"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## What's wrong with modularity-maximization or similar methods?\n",
"\n",
"They are not necessarilly wrong! Those methods we tested last time may work perfectly fine for many networks and the community structure that you are interested in. However, there is an important implicit assumption shared by most community detection methods. That is, the communities are _disjoint_ or _non-overlapping_, which means that each node belongs to exactly one community.\n",
"\n",
"Imagine the social network around you. Do you belong to exactly one community? Probably not, because you have friends, family, and colleagues in many different contexts (a figure from [Palla et al., 2005](https://www.nature.com/articles/nature03607)). \n",
"\n",
"\n",
"\n",
"Moreover, this is not only true for yourself, but also for all other nodes in the network. If this is how the network is structured, then community detection methods that assume disjoint communities will not be able to capture the true community structure of the network.\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Another way to think about this situation is to use a bipartite network of people and communities. There are many people and many communities and each person can belong to multiple communities. Then, the social network we see is a projection of this bipartite network. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at a simple example. Here, there are two communities. Most people belong to only one of them, but person \"D\" belongs to both. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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",
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