98,510 research outputs found
Resolution of ranking hierarchies in directed networks
Identifying hierarchies and rankings of nodes in directed graphs is
fundamental in many applications such as social network analysis, biology,
economics, and finance. A recently proposed method identifies the hierarchy by
finding the ordered partition of nodes which minimises a score function, termed
agony. This function penalises the links violating the hierarchy in a way
depending on the strength of the violation. To investigate the resolution of
ranking hierarchies we introduce an ensemble of random graphs, the Ranked
Stochastic Block Model. We find that agony may fail to identify hierarchies
when the structure is not strong enough and the size of the classes is small
with respect to the whole network. We analytically characterise the resolution
threshold and we show that an iterated version of agony can partly overcome
this resolution limit.Comment: 27 pages, 9 figure
Dynamic hierarchies in temporal directed networks
The outcome of interactions in many real-world systems can be often explained
by a hierarchy between the participants. Discovering hierarchy from a given
directed network can be formulated as follows: partition vertices into levels
such that, ideally, there are only forward edges, that is, edges from upper
levels to lower levels. In practice, the ideal case is impossible, so instead
we minimize some penalty function on the backward edges. One practical option
for such a penalty is agony, where the penalty depends on the severity of the
violation. In this paper we extend the definition of agony to temporal
networks. In this setup we are given a directed network with time stamped
edges, and we allow the rank assignment to vary over time. We propose 2
strategies for controlling the variation of individual ranks. In our first
variant, we penalize the fluctuation of the rankings over time by adding a
penalty directly to the optimization function. In our second variant we allow
the rank change at most once. We show that the first variant can be solved
exactly in polynomial time while the second variant is NP-hard, and in fact
inapproximable. However, we develop an iterative method, where we first fix the
change point and optimize the ranks, and then fix the ranks and optimize the
change points, and reiterate until convergence. We show empirically that the
algorithms are reasonably fast in practice, and that the obtained rankings are
sensible
Detecting Evolving Patterns of Self-Organizing Networks by Flow Hierarchy Measurement
Hierarchies occur widely in evolving self-organizing ecological, biological, technological and social networks, but detecting and comparing hierarchies is difficult. Here we present a metric and technique to quantitatively assess the extent to which self-organizing directed networks exhibit a flow hierarchy. Flow hierarchy is a commonly observed but theoretically overlooked form of hierarchy in networks. We show that the ecological, neurobiological, economic and information processing networks are generally more hierarchical than their comparable random networks. We further discovered that hierarchy degree has increased over the course of the evolution of Linux kernels, confirming an early hypothesis by Herbert Simon on the emergence of hierarchy in evolutionary processes. Taken together, our results suggest that hierarchy is a central organizing feature of real-world evolving networks, and the measurement of hierarchy opens the way to understand the structural regimes and evolutionary patterns of self-organizing networks. Our measurement technique makes it possible to objectively compare hierarchies of different networks and of different evolutionary stages of a single network, and compare evolving patterns of different networks. It can be applied to various complex systems, which can be represented as directed networks
Global network structure of dominance hierarchy of ant workers
Dominance hierarchy among animals is widespread in various species and
believed to serve to regulate resource allocation within an animal group.
