136,264 research outputs found
Graph measures and network robustness
Network robustness research aims at finding a measure to quantify network
robustness. Once such a measure has been established, we will be able to
compare networks, to improve existing networks and to design new networks that
are able to continue to perform well when it is subject to failures or attacks.
In this paper we survey a large amount of robustness measures on simple,
undirected and unweighted graphs, in order to offer a tool for network
administrators to evaluate and improve the robustness of their network. The
measures discussed in this paper are based on the concepts of connectivity
(including reliability polynomials), distance, betweenness and clustering. Some
other measures are notions from spectral graph theory, more precisely, they are
functions of the Laplacian eigenvalues. In addition to surveying these graph
measures, the paper also contains a discussion of their functionality as a
measure for topological network robustness
Small-worlds: How and why
We investigate small-world networks from the point of view of their origin.
While the characteristics of small-world networks are now fairly well
understood, there is as yet no work on what drives the emergence of such a
network architecture. In situations such as neural or transportation networks,
where a physical distance between the nodes of the network exists, we study
whether the small-world topology arises as a consequence of a tradeoff between
maximal connectivity and minimal wiring. Using simulated annealing, we study
the properties of a randomly rewired network as the relative tradeoff between
wiring and connectivity is varied. When the network seeks to minimize wiring, a
regular graph results. At the other extreme, when connectivity is maximized, a
near random network is obtained. In the intermediate regime, a small-world
network is formed. However, unlike the model of Watts and Strogatz (Nature {\bf
393}, 440 (1998)), we find an alternate route to small-world behaviour through
the formation of hubs, small clusters where one vertex is connected to a large
number of neighbours.Comment: 20 pages, latex, 9 figure
On the extremal properties of the average eccentricity
The eccentricity of a vertex is the maximum distance from it to another
vertex and the average eccentricity of a graph is the mean value
of eccentricities of all vertices of . The average eccentricity is deeply
connected with a topological descriptor called the eccentric connectivity
index, defined as a sum of products of vertex degrees and eccentricities. In
this paper we analyze extremal properties of the average eccentricity,
introducing two graph transformations that increase or decrease .
Furthermore, we resolve four conjectures, obtained by the system AutoGraphiX,
about the average eccentricity and other graph parameters (the clique number,
the Randi\' c index and the independence number), refute one AutoGraphiX
conjecture about the average eccentricity and the minimum vertex degree and
correct one AutoGraphiX conjecture about the domination number.Comment: 15 pages, 3 figure
Generative models of the human connectome
The human connectome represents a network map of the brain's wiring diagram
and the pattern into which its connections are organized is thought to play an
important role in cognitive function. The generative rules that shape the
topology of the human connectome remain incompletely understood. Earlier work
in model organisms has suggested that wiring rules based on geometric
relationships (distance) can account for many but likely not all topological
features. Here we systematically explore a family of generative models of the
human connectome that yield synthetic networks designed according to different
wiring rules combining geometric and a broad range of topological factors. We
find that a combination of geometric constraints with a homophilic attachment
mechanism can create synthetic networks that closely match many topological
characteristics of individual human connectomes, including features that were
not included in the optimization of the generative model itself. We use these
models to investigate a lifespan dataset and show that, with age, the model
parameters undergo progressive changes, suggesting a rebalancing of the
generative factors underlying the connectome across the lifespan.Comment: 38 pages, 5 figures + 19 supplemental figures, 1 tabl
Centralized and distributed cognitive task processing in the human connectome
A key question in modern neuroscience is how cognitive changes in a human
brain can be quantified and captured by functional connectomes (FC) . A
systematic approach to measure pairwise functional distance at different brain
states is lacking. This would provide a straight-forward way to quantify
differences in cognitive processing across tasks; also, it would help in
relating these differences in task-based FCs to the underlying structural
network. Here we propose a framework, based on the concept of Jensen-Shannon
divergence, to map the task-rest connectivity distance between tasks and
resting-state FC. We show how this information theoretical measure allows for
quantifying connectivity changes in distributed and centralized processing in
functional networks. We study resting-state and seven tasks from the Human
Connectome Project dataset to obtain the most distant links across tasks. We
investigate how these changes are associated to different functional brain
networks, and use the proposed measure to infer changes in the information
processing regimes. Furthermore, we show how the FC distance from resting state
is shaped by structural connectivity, and to what extent this relationship
depends on the task. This framework provides a well grounded mathematical
quantification of connectivity changes associated to cognitive processing in
large-scale brain networks.Comment: 22 pages main, 6 pages supplementary, 6 figures, 5 supplementary
figures, 1 table, 1 supplementary table. arXiv admin note: text overlap with
arXiv:1710.0219
The specificity and robustness of long-distance connections in weighted, interareal connectomes
Brain areas' functional repertoires are shaped by their incoming and outgoing
structural connections. In empirically measured networks, most connections are
short, reflecting spatial and energetic constraints. Nonetheless, a small
number of connections span long distances, consistent with the notion that the
functionality of these connections must outweigh their cost. While the precise
function of these long-distance connections is not known, the leading
hypothesis is that they act to reduce the topological distance between brain
areas and facilitate efficient interareal communication. However, this
hypothesis implies a non-specificity of long-distance connections that we
contend is unlikely. Instead, we propose that long-distance connections serve
to diversify brain areas' inputs and outputs, thereby promoting complex
dynamics. Through analysis of five interareal network datasets, we show that
long-distance connections play only minor roles in reducing average interareal
topological distance. In contrast, areas' long-distance and short-range
neighbors exhibit marked differences in their connectivity profiles, suggesting
that long-distance connections enhance dissimilarity between regional inputs
and outputs. Next, we show that -- in isolation -- areas' long-distance
connectivity profiles exhibit non-random levels of similarity, suggesting that
the communication pathways formed by long connections exhibit redundancies that
may serve to promote robustness. Finally, we use a linearization of
Wilson-Cowan dynamics to simulate the covariance structure of neural activity
and show that in the absence of long-distance connections, a common measure of
functional diversity decreases. Collectively, our findings suggest that
long-distance connections are necessary for supporting diverse and complex
brain dynamics.Comment: 18 pages, 8 figure
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