"Graph" - what is it, definition of the term
«Graph» is a mathematical construct composed of a finite set of vertices and a set of edges that join pairs of vertices; edges may be unordered, representing bidirectional connections, or ordered, representing directed links. This structure enables precise description of relationships, supports analysis of connectivity, paths, cycles, and serves as a foundational model for networks, algorithmic processes, and combinatorial optimization.
Detailed information
A network diagram consists of entities called vertices and connections called edges. Vertices represent distinct items such as individual organisms, while edges denote relationships, interactions, or pathways between them. When modeling parasitic arthropods—ticks, true bugs, lice, and fleas—the diagram captures host‑parasite associations, transmission routes, and co‑occurrence patterns.
Key classifications of such diagrams include:
- Directed structures, where edges have orientation to indicate direction of transmission or influence.
- Undirected structures, suitable for mutual associations without inherent direction.
- Weighted structures, assigning numerical values to edges to reflect frequency, intensity, or risk level.
- Bipartite structures, separating two distinct sets of vertices (e.g., hosts and parasites) and allowing connections only across sets.
Common representations for computational handling are:
- Adjacency matrix – a square array where entry (i, j) records the presence or weight of an edge between vertex i and vertex j.
- Adjacency list – a collection of lists, each list containing neighboring vertices of a given vertex, efficient for sparse networks.
- Incidence matrix – a matrix linking vertices to edges, useful for analyses involving edge‑centric properties.
Algorithmic operations frequently applied to these structures include:
- Depth‑first and breadth‑first traversals to explore connectivity and component structure.
- Shortest‑path calculations (e.g., Dijkstra’s algorithm) to assess minimal transmission routes between hosts.
- Cycle detection to identify recurring transmission loops among parasite populations.
- Centrality measures (degree, betweenness, eigenvector) to pinpoint influential hosts or vectors within the network.
In epidemiological contexts, the diagram supports quantitative assessments such as:
- Estimating basic reproduction numbers by aggregating weighted edges.
- Identifying super‑spreaders among host species through centrality analysis.
- Simulating intervention scenarios by removing or weighting edges corresponding to control measures.
Overall, the vertex‑edge model provides a rigorous framework for describing and analyzing the complex interrelations among ticks, bugs, lice, and fleas, enabling data‑driven decision making in pest management and disease prevention.