Unlike small groups, however, detection and quantification of linear hierarchy
in large groups of animals are a difficult task. Here, we analyse
aggression-based dominance hierarchies formed by worker ants in Diacamma sp. as
large directed networks. We show that the observed dominance networks are
perfect or approximate directed acyclic graphs, which are consistent with
perfect linear hierarchy. The observed networks are also sparse and random but
significantly different from networks generated through thinning of the perfect
linear tournament (i.e., all individuals are linearly ranked and dominance
relationship exists between every pair of individuals). These results pertain
to global structure of the networks, which contrasts with the previous studies
inspecting frequencies of different types of triads. In addition, the
distribution of the out-degree (i.e., number of workers that the focal worker
attacks), not in-degree (i.e., number of workers that attack the focal worker),
of each observed network is right-skewed. Those having excessively large
out-degrees are located near the top, but not the top, of the hierarchy. We
also discuss evolutionary implications of the discovered properties of
dominance networks.Comment: 5 figures, 2 tables, 4 supplementary figures, 2 supplementary table
Word Activation Forces Map Word Networks
Words associate with each other in a manner of intricate clusters^1-3^. Yet the brain capably encodes the complex relations into workable networks^4-7^ such that the onset of a word in the brain automatically and selectively activates its associates, facilitating language understanding and generation^8-10^. One believes that the activation strength from one word to another forges and accounts for the latent structures of the word networks. This implies that mapping the word networks from brains to computers^11,12^, which is necessary for various purposes^1,2,13-15^, may be achieved through modeling the activation strengths. However, although a lot of investigations on word activation effects have been carried out^8-10,16-20^, modeling the activation strengths remains open. Consequently, huge labor is required to do the mappings^11,12^. Here we show that our found word activation forces, statistically defined by a formula in the same form of the universal gravitation, capture essential information on the word networks, leading to a superior approach to the mappings. The approach compatibly encodes syntactical and semantic information into sparse coding directed networks, comprehensively highlights the features of individual words. We find that based on the directed networks, sensible word clusters and hierarchies can be efficiently discovered. Our striking results strongly suggest that the word activation forces might reveal the encoding of word networks in the brain
Directed Network Laplacians and Random Graph Models
We consider spectral methods that uncover hidden structures in directed
networks. We develop a general framework that allows us to associate methods
based on optimization formulations with maximum likelihood problems on random
graphs. We focus on two existing spectral approaches that build and analyse
Laplacian-style matrices via the minimization of frustration and trophic
incoherence. These algorithms aim to reveal directed periodic and linear
hierarchies, respectively. We show that reordering nodes using the two
algorithms, or mapping them onto a specified lattice, is associated with new
classes of directed random graph models. Using this random graph setting, we
are able to compare the two algorithms on a given network and quantify which
structure is more likely to be present. We illustrate the approach on synthetic
and real networks, and discuss practical implementation issues
Directed Scattering for Knowledge Graph-based Cellular Signaling Analysis
Directed graphs are a natural model for many phenomena, in particular
scientific knowledge graphs such as molecular interaction or chemical reaction
networks that define cellular signaling relationships. In these situations,
source nodes typically have distinct biophysical properties from sinks. Due to
their ordered and unidirectional relationships, many such networks also have
hierarchical and multiscale structure. However, the majority of methods
performing node- and edge-level tasks in machine learning do not take these
properties into account, and thus have not been leveraged effectively for
scientific tasks such as cellular signaling network inference. We propose a new
framework called Directed Scattering Autoencoder (DSAE) which uses a directed
version of a geometric scattering transform, combined with the non-linear
dimensionality reduction properties of an autoencoder and the geometric
properties of the hyperbolic space to learn latent hierarchies. We show this
method outperforms numerous others on tasks such as embedding directed graphs
and learning cellular signaling networks.Comment: 5 pages, 3 figure
Directed Mammalian Gene Regulatory Networks Using Expression and Comparative Genomic Hybridization Microarray Data from Radiation Hybrids
Meiotic mapping of quantitative trait loci regulating expression (eQTLs) has allowed the construction of gene networks. However, the limited mapping resolution of these studies has meant that genotype data are largely ignored, leading to undirected networks that fail to capture regulatory hierarchies. Here we use high resolution mapping of copy number eQTLs (ceQTLs) in a mouse-hamster radiation hybrid (RH) panel to construct directed genetic networks in the mammalian cell. The RH network covering 20,145 mouse genes had significant overlap with, and similar topological structures to, existing biological networks. Upregulated edges in the RH network had significantly more overlap than downregulated. This suggests repressive relationships between genes are missed by existing approaches, perhaps because the corresponding proteins are not present in the cell at the same time and therefore unlikely to interact. Gene essentiality was positively correlated with connectivity and betweenness centrality in the RH network, strengthening the centrality-lethality principle in mammals. Consistent with their regulatory role, transcription factors had significantly more outgoing edges (regulating) than incoming (regulated) in the RH network, a feature hidden by conventional undirected networks. Directed RH genetic networks thus showed concordance with pre-existing networks while also yielding information inaccessible to current undirected approaches
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