In the above definitions, a subgraph has been defined only in reference to itself. A different approach is to compare the number of internal edges to the number of external edges, arising from the intuitive notion that a community will be denser in terms of edges than its surroundings. One such definition, the definition of community in the strong sense, is defined as a subgraph in which each node has more edges to other nodes within the subgraph than to any other nodes in the network. Again, this definition is quite restrictive, and in order to relax these constraints, the most commonly used (and most intuitive) definition of communities is groups of nodes that have a high density of edges within them and a lower density of edges between groups. This intuitive definition is behind the most widely used approach for studying community structure in networks. Newman and Girvan formalised this in terms of the modularity measure Q [99] . Given a particular network which is partitioned into communities, the modularity measure compares the expected number of edges within communities to the actual number of edges within communities.