mbjallow6 / analysis-of-node2vec-random-walks-on-networks

Analysis of node2vec random walks on networks

Spectral gap for empirical networks

Select Spectral gap analysis.ipynb to evaluate and plot the spectral gap for the node2vec random walks on empirical networks. The vole network is used in the cell [2].

• One can download the data set from Network Repository. To save the readers' time, we present the hyperlinks for the data used in Fig. 2 in our main text:

Vole, Dolphin, Enron, Jazz, Coauthorship, Email

• If you need to consider a different network data set (other than the Vole network), you can

Step 1. Download the empirical data set from the hyperlink above or some other sources.

Step 2. Replace the code in the cell [2] by your target data set.

Step 3. Restart the kernel in Jupyter notebook.

Spectral gap for extended ring networks

Select Extended ring network.ipynb to evaluate and plot the spectral gap for the node2vec random walks on extended ring networks. You can change the number of nodes in the extended ring network by changing size in cell [3]. The number of nodes in the example code is 100.

Spectral gap for two-layer extended ring networks

Select Two layer extended ring network.ipynb to evaluate and plot the spectral gap for the node2vec random walks on two-layer extended ring networks. You can change the number of nodes in mono-layer $N^\prime$ and the weight $w$ in the two-layer extended ring networks. Note that the variable size in cell [3] is the same as $N^\prime$ in Fig. 6 in our paper, NOT $N$. The number of nodes in mono-layer in our example code is 100, and the weight is 1.

Mean coalescence time evaluation

Select Mean coalescence time.ipynb to evaluate and plot the mean coalescence time on two-clique networks. You can change the initial conditions, clique size, and weight of the bridge by changing p, size, and weight respectively. Note that the variable size in cell [3] is the same as $N/2$ in Fig.9 in our paper, NOT $N$. The initial condition is in the example code is the uniformly random condition. The clique size is 100, i.e., N=200, and weight $w=1$. The other two initial condidtions (the two walkers are initially in the same clique or opposite cliques) can be found at the end of the comments in cell [2].

Dependence of the relaxation speed on the second largest eigenvalue of T

Please run Relaxation time.ipynb to see the numerical result. If you need to consider a different network other than the vole network, change the code in cells [2] and [6]. The instruction is the same as the one in Spectral gap for empirical networks.