The phrase "average degree over" is correct and usable in written English.
It can be used in contexts involving mathematics, statistics, or graph theory, where you are discussing the average degree of nodes in a network or graph over a certain set or range.
Example: "To analyze the connectivity of the network, we calculated the average degree over all nodes."
Alternatives: "mean degree across" or "average connectivity among".
In the case of road network nodes are defined as road junctions, therefore it is hard to expect many nodes of degree more than 10 and large variations in the average degree over time.
The network which they study exhibits a rather constant average degree over time, with only a very slight increase of the order of 0.2, this however can be due to the nature of the road network, which is planar, which means that it can be drawn on a sphere in such a way that no links will overlap or cross.
The maximum average degree, m(G), of a graph G is the largest average degree over all subgraphs of G.
We applied a wide range sparsity threshold S to all correlation matrices, which is determined in this procedure to guarantee that the threshold networks were estimable for small-worldness (scalar σ was larger than 1.1) and had sparse properties with as few spurious edges as possible and the average degree over all nodes of each threshold network was larger than 2 × log 90) [ 29, 32].
There exist models, especially the well-known Preferential Attachment, which predict that the increase in the number of edges should be linear in the number of nodes, which means that the average degree should not change over time.
Thus, the degree of promiscuity of this compound increased from 1 over 3 to 4. For a given year, the average degree of promiscuity was calculated over all qualifying compounds.
The average degree is the degree averaged over all the nodes in a graph [ 44].
4. Changes in structural properties such as number of chain ends, average degree of polymerization and crystallinity over time can be followed during hydrolysis.
For compounds in the high- and low-confidence data sets, the average degree of compound promiscuity was determined over the years, as reported in Figure 2. Early on, compounds from both data sets were mostly associated with single-target activities (corresponding to a promiscuity degree of 1).
The fitness function measuring the adaptation of each rule of the population is a multiobjective function-based high three criteria: frequency value, high average covering degree over positive examples and high average covering degree over positive examples, shown in Fig. 4.
From (k=1) to (max(mathrm {degree})), we average over k-degree nodes for local clustering coefficient ((mathrm{CC} k))), the local transitivity of collaborations ((mathrm{TC} k))), the average degree of node neighbors ((mathrm{DN} k))), and the average hyperdegree of node neighbors ((mathrm{HN} k))).
