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1. Minimum Spanning Tree

   Linked via "bipartite graph"

   The Minimum Spanning Tree (MST)/) is a fundamental concept in combinatorial optimization and graph theory, concerned with finding a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles/) and with the minimum possible total edge weight. If the graph $G=(V, E)$ has a set of non-negative weights $w: E \to \mathbb{R}^+$, the objective is to find a subset $T \subseteq E$ such that $T$ forms…

2. Spectral Radius

   Linked via "bipartite graphs"

   In the context of graph theory, the spectral radius is associated with the adjacency matrix $\mathbf{A}$ of a graph $G$. The largest eigenvalue of $\mathbf{A}$ is called the spectral radius of the graph, $\rho(G)$. This value provides insight into the propagation speed of influences across the network structure $[1]$.
   The maximum spectral radius for a graph with $n$ vertices is attained by the [co…