>>Can you tell me if it is possible to have a node border in un-selected state, similar to border in selected state?

Yes. You need to open main.js and replace this code

	if (selected)
	{
		ctx.fillStyle = LiteGraph.NODE_SELECTION;
		ctx.roundRect(-1,no_title ? -1 : -title_height -1, size[0]+2, no_title ? (size[1]+2) : (size[1] + title_height+2), 6);
		ctx.fill();
		ctx.fillStyle = bgcolor || LiteGraph.NODE_DEFAULT_BGCOLOR;
	}

with something like this

	ctx.fillStyle = (selected)?LiteGraph.NODE_SELECTION:LiteGraph.NODE_DEFAULT_COLOR;
	ctx.roundRect(-1,no_title ? -1 : -title_height -1, size[0]+2, no_title ? (size[1]+2) : (size[1] + title_height+2), 6);
	ctx.fill();
	ctx.fillStyle = bgcolor || LiteGraph.NODE_DEFAULT_BGCOLOR;

You can use any other color instead of LiteGraph.NODE_DEFAULT_COLOR