331 research outputs found
Discussion on "Sparse graphs using exchangeable random measures" by F. Caron and E. B. Fox
Discussion on "Sparse graphs using exchangeable random measures" by F. Caron
and E. B. Fox. In this discussion we contribute to the analysis of the GGP
model as compared to the Erdos-Renyi (ER) and the preferential attachment (AB)
models, using different measures such as number of connected components, global
clustering coefficient, assortativity coefficient and share of nodes in the
core.Comment: 2 pages, 1 figur
Mathematical evolution in discrete networks
This paper provides a mathematical explanation for the phenomenon of
\triadic closure" so often seen in social networks. It appears to be a natural consequence
when network change is constrained to be continuous. The concept of
chordless cycles in the network's \irreducible spine" is used in the analysis of the
network's dynamic behavior.
A surprising result is that as networks undergo random, but continuous, perturbations
they tend to become more structured and less chaotic
Multitask Learning on Graph Neural Networks: Learning Multiple Graph Centrality Measures with a Unified Network
The application of deep learning to symbolic domains remains an active
research endeavour. Graph neural networks (GNN), consisting of trained neural
modules which can be arranged in different topologies at run time, are sound
alternatives to tackle relational problems which lend themselves to graph
representations. In this paper, we show that GNNs are capable of multitask
learning, which can be naturally enforced by training the model to refine a
single set of multidimensional embeddings and decode them
into multiple outputs by connecting MLPs at the end of the pipeline. We
demonstrate the multitask learning capability of the model in the relevant
relational problem of estimating network centrality measures, focusing
primarily on producing rankings based on these measures, i.e. is vertex
more central than vertex given centrality ?. We then show that a GNN
can be trained to develop a \emph{lingua franca} of vertex embeddings from
which all relevant information about any of the trained centrality measures can
be decoded. The proposed model achieves accuracy on a test dataset of
random instances with up to 128 vertices and is shown to generalise to larger
problem sizes. The model is also shown to obtain reasonable accuracy on a
dataset of real world instances with up to 4k vertices, vastly surpassing the
sizes of the largest instances with which the model was trained ().
Finally, we believe that our contributions attest to the potential of GNNs in
symbolic domains in general and in relational learning in particular.Comment: Published at ICANN2019. 10 pages, 3 Figure
Analysis and evaluation of the entropy indices of a static network structure
Although degree distribution entropy (DDE), SD structure entropy (SDSE), Wu structure entropy (WSE) and FB structure entropy (FBSE) are four static network structure entropy indices widely used to quantify the heterogeneity of a complex network, previous studies have paid little attention to their differing abilities to describe network structure. We calculate these four structure entropies for four benchmark networks and compare the results by measuring the ability of each index to characterize network heterogeneity. We find that SDSE and FBSE more accurately characterize network heterogeneity than WSE and DDE. We also find that existing benchmark networks fail to distinguish SDSE and FBSE because they cannot discriminate local and global network heterogeneity. We solve this problem by proposing an evolving caveman network that reveals the differences between structure entropy indices by comparing the sensitivities during the network evolutionary process. Mathematical analysis and computational simulation both indicate that FBSE describes the global topology variation in the evolutionary process of a caveman network, and that the other three structure entropy indices reflect only local network heterogeneity. Our study offers an expansive view of the structural complexity of networks and expands our understanding of complex network behavior.The authors would like to thank the financial support of the National Natural Science Foundation of China (71501153), Natural Science Foundation of Shaanxi Province of China (2016JQ6072), and the Foundation of China Scholarship Council (201506965039, 201606965057). (71501153 - National Natural Science Foundation of China; 2016JQ6072 - Natural Science Foundation of Shaanxi Province of China; 201506965039 - Foundation of China Scholarship Council; 201606965057 - Foundation of China Scholarship Council)Published versio
The Impact of Network Flows on Community Formation in Models of Opinion Dynamics
We study dynamics of opinion formation in a network of coupled agents. As the
network evolves to a steady state, opinions of agents within the same community
converge faster than those of other agents. This framework allows us to study
how network topology and network flow, which mediates the transfer of opinions
between agents, both affect the formation of communities. In traditional models
of opinion dynamics, agents are coupled via conservative flows, which result in
one-to-one opinion transfer. However, social interactions are often
non-conservative, resulting in one-to-many transfer of opinions. We study
opinion formation in networks using one-to-one and one-to-many interactions and
show that they lead to different community structure within the same network.Comment: accepted for publication in The Journal of Mathematical Sociology.
arXiv admin note: text overlap with arXiv:1201.238
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