Postmortem Analysis of Decayed Online Social Communities: Cascade Pattern Analysis and Prediction
Table 1
Definitions of the network-based measures used in this work.
Measure
Description
The degree of a node ,, is the cardinality of the set of neighbors .
The betweenness of a node is defined as , where is the number of the shortest paths between nodes and that include the node and is the number of all the shortest paths between nodes and .
The closeness of a node is defined as , where is the distance between nodes and .
A -core subgraph of a graph is the maximal subgraph such that each node has a degree at least . The coreness of a node if the node is in the -core subgraph and not in the -core subgraph.
The eccentricity of a node ,, is the maximum distance between node and node .
A minimum cut of two nodes , is the minimum number of edges that are required to be removed in order to separate the two nodes. The averaged minimum cut of a node is defined as , where is the number of nodes in a graph.
The eigenvector centrality of a node which is defined as , where is a constant and is a location defined by in the adjacency matrix. The measure can be written in matrix form as .
Edge betweenness measures the number of times an edge appears in the shortest path between any two nodes in a graph. It is defined as . The incident edge betweenness of a node is defined as the average edge betweenness for all edges incident to a node .
