Graph density is the proportion of possible edges present among a graph’s nodes. A density of 1 means every node in the analyzed community is connected to every other node. section 9.3.3
In fraud analysis, density helps characterize communities detected with Louvain. Compare it with community size and counts of entity types—such as users, IPs, devices, phones, and cards—to investigate potentially suspicious groups. section 9.3.3
Listing 9.4 Preparing for detailed community analysis
if G is not None and partition is not None:
# Group nodes by their community ID
communities_dict_nodes = defaultdict(list)
for node, comm_id in partition.items():
communities_dict_nodes[comm_id].append(node)
all_community_node_lists_sorted = [
nodes for comm_id, nodes in sorted(communities_dict_nodes.items())
]
print(f"Prepared {len(all_community_node_lists_sorted)} communities for detailed analysis.")
# Define a function to analyze the characteristics of a single community
def analyze_community_details_func(nodes_in_comm):
"""
Calculates density, size, and node type counts for a given list of nodes
representing a community within the graph G.
"""
if not nodes_in_comm:
# Return default values for an empty community node list
return [0.0, 0, {}]
# Create a subgraph containing only the nodes of the current community
subgraph_comm = G.subgraph(nodes_in_comm)
# Calculate the density of the subgraph
# Density is the ratio of actual edges to all possible edges in the subgraph.
density_comm = nx.density(subgraph_comm)
# Get the size of the community (number of nodes)
size_comm = len(nodes_in_comm)
# Count the occurrences of each node type within this community
type_counts_comm = defaultdict(int)
for node_item in nodes_in_comm:
# G.nodes[node_item] gives attributes of the node, including 'type'
type_counts_comm[G.nodes[node_item].get('type', 'Unknown')] += 1
return [density_comm, size_comm, dict(type_counts_comm)] # Return calculated metrics
print("Function 'analyze_community_details_func' defined for community analysis.")
else:
print("Graph G or partition not available. Skipping community analysis preparation.")
all_community_node_lists_sorted = [] # Define for subsequent cells not to fail
Inspect the community-analysis function that calculates density alongside community size and node-type counts. section 9.3.3
