Team # 31262 Page 4 of 20
Spreading characteristics, such as closeness centrality, spreading breadth index and spreading depth index, are to
quantify the efficiency of information dissemination for the whole network with the information starting from a
particular vertice. Based on the fact that any vertice in our model is an information source (people or paper) and all any
other vertices connected to it may receive the information released by it, we must think up a standard to assess the
information spreading ability of each vertice. So we design a brand-new submodel (spreading breadth index and
spreading depth index are the characteristic parameters obtained from it), along with an existing standard (closeness
centrality), to describe the information spreading ability for each vertice in the network. This kind of feature naturally
should be regarded as another aspect for vertice evaluation.
Our data-processing procedure is based on the classification method above. After getting the nine parameters of a
vertice through computer programming or gephi(a visualization software) calculation, we classify the parameters into
three groups according to above analysis. And for each group, we use Principal Component Analysis (PCA) to get a
comprehensive result of the three parameters in a group. Now with three parameters obtained from three groups
correspondingly after PCA, we use three weight factor to operate on the three parameters to work out a final evaluation
result of a vertice.
3.1 Centralizing Characteristics
The first type of characteristics of a network is centralizing characteristics. Actually while taking vertex-influence-
evaluation into consideration, the first idea coming to our mind is to check to what extent a vertex is in the center of the
network. Centralizing characteristic parameters are defined to quantify such kind of extent
3.1.1 Degree Centrality (
)
Degree centrality, or degree, of a vertice equals to the number of edges a vertex has in common with other neighbor
vertices. If there are totally
vertices and
edges in the network, the two sums have the following relation
(1)
Generally, the vertice with a higher degree or more connection edges is more central in structure and has the tendency
to possess a greater ability to influence others. Those nodes should have a relatively more important role among all the
nodes in the network.
3.1.2 Eigenvector Centrality (
)
In a network, if we merely use the degree centrality to describe the extent a vertex is located in the center, the standard
could be too one-sided and we may miss some important features of the network.
As a result, eigenvector centrality is defined. In some networks, some vertices with a high degree are connected to lots
of low-degree vertices and the eigenvector centrality is to quantify the extent of such situations. This parameter is
defined to standardize the centrality of vertices from another angle.
3.1.3 PageRank (PR)
PageRank is initially proposed, over ten years ago, by Page and Brin (1998). This parameter is used to assess the rank
or importance of a vertice in a network according to a method of iteration using the following equation:
(2)
where
is the number of vertices in the network, d is a damping factor, and
is all other vertices linking to the
selected vertice p. After continuous operations of iteration, each point refresh its PR once and once again. Finally all
the vertices will have a weight to indicate the importance of it in the whole network.