When we look at complex systems with
Related Work
Methods
To test this hypothesis, we collected natural networks and built out a series of artificial and random networks. To setup, build, run analysis on, and visualize the networks, a Python module named graph-tool was used, which allows for multi-core analysis.
// NAREN ANN BUILDING DESCRIPTION HERE
Similar to the ANNs, natural networks were imported into graph-tool using their edge lists. Random networks were generated using packages found within the graph-tool module.
Evaluated Networks
Artifical Networks
For the artificial network, a fully connected ANN with 5 layers was designed. The network was trained on the task of converting a binary value of length 10 to a decimal value. For example, $1001011011$ to $603$. Three networks of this class were created: Narrow, Constant, and Wide. The differences in the network were the counts of nodes in the hidden layers, which were as follows:
- Narrow: 10 -> 25 -> 20 -> 15-> 10 -> 1
- Constant: 10 -> 18 -> 18 -> 18 -> 18 -> 1
- Wide: 10 -> 10 -> 15 -> 20 -> 25 -> 1
\citep{liang2016deep}
Naturally Occuring Netwroks
Two naturally occurring networks were used were an airport connection network, where directed edges show connections between airports, and the weights of the edges represent the amount of traffic between the nodes. The second network is an ecology network, where nodes are species in an environment, edges represent dependence of one species on another, and the weight is the amount of dependence of one species on another.
Random Networks
Random networks were built using a Poisson random distribution that determined both the degree of each node, and the weight of each is defined as the inverse of the Euclidean distance between two nodes in a Delaunay triangulation layout.
Metrics Used
To evaluate the networks, and note the differences the networks, a variety of metrics were used. We will go through each metric, and the reasoning for using the metric.
Results
\cite{nr}
\cite{nr}
Edges are the main variable
Limitations of This Work
Conclusion
\cite{altacs2013analyzing}
\cite{dunn2006novel}
\cite{sporns2003graph}
\cite{xu2002neural}
\cite{de2014laplacian}
\cite{zhang2017network}
\cite{zhou2014object}
\cite{lettvin1959frog}
\cite{guss2018characterizing}
\cite{papo2015network}
\cite{golden1996mathematical}
\cite{michel1989qualitative}
\cite{pearson2013visualizing}
\cite{stam2007graph}
\cite{wiatowski2018mathematical}
\cite{pellionisz1987tensor}
\cite{pellionisz1988tensorial}
\cite{pellionisz1980tensorial}
\cite{pellionisz1985tensor}
\cite{grassi2010centrality}
\cite{lee2010role}
\cite{borgatti2005centrality}
\cite{breza2015network}
\cite{belau2014consequences}
\cite{del:Pozo:2011}
\cite{batool2014towards}
\cite{joyce2010new}
\cite{grassi2010centrality}
Future Work
Constant edge number, The nature of skip connections in layered systems is an interesting one,