  Triangle counting in a graph is a fundamental problem and has a wide range of
applications in various domains. It is crucial in understanding the structural
properties of a graph and is often used as a building block for more complex
graph analytics. In this paper, we solve the triangle counting problem in an
anonymous graph in a distributed setting using mobile agents and subsequently
use this as a subroutine to tackle the truss decomposition and triangle
centrality problem. The paper employs mobile agents, placed on the nodes of the
graph to coordinate among themselves to solve the triangle enumeration problem
for the graph. Following the literature, we consider the synchronous systems
where each robot executes its tasks concurrently with all others and hence time
complexity can be measured as the number of rounds needed to complete the task.
The graph is anonymous, i.e., without any node labels or IDs, but the agents
are autonomous with distinct IDs and have limited memory. Agents can only
communicate with other agents locally i.e., if and only if they are at the same
node. The goal is to devise algorithms that minimise both the time required for
triangle counting and the memory usage at each agent. We further demonstrate
how the triangle count obtained through the mobile agent approach can be
leveraged to address the truss decomposition, triangle centrality and local
clustering coefficient problems, which involves finding maximal sub-graphs with
strong interconnections. Truss decomposition helps in identifying maximal,
highly interconnected sub-graphs, or trusses, within a network, thus, revealing
the structural cohesion and tight-knit communities in complex graphs,
facilitating the analysis of relationships and information flow in various
fields, such as social networks, biology, and recommendation systems.
