same cliques with all high-flow links. The
representativity of these low-flow cliques is higher in the temporal framework.
Our results suggest that the flow between vertices connected in cliques depend
on the topological context in which they are placed and in the time sequence in
which the links are established. The structure of the clique alone does not
completely characterize the potential of flow between the vertices
Robustness of journal rankings by network flows with different amounts of memory
As the number of scientific journals has multiplied, journal rankings have
become increasingly important for scientific decisions. From submissions and
subscriptions to grants and hirings, researchers, policy makers, and funding
agencies make important decisions with influence from journal rankings such as
the ISI journal impact factor. Typically, the rankings are derived from the
citation network between a selection of journals and unavoidably depend on this
selection. However, little is known about how robust rankings are to the
selection of included journals. Here we compare the robustness of three journal
rankings based on network flows induced on citation networks. They model
pathways of researchers navigating scholarly literature, stepping between
journals and remembering their previous steps to different degree: zero-step
memory as impact factor, one-step memory as Eigenfactor, and two-step memory,
corresponding to zero-, first-, and second-order Markov models of citation flow
between journals. We conclude that higher-order Markov models perform better
and are more robust to the selection of journals. Whereas our analysis
indicates that higher-order models perform better, the performance gain for the
second-order Markov model comes at the cost of requiring more citation data
over a longer time period.Comment: 9 pages, 5 figure
Generalized Markov stability of network communities
We address the problem of community detection in networks by introducing a
general definition of Markov stability, based on the difference between the
probability fluxes of a Markov chain on the network at different time scales.
The specific implementation of the quality function and the resulting optimal
community structure thus become dependent both on the type of Markov process
and on the specific Markov times considered. For instance, if we use a natural
Markov chain dynamics and discount its stationary distribution -- that is, we
take as reference process the dynamics at infinite time -- we obtain the
standard formulation of the Markov stability. Notably, the possibility to use
finite-time transition probabilities to define the reference process naturally
allows detecting communities at different resolutions, without the need to
consider a continuous-time Markov chain in the small time limit. The main
advantage of our general formulation of Markov stability based on dynamical
flows is that we work with lumped Markov chains on network partitions, having
the same stationary distribution of the original process. In this way the form
of the quality function becomes invariant under partitioning, leading to a
self-consistent definition of community structures at different aggregation
scales
Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
Unveiling the community structure of networks is a powerful methodology to
comprehend interconnected systems across the social and natural sciences. To
identify different types of functional modules in interaction data aggregated
in a single network layer, researchers have developed many powerful methods.
For example, flow-based methods have proven useful for identifying modular
dynamics in weighted and directed networks that capture constraints on flow in
the systems they represent. However, many networked systems consist of agents
or components that exhibit multiple layers of interactions. Inevitably,
representing this intricate network of networks as a single aggregated network
leads to information loss and may obscure the actual organization. Here we
propose a method based on compression of network flows that can identify
modular flows in non-aggregated multilayer networks. Our numerical experiments
on synthetic networks show that the method can accurately identify modules that
cannot be identified in aggregated networks or by analyzing the layers
separately. We capitalize on our findings and reveal the community structure of
two multilayer collaboration networks: scientists affiliated to the Pierre
Auger Observatory and scientists publishing works on networks on the arXiv.
Compared to conventional aggregated methods, the multilayer method reveals
smaller modules with more overlap that better capture the actual organization