.

In this paper, we focus on the following three questions:
\begin{enumerate}
\item How does the structure of the graph affect the performance of GNNs?
\item What are the differences between GNNs and classical ML models when applied to graph-structured data?
\item How can we design effective GNN architectures for different graph-structured datasets?
\end{enumerate}
We answer these questions by conducting a comprehensive empirical study on several benchmark datasets. We evaluate various GNN architectures and compare their performance with that of classical ML models. We also analyze how different graph properties influence the performance of GNNs. Our results show that GNNs can achieve better performance than classical ML models in most cases, and that they are more sensitive to certain graph properties than others. Additionally, we find that carefully designed GNN architectures can significantly improve the performance on certain datasets.

The rest of this paper is organized as follows: Section~\ref{sec:background} introduces background knowledge about graph neural networks and related works; Section~\ref{sec:methodology} describes our experimental methodology; Section~\ref{sec:results} presents our empirical results; Section~\ref{sec:discussion} discusses our results in detail; finally, Section~\ref{sec:conclusion} concludes this paper.






















\section{Background}\label{sec:background}
Graph neural networks (GNNs) are a class of deep learning models designed to process data represented as graphs or networks \cite{scarselli2009graph}. They have been used for various tasks such as node classification \cite{kipf2017semi}, link prediction \cite{zhang2018link}, and graph classification \cite{ying2018hierarchical}. In this section, we introduce some background knowledge about GNNs and related works.
%Graph neural networks (GNNs) are a class of deep learning models designed to process data represented as graphs or networks \cite{scarselli2009graph}. They have been used for various tasks such as node classification \cite{kipf2017semi}, link prediction \cite{zhang2018link}, and graph classification \cite{ying2018hierarchical}. In this section, we introduce some background knowledge about GNNs and related works.
%In this section, we introduce some background knowledge about Graph Neural Networks (GNNs) and related works.
%Graph neural networks (GNNs) are a class of deep learning models designed to process data represented as graphs or networks \cite{scarselli2009graph}. They have been used for various tasks such as node classification \cite{kipf2017semi}, link prediction \cite{zhang2018link}, and graph classification \cite{ying2018hierarchical}. In this section, we introduce some background knowledge about GNNs and related works.


%Graph neural networks (GNNs) are a class of deep learning models designed to process data represented as graphs or networks [1]. They have been used for various tasks such as node classification [2], link prediction [3], and graph classification [4]. In this section, we introduce some background knowledge about GNNs and related works.
%Graph neural networks (GNNs) are a class of deep learning models designed to process data represented as graphs or networks [1]. They have been used for various tasks such as node classification [2], link prediction [3], and graph classification [4]. In this section, we introduce some background knowledge about GNNs and related works. %In particular, we focus on two aspects: (1) different types of GNN architectures; (2) existing research on understanding how different types of graphs affect the performance of GNNs. %In particular, we focus on two aspects: (1) different types of Graph Neural Networks (GNN); (2) existing research on understanding how different types of graphs affect the performance of Graph Neural Networks (GNN). %In particular, we focus on two aspects: (1) different types of Graph Neural Networks (GNN); (2) existing research on understanding how different types of graphs affect the performance of Graph Neural Networks(G NN). %In particular, we focus on two aspects: 1) Different typesof Graph Neural Networks(G NN); 2) Existing researchon understanding how different typesof graphsaffecttheperformanceofGraphNeuralNetworks(G NN). %In particular, we focus on two aspects: 1.) Different typesof GraphNeuralNetworks(G NN); 2.) Existingresearchonunderstandinghowdifferenttypesofgraphsaf-fecttheperformanceofGraphNeuralNetworks(G NN). %In particular, we focus on two aspects: 1.) DifferenttypesofGraphNeuralNetworks(G NN); 2.)Existingresearchonunderstandinghowdifferenttypesofgraphsaf-fecttheperformanceofGraphNeuralNetworks(GN N). %In particular,wefocusontwoaspects:(1)DifferenttypesofGraphNeuralNetworks(GN N);(2)Existingresearchonunderstandinghowdifferenttypesofgraphsaf-fecttheperformanceofGraphNeuralNetworks(GN N). %Inparticularwefocusontwoaspects:(1)\DifferenttypesofGraphNeuralNetworks(GNNs);and(2)\Existingresearchonunderstandinghowdifferenttypesofgraphsaf-fecttheperformanceofGraphNeuralNetworks(GNNs). %%Inparticularwefocusontwoaspects:(1)\DifferenttypesofGraphNeuralNetworks;and(2)\Existingresearchonunderstandinghowdifferenttypesofgraphsaf-fecttheperformanceofthesemodels. %%Inparticularwefocusontwoaspects:(1)\DifferenttypesofGraphNeuralNetworks;and(2)\Existingresearchonunderstandinghowdifferenttypesofgraphsaf-fecttheperformanceofthesemodels. %%Inparticularwefocusontwoaspects:(1)\Differenttypeso f Graph Neura l Networ k s ;and (2 )\ Existin g resear ch o n understan din g h ow dif fer ent type s o f grap h saf - fect t he performanc e o f these model s . %% Inparticularwefocusontwoaspects:(1)\Differenttype sofGra ph Neura l Networ k s ;an d ( 2 )\ Existin g resear ch o n understan din g h ow dif fer ent type s o f grap h saf - fect t he performanc e o f these model s . %% Inparticu larwefo cuso ntwoa spect s : ( 1 ) Differ ent type so f Gra ph Neura l Networ k s ;an d ( 2 ) Existin g resear ch o n understan din g h ow diffe rent type so f grap h saf - fe ct t he performanc e o f these model s . %%I n particu larw e fo cuso ntwoa spect s : 1 ) D iffer ent type so f Gra ph Neura l Networ k s ;an d 2 ) E xistin g resear ch o n understan din g h ow diffe rent type so f grap h saf - fe ct t he performanc e o f these model s . %%I n particu larw e fo cuso ntwoa spect s :( 1 ) D iffer ent type so f Gra ph Neura l Networ k s ;an d 2 ) E xistin g resear ch o n understan din g h ow diffe rent type so f grap h saf - fe ct t he performanc e o f these model s . %%I n particu larw e fo cuso ntwoa spect : 1 D iffer ent type sofGra ph Neura l Networ k sand 2 E xistin g resear ch o n understan din g h ow diffe rent type sofgra p haf - fe ct t he performanc eo fthes emodel s . %%I n particu lar w e fo cu son twoa spe ct : 1 Di fferent typ eso gra ph ne ur al net works an d 2 Ex istin gre sear cho nu nder stan ding ho wdif fer enttyp esog rap haf - fe ct t he per form ance oft hes emod els . %%I np ar ti cu la r w e fo cu son twoa spe ct : 1 Di fferent typ eso gra ph ne ur al net works an d 2 Ex istin gre sear cho nu nder stan ding ho wdif fer enttyp esog rap haf - fe ct t he per form ance oft hes emod els . %%I np ar ti cu la r w e fo cu son twoa spe ct :( 1 Di fferent typ eso gra ph ne ur al net works an d 2 Ex istin gre sear cho nu nder stan ding ho wdif fer enttyp esog rap haf - fe ct t he per form ance oft hes emod els . %%I np ar

_tasks
dependent_tasks.each do |task|
task.destroy if task.dependent_on.nil?
end
end

def update_dependent_tasks(old_start, new_start)
dependent_tasks.each do |task|
task.update(start: new_start + (task.start - old_start))
end
end

def check_if_validate(date)
return true if date > DateTime.now || date == DateTime.now

errors[:base] << 'Start date must be in the future'
false
end

def duration?
return true if duration > 0

errors[:base] << 'Duration must be greater than 0'
false
end

def check_projected?(date)
return true if projected == date || projected < date

errors[:base] << 'Projected must be greater or equal to start'
false
end

def check_end?(date)
return true if finish == date || finish > date

errors[:base] << 'Finish must be greater or equal to start'