# Special Issue on \"Graph Algorithms and Applications\"
## 2 Special Issue  
In response to the call for papers, a total of eighteen manuscripts were submitted. Out of them, we selected six submissions to appear in this Special Issue. In what follows, we summarize the contents of all six published papers. In [1], the authors faced a typical problem concerning the visual analysis of real-world networks. To this end, they introduce and study the following beyond-planarity problem that they call _h_-Clique2 Path Planarity. Let \(G\) be a simple topological graph for which the vertices are partitioned into subsets of size at most \(h\), each inducing a clique: _h_-Clique2 Path Planarity asks whether it is possible to obtain a planar subgraph of \(G\) by removing edges from each clique so that the subgraph induced by each subset is a path. They investigate the complexity of this problem in relation to \(k\)-planarity. In particular, they prove that _h_-Clique2 Path Planarity is NP-complete even when \(h=4\) and \(G\) is a simple 3-plane graph, while it can be solved in linear time when \(G\) is a simple 1-plane graph, for any value of \(h\). The results provided contribute to the growing fields of hybrid planarity and of graph drawing beyond planarity. In [2], the authors used graph theory models to cope with problems arising in the field of molecular biology and bioinformatics. They considered the ancestral mixture model proposed by [PERSON] and [PERSON] in 2006, an important model building a hierarchical tree from high dimensional binary sequences. As a phylogenetic tree (or evolutionary tree), a mixture tree created from ancestral mixture models involves the inferred evolutionary relationships among various biological species. Moreover, it contains the information of time when the species mutates. The tree comparison metric, an essential issue in bioinformatics, is used to measure the similarity between trees. Since the approach to the comparison between two mixture trees is still unknown, the authors proposed a new metric to measure the similarity of two mixture trees and designed efficient algorithms for computing it. In [3], the authors proposed graph models and algorithms for social network analysis. In particular, they considered the phenomenon occurring in many political campaigns where social influence is used in order to convince voters to support/oppose a specific candidate/party. In election control via the social influence problem, an attacker tries to find a set of limited influencers to start disseminating a political message in a social network of voters. A voter changes their opinion when they receive and accept the message. In constructive case, the goal is to maximize the number of votes/winners of a target candidate/party, while in the destructive case, the attacker tries to minimize them. Recent works considered the problem in different models and presented some hardness and approximation results. In that paper, the authors considered multi-winner election control through social influence on different graph structures and diffusion models, and the goal was to maximize/minimize the number of winners in our target party. They showed that the problem is hard to approximate when voters' connections form a graph, and the diffusion model is the linear threshold model. They also proved the same result considering an arborescence under independent cascade model. Moreover, they presented a dynamic programming algorithm for the cases that the voting system is a variation of straight-party voting and voters form a tree. In [4], the authors considered congestion games, a well-known class of noncooperative games that have the capability to model several interesting competitive scenarios while maintaining nice properties. In these games, there is a set of players sharing a set of resources. Each resource has an associated cost function, which depends on the number of players using it (the so-called congestion). Players aim to choose subsets of resources to minimize the sum of resource costs.