  Graph embedding, representing local and global neighborhood information by
numerical vectors, is a crucial part of the mathematical modeling of a wide
range of real-world systems. Among the embedding algorithms, random walk-based
algorithms have proven to be very successful. These algorithms collect
information by creating numerous random walks with a redefined number of steps.
Creating random walks is the most demanding part of the embedding process. The
computation demand increases with the size of the network. Moreover, for
real-world networks, considering all nodes on the same footing, the abundance
of low-degree nodes creates an imbalanced data problem. In this work, a
computationally less intensive and node connectivity aware uniform sampling
method is proposed. In the proposed method, the number of random walks is
created proportionally with the degree of the node. The advantages of the
proposed algorithm become more enhanced when the algorithm is applied to large
graphs. A comparative study by using two networks namely CORA and CiteSeer is
presented. Comparing with the fixed number of walks case, the proposed method
requires 50% less computational effort to reach the same accuracy for node
classification and link prediction calculations.
