Sigcon: Simplifying a Graph Based on Degree Correlation and Clustering Coefficient

Depicting a complex system like social networks as a graph helps understand its structure and relation. As advances in technology increase the amount of data, simplifying a large-scale graph has attracted interests. Simplification reduces the size of a graph while preserving its important properties. In this paper, we propose the summarization algorithm to simplify a graph focusing on degree correlation and clustering coefficient. The degree correlation is a measure to assess the influence of each vertex and their connections. The clustering coefficient estimates latent connections between two distinct vertices. To this end, we first separate a graph into communities. Looking at groups instead of a graph itself allows us to extract important vertices and edges more easily. We then categorize communities into four cases and simplify them in different ways to preserve the innate characteristics. The quantitative and qualitative evaluations demonstrate how effectively our algorithm serves the goal. Overall, our contributions are as follows: (a) unique pattern: We found that hubs are connected indirectly via low-degree vertices. Sigcon preserves these vertices during simplification. (b) efficient algorithm: Sigcon identifies influential vertices and edges to simplify a graph on the basis of degree correlation and clustering coefficient connecting vertices effectively